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Solving forward and inverse problems of the nonlinear Schrödinger equation with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential via PINN deep learning
Jiaheng Li,Biao Li
Communications in Theoretical Physics    2021, 73 (12): 125001-.   DOI: 10.1088/1572-9494/ac2055
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In this paper, based on physics-informed neural networks (PINNs), a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations (PDEs) and other types of nonlinear physical models, we study the nonlinear Schrödinger equation (NLSE) with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential, which is an important physical model in many fields of nonlinear physics. Firstly, we choose three different initial values and the same Dirichlet boundary conditions to solve the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential via the PINN deep learning method, and the obtained results are compared with those derived by the traditional numerical methods. Then, we investigate the effects of two factors (optimization steps and activation functions) on the performance of the PINN deep learning method in the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential. Ultimately, the data-driven coefficient discovery of the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential or the dispersion and nonlinear items of the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential can be approximately ascertained by using the PINN deep learning method. Our results may be meaningful for further investigation of the nonlinear Schrödinger equation with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential in the deep learning.

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A survey of heavy–heavy hadronic molecules
Xiang-Kun Dong, Feng-Kun Guo, Bing-Song Zou
Communications in Theoretical Physics    2021, 73 (12): 125201-.   DOI: 10.1088/1572-9494/ac27a2
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The spectrum of hadronic molecules composed of heavy–antiheavy charmed hadrons has been obtained in our previous work. The potentials are constants at the leading order, which are estimated from resonance saturation. The experimental candidates of hadronic molecules, say X(3872), Y(4260), three Pc states and Pcs(4459), fit the spectrum well. The success in describing the pattern of heavy–antiheavy hadronic molecules stimulates us to give more predictions for the heavy–heavy cases, which are less discussed in literature than the heavy–antiheavy ones. Given that the heavy–antiheavy hadronic molecules, several of which have strong experimental evidence, emerge from the dominant constant interaction from resonance saturation, we find that the existence of many heavy–heavy hadronic molecules is natural. Among these predicted heavy–heavy states we highlight the DD* molecule and the ${D}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$ molecules, which are the partners of the famous X(3872) and Pc states. Quite recently, LHCb collaboration reported a doubly charmed tetraquark state, Tcc, which is in line with our results for the DD* molecule. With the first experimental signal of this new kind of exotic states, the upcoming update of the LHCb experiment as well as other experiments will provide more chances of observing the heavy–heavy hadronic molecules.

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Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation
Mostafa M A Khater,S K Elagan,M A El-Shorbagy,S H Alfalqi,J F Alzaidi,Nawal A Alshehri
Communications in Theoretical Physics    2021, 73 (9): 95003-.   DOI: 10.1088/1572-9494/ac049f
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This paper studies the analytical and semi-analytic solutions of the generalized Calogero–Bogoyavlenskii–Schiff (CBS) equation. This model describes the (2 + 1)–dimensional interaction between Riemann-wave propagation along the y-axis and the x-axis wave. The extended simplest equation (ESE) method is applied to the model, and a variety of novel solitary-wave solutions is given. These solitary-wave solutions prove the dynamic behavior of soliton waves in plasma. The accuracy of the obtained solution is verified using a variational iteration (VI) semi-analytical scheme. The analysis and the match between the constructed analytical solution and the semi-analytical solution are sketched using various diagrams to show the accuracy of the solution we obtained. The adopted scheme’s performance shows the effectiveness of the method and its ability to be applied to various nonlinear evolution equations.

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Dynamics of mixed lump-soliton for an extended (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equation
Kai-Zhong Shi,Shou-Feng Shen,Bo Ren,Wan-Li Wang
Communications in Theoretical Physics    2022, 74 (3): 35001-.   DOI: 10.1088/1572-9494/ac53a1
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A new (2+1)-dimensional higher-order extended asymmetric Nizhnik–Novikov–Veselov (eANNV) equation is proposed by introducing the additional bilinear terms to the usual ANNV equation. Based on the independent transformation, the bilinear form of the eANNV equation is constructed. The lump wave is guaranteed by introducing a positive constant term in the quadratic function. Meanwhile, different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions. For the interaction between the lump wave and one-soliton, the energy of the lump wave and one-soliton can transfer to each other at different times. The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term. The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional, contour and density plots.

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Shape-changed propagations and interactions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids
Dan-Dan Zhang,Lei Wang,Lei Liu,Tai-Xing Liu,Wen-Rong Sun
Communications in Theoretical Physics    2021, 73 (9): 95001-.   DOI: 10.1088/1572-9494/ac0ba5
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In this article, we consider the (3+1)-dimensional generalized Kadomtsev–Petviashvili (GKP) equation in fluids. We show that a variety of nonlinear localized waves can be produced by the breath wave of the GKP model, such as the (oscillating-) W- and M-shaped waves, rational W-shaped waves, multi-peak solitary waves, (quasi-) Bell-shaped and W-shaped waves and (quasi-) periodic waves. Based on the characteristic line analysis and nonlinear superposition principle, we give the transition conditions analytically. We find the interesting dynamic behavior of the converted nonlinear waves, which is known as the time-varying feature. We further offer explanations for such phenomenon. We then discuss the classification of the converted solutions. We finally investigate the interactions of the converted waves including the semi-elastic collision, perfectly elastic collision, inelastic collision and one-off collision. And the mechanisms of the collisions are analyzed in detail. The results could enrich the dynamic features of the high-dimensional nonlinear waves in fluids.

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The Lindblad and Redfield forms derived from the Born–Markov master equation without secular approximation and their applications
Chang-Yao Liao,Xian-Ting Liang
Communications in Theoretical Physics    2021, 73 (9): 95101-.   DOI: 10.1088/1572-9494/abec65
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In this paper, we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems. The coefficients of the equations are re-evaluated according to the scheme in [(2019), Phys. Rev. A 99, 022118]. They are complex numbers rather than the real numbers obtained from traditional simplified methods. The dynamics of two models (one is an open three-level quantum system model, and the other is the model of phycoerythrin 545 (PE545) in a photosynthesis system) are studied. It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments, but a large distortion of the dynamics in others. These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.

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Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrödinger equation
Wei-Jing Tang,Zhang-nan Hu,Liming Ling
Communications in Theoretical Physics    2021, 73 (10): 105001-.   DOI: 10.1088/1572-9494/ac08fb
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In this paper, we construct the Darboux transformation (DT) for the reverse-time integrable nonlocal nonlinear Schrödinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions. Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula.

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Propagation of local spatial solitons in power-law nonlinear PT-symmetric potentials based on finite difference
Hao Ji,Yinghong Xu,Chaoqing Dai,Lipu Zhang
Communications in Theoretical Physics    2021, 73 (12): 125002-.   DOI: 10.1088/1572-9494/ac29b6
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We consider the (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity under the parity-time-symmetry potential by using the Crank–Nicolson alternating direction implicit difference scheme, which can also be used to solve general boundary problems under the premise of ensuring accuracy. We use linear Fourier analysis to verify the unconditional stability of the scheme. To demonstrate the effectiveness of the scheme, we compare the numerical results with the exact soliton solutions. Moreover, by using the scheme, we test the stability of the solitons under the small environmental disturbances.

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Representation of the coherent state for a beam splitter operator and its applications
Mingxia Zhan,Fang Jia,Jiali Huang,Huan Zhang,Liyun Hu
Communications in Theoretical Physics    2022, 74 (3): 35101-.   DOI: 10.1088/1572-9494/ac5244
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A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.

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Fractional soliton dynamics of electrical microtubule transmission line model with local M-derivative
Nauman Raza,Saima Arshed,Kashif Ali Khan,Mustafa Inc
Communications in Theoretical Physics    2021, 73 (9): 95002-.   DOI: 10.1088/1572-9494/ac0a67
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In this paper, two integrating strategies namely $\exp [-\phi (\chi )]$ and $\tfrac{{G}^{{\prime} }}{{G}^{2}}$-expansion methods together with the attributes of local-M derivatives have been acknowledged on the electrical microtubule (MT) model to retrieve soliton solutions. The said model performs a significant role in illustrating the waves propagation in nonlinear systems. MTs are also highly productive in signaling, cell motility, and intracellular transport. The proposed algorithms yielded solutions of bright, dark, singular, and combo fractional soliton type. The significance of the fractional parameters of the fetched results is explained and presented vividly.

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Electron Acceleration by a radially polarised cosh-Gaussian laser beam in vacuum
Jitender Singh,Jyoti Rajput,Harjit Singh Ghotra,Niti Kant
Communications in Theoretical Physics    2021, 73 (9): 95502-.   DOI: 10.1088/1572-9494/ac02b6
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In this paper, a radially polarised cosh-Gaussian laser beam (CGLB) is used to study the electron acceleration produced in vacuum. A highly energetic electron beam can be achieved by a CGLB, even with comparatively low-powered lasers. The properties of a CGLB cause it to focus earlier, over a shorter duration than a Gaussian laser beam, which makes it suitable for obtaining high energies over small durations. It is found that the energy gained by the electrons strongly depends upon the decentering parameter of the laser profile. It is also observed that for a fixed value of energy gain, if the decentering parameter is increased, then the intensity of the laser field decreases. The dependence of the energy gained by electrons on the laser intensity and the laser-spot size is also studied.

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(2+1)-dimensional coupled Boussinesq equations for Rossby waves in two-layer cylindrical fluid*
Zheyuan Yu,Zongguo Zhang,Hongwei Yang
Communications in Theoretical Physics    2021, 73 (11): 115005-.   DOI: 10.1088/1572-9494/ac1ef7
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In this paper, the existence and propagation characteristics of Rossby waves in a two-layer cylindrical fluid are studied. Firstly, based on the dimensionless baroclinic quasi-geostrophic vortex equations including exogenous and dissipative, we derive new (2+1)-dimensional coupled Boussinesq equations describing wave propagation in polar coordinates by employing a multiscale analysis and perturbation method. Then, the Lie symmetries and conservation laws of the coupled Boussinesq equations are analyzed. Subsequently, by using the $(G^{\prime} /G)$-expansion method, the exact solutions of the (2+1)-dimensional coupled Boussinesq equations are obtained. Finally, the effects of coupling term coefficients on the propagation characteristics of Rossby waves are analyzed.

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The Sharma-Tasso-Olver-Burgers equation: its conservation laws and kink solitons
K Hosseini,A Akbulut,D Baleanu,S Salahshour
Communications in Theoretical Physics    2022, 74 (2): 25001-.   DOI: 10.1088/1572-9494/ac4411
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The present paper deals with the Sharma–Tasso–Olver–Burgers equation (STOBE) and its conservation laws and kink solitons. More precisely, the formal Lagrangian, Lie symmetries, and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws. Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods. Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons. According to the authors’ knowledge, the outcomes of the current investigation are new and have been listed for the first time.

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The angular momentum and parity projected multidimensionally constrained relativistic Hartree–Bogoliubov model
Kun Wang(王琨),Bing-Nan Lu(吕炳楠)
Communications in Theoretical Physics    2022, 74 (1): 15303-.   DOI: 10.1088/1572-9494/ac3999
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Nuclear deformations are fundamentally important in nuclear physics. We recently developed a multidimensionally constrained relativistic Hartree–Bogoliubov (MDCRHB) model, in which all multipole deformations respecting the V4 symmetry can be considered self-consistently. In this work we extend this model by incorporating the angular momentum projection and parity projection to restore the rotational and parity symmetries broken in the mean-field level. This projected MDCRHB (p-MDCRHB) model enables us to connect certain nuclear spectra to exotic intrinsic shapes such as triangles or tetrahedrons. We present the details of the method and an exemplary calculation for 12C. We develop a triangular moment constraint to generate the triangular configurations consisting of three α clusters arranged as an equilateral triangle. The resulting 12C spectra are consistent with that from a triangular rigid rotor for large separations between the α clusters. We also calculate the B(E2) and B(E3) values for low-lying states and find good agreement with the experiments.

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Exact solutions of the nonlocal Gerdjikov-Ivanov equation
Miao Li,Yi Zhang,Rusuo Ye,Yu Lou
Communications in Theoretical Physics    2021, 73 (10): 105005-.   DOI: 10.1088/1572-9494/ac1065
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The nonlocal nonlinear Gerdjikov-Ivanov (GI) equation is one of the most important integrable equations, which can be reduced from the third generic deformation of the derivative nonlinear Schrödinger equation. The Darboux transformation is a successful method in solving many nonlocal equations with the help of symbolic computation. As applications, we obtain the bright-dark soliton, breather, rogue wave, kink, W-shaped soliton and periodic solutions of the nonlocal GI equation by constructing its 2n-fold Darboux transformation. These solutions show rich wave structures for selections of different parameters. In all these instances we practically show that these solutions have different properties than the ones for local case.

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Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems
Weiying Wang,Xiubin Wang
Communications in Theoretical Physics    2022, 74 (4): 45001-.   DOI: 10.1088/1572-9494/ac5238
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In this paper, we propose a new method, the variable separation technique, for obtaining a breather and rogue wave solution to the nonlinear evolution equation. Integrable systems of the derivative nonlinear Schrödinger type are used as three examples to illustrate the effectiveness of the presented method. We then obtain a family of rational solutions. This family of solutions includes the Akhmediev breather, the Kuznetsov-Ma breather, versatile rogue waves, and various interactions of localized waves. Moreover, the main characteristics of these solutions are discussed and some graphics are presented. More importantly, our results show that more abundant and novel localized waves may exist in the multicomponent coupled equations than in the uncoupled ones.

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Precision measurements and tau neutrino physics in a future accelerator neutrino experiment
Jian Tang,Sampsa Vihonen,Yu Xu
Communications in Theoretical Physics    2022, 74 (3): 35201-.   DOI: 10.1088/1572-9494/ac5245
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We investigate prospects of building a future accelerator-based neutrino oscillation experiment in China, including site selection, beam optimization and tau neutrino physics aspects. CP violation, non-unitary mixing and non-standard neutrino interactions are discussed. We simulate neutrino beam setups based on muon and beta decay techniques and compare Chinese laboratory sites by their expected sensitivities. A case study on the Super Proton–Proton Collider and the China JinPing Laboratory is also presented. It is shown that the muon-decay-based beam setup can measure the Dirac CP phase by about 14.2° precision at 1σ CL, whereas non-unitarity can be probed down to ∣αij∣ ≲ 0.37 (ij = 1, 2, 3) and non-standard interactions to $| {\epsilon }_{{\ell }{\ell }^{\prime} }^{m}| \lesssim $ 0.11 (${\ell }\ne {\ell }^{\prime} =e$, μ, τ) at 90% CL, respectively.

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Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle
A M Jyothi,R Naveen Kumar,R J Punith Gowda,B C Prasannakumara
Communications in Theoretical Physics    2021, 73 (9): 95005-.   DOI: 10.1088/1572-9494/ac0a65
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The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model. The influences of Stefan blowing, Dufour and Soret effects are also considered in the model. The equations which represent the described flow pattern are reduced to ordinary differential equations (ODEs) by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method (RKF-45) with shooting process. The impacts of pertinent parameters on thermal, mass and velocity curves are deliberated graphically. Skin friction, rate of heat and mass transfer are also discussed graphically. Results reveal that, the increase in values of Brownian motion, thermophoresis, Dufour number, heating and radiative parameters improves the heat transfer. The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number. Finally, the escalating values of the radiative parameter decays the rate of heat transfer.

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Joule–Thomson expansion of RN-AdS black hole immersed in perfect fluid dark matter
Yihe Cao,Hanwen Feng,Wei Hong,Jun Tao
Communications in Theoretical Physics    2021, 73 (9): 95403-.   DOI: 10.1088/1572-9494/ac1066
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In this paper, we study the Joule–Thomson expansion for RN-AdS black holes immersed in perfect fluid dark matter. As perfect fluid dark matter is one of the dark matter candidates, we are interested in how it influences the thermodynamic properties of black holes. Firstly, the negative cosmological constant could be interpreted as thermodynamic pressure and its conjugate quantity as the thermodynamic volume, which give us more physical insights into the black hole. Moreover, we derive the thermodynamic definitions and study the critical behaviour of the black hole. Secondly, the explicit expression of Joule–Thomson coefficient is obtained from the basic formulas of the pressure, the volume, the entropy and the temperature. Then, we obtain the inversion curves in terms of charge Q and parameter λ. Furthermore, we analyse the isenthalpic curve in TP graph with the cooling–heating region determined by the inversion curve. At last, we derive the ratio of minimum inversion temperature to critical temperature and compare the result with that in the RN-AdS case.

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Diverse acoustic wave propagation to confirmable time–space fractional KP equation arising in dusty plasma
Aly R Seadawy,Muhammad Younis,Muhammad Z Baber,Syed T R Rizvi,Muhammad S Iqbal
Communications in Theoretical Physics    2021, 73 (11): 115004-.   DOI: 10.1088/1572-9494/ac18bb
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In this study, the (3+1)-dimensional fractional time–space Kadomtsev–Petviashivili (FTSKP) equation is considered and analyzed analytically, which propagates the acoustic waves in an unmagnetized dusty plasma. The fractional derivatives are studied in a confirmable sense. The new modified extended direct algebraic (MEDA) approach is adopted to investigate the diverse nonlinear wave structures. A variety of new families of hyperbolic and trigonometric solutions are obtained in single and different combinations. The obtained results are also constructed graphically with the different parametric choices.

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Effect of layer sliding on the interfacial electronic properties of intercalated silicene/indium selenide van der Waals heterostructure
Masood Yousaf,M W Younis,Ahmed S Jbara,M Junaid Iqbal Khan,G Murtaza,M A Saeed
Communications in Theoretical Physics    2022, 74 (3): 35701-.   DOI: 10.1088/1572-9494/ac450f
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Methods capable of tuning the properties of van der Waals (vdW) layered materials in a controlled and reversible manner are highly desirable. Interfacial electronic properties of two-dimensional vdW heterostructure consisting of silicene and indium selenide (InSe) have been calculated using density functional theory-based computational code. Furthermore, in order to vary the aforementioned properties, silicene is slid over a InSe layer in the presence of Li intercalation. On intercalation of the heterostructure, the buckling parameter associated with the corrugation of silicene decreases from 0.44 Å to 0.36 Å, whereas the InSe structure remains unaffected. Potential energy scans reveal a significant increase in the sliding energy barrier for the case of intercalated heterostructure as compared with the unintercalated heterostructure. The sliding of the silicene encounters the maximum energy barrier of 0.14 eV. Anisotropic analysis shows the noteworthy differences between calculated in-plane and out-of-plane part of dielectric function. A variation of the planar average charge density difference, dipole charge transfer and dipole moment have been discussed to elucidate the usability spectrum of the heterostructure. The employed approach based on intercalation and layer sliding can be effectively utilized for obtaining next-generation multifunctional devices.

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Rogue waves of the sixth-order nonlinear Schrödinger equation on a periodic background
Wei Shi, Zha qilao
Communications in Theoretical Physics    2022, 74 (5): 55001-.   DOI: 10.1088/1572-9494/ac6155
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In this paper, we construct the rogue wave solutions of the sixth-order nonlinear Schrödinger equation on a background of Jacobian elliptic functions dn and cn by means of the nonlinearization of a spectral problem and Darboux transformation approach. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.

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Alkali-metal(Li, Na, and K)-adsorbed MoSi2N4 monolayer: an investigation of its outstanding electronic, optical, and photocatalytic properties
Zhiyuan Sun,Jing Xu,Nsajigwa Mwankemwa,Wenxing Yang,Xianwen Wu,Zao Yi,Shanjun Chen,Weibin Zhang
Communications in Theoretical Physics    2022, 74 (1): 15503-.   DOI: 10.1088/1572-9494/ac3ada
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Single-layer MoSi2N4, a high-quality two-dimensional material, has recently been fabricated by chemical vapor deposition. Motivated by this latest experimental work, herein, we apply first principles calculations to investigate the electronic, optical, and photocatalytic properties of alkali-metal(Li, Na, and K)-adsorbed MoSi2N4 monolayer. The electronic structure analysis shows that pristine MoSi2N4 monolayer exhibits an indirect bandgap (Eg = 1.89 eV). By contrast, the bandgaps of one Li-, Na-, and K-adsorbed MoSi2N4 monolayer are 1.73 eV, 1.61 eV, and 1.75 eV, respectively. Moreover, the work function of MoSi2N4 monolayer (4.80 eV) is significantly reduced after the adsorption of alkali metal atoms. The work functions of one Li-, Na-, and K-adsorbed MoSi2N4 monolayer are 1.50 eV, 1.43 eV, and 2.03 eV, respectively. Then, optical investigations indicate that alkali metal adsorption processes substantially increase the visible light absorption range and coefficient of MoSi2N4 monolayer. Furthermore, based on redox potential variations after alkali metals are adsorbed, Li- and Na-adsorbed MoSi2N4 monolayers are more suitable for the water splitting photocatalytic process, and the Li-adsorbed case shows the highest potential application for CO2 reduction. In conclusion, alkali-metal-adsorbed MoSi2N4 monolayer exhibits promising applications as novel optoelectronic devices and photocatalytic materials due to its unique physical and chemical properties.

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Representations of hypergraph states with neural networks*
Ying Yang(杨莹),Huaixin Cao(曹怀信)
Communications in Theoretical Physics    2021, 73 (10): 105103-.   DOI: 10.1088/1572-9494/ac1101
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The quantum many-body problem (QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the QMBP, even with the most powerful computers. With the rapid development of machine learning, artificial neural networks provide a powerful tool that can represent or approximate quantum many-body states. In this paper, we aim to explicitly construct the neural network representations of hypergraph states. We construct the neural network representations for any k-uniform hypergraph state and any hypergraph state, respectively, without stochastic optimization of the network parameters. Our method constructively shows that all hypergraph states can be represented precisely by the appropriate neural networks introduced in [Science 355 (2017) 602] and formulated in [Sci. China-Phys. Mech. Astron. 63 (2020) 210312].

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Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating
Aamar Abbasi,Waseh Farooq,M Ijaz Khan,Sami Ullah Khan,Yu-Ming Chu,Zahid Hussain,M Y Malik
Communications in Theoretical Physics    2021, 73 (9): 95004-.   DOI: 10.1088/1572-9494/ac0c75
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Entropy generation is the loss of energy in thermodynamical systems due to resistive forces, diffusion processes, radiation effects and chemical reactions. The main aim of this research is to address entropy generation due to magnetic field, nonlinear thermal radiation, viscous dissipation, thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk. The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow, heat and mass transfer, while the second law of thermodynamics is used to analyze the entropy and irreversibility. The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method. The effects of thermophoresis, Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks. The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks. Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks. The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion. The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant. It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip. The current results present many applications in the lubrication phenomenon, heating processes, cooling of devices, thermal engineering, energy production, extrusion processes etc.

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Magnetic impact on heat and mass transfer utilizing nonofluid in an annulus between a superellipse obstacle and a cavity with periodic side-wall temperature and concentration
Abdelraheem M Aly,Noura Alsedais
Communications in Theoretical Physics    2021, 73 (11): 115001-.   DOI: 10.1088/1572-9494/ac1a6b
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The magnetic impacts upon the transport of heat and mass of an electrically conducting nanofluid within an annulus among an inner rhombus with convex and outer cavity with periodic temperature/concentration profiles on its left wall are assessed by the ISPH method. The right wall has ${T}_{c}$ and ${C}_{c},$ flat walls are adiabatic, and the temperature and concentration of the left wall are altered sinusoidally with time. The features of the heat and mass transfer and fluid flow through an annulus are assessed across a wide scale of Hartmann number $Ha,$ Soret number $Sr,$ oscillation amplitude $A,$ Dufour number $Du,$ nanoparticles parameter $\phi ,$ oscillation frequency $f,$ Rayleigh number $Ra,$ and radius of a superellipse $a$ at Lewis number $Le=20,$ magnetic field's angle $\gamma =45^\circ ,$ Prandtl number ${\Pr }=6.2,$ a superellipse coefficient $n=3/2,$ and buoyancy parameter $N=1.$ The results reveal that the velocity's maximum reduces by $70.93 \% $ as $Ha$ boosts from 0 to 50, and by $66.24 \% $ as coefficient $a$ boosts from $0.1$ to $0.4.$ Whilst the velocity's maximum augments by $83.04 \% $ as $Sr$ increases from 0.6 to 2 plus a decrease in $Du$ from 1 to 0.03. The oscillation amplitude $A,$ and frequency $f$ are significantly affecting the nanofluid speed, and heat and mass transfer inside an annulus. Increasing the parameters $A$ and $f$ is augmenting the values of mean Nusselt number $\overline{Nu}$ and mean Sherwood number $\overline{Sh}.$ Increasing the radius of a superellipse $a$ enhances the values of $\overline{Nu}$ and $\overline{Sh}.$

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Detecting entanglement of quantum channels
Chaojian Li,Bang-Hai Wang,Bujiao Wu,Xiao Yuan
Communications in Theoretical Physics    2021, 73 (11): 115101-.   DOI: 10.1088/1572-9494/ac1da1
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Entanglement is the crucial resource for different quantum information processing tasks. While conventional studies focus on the entanglement of bipartite or multipartite quantum states, recent works have extended the scenario to the entanglement of quantum channels, an operational quantification of the channel entanglement manipulation capability. Based on the recently proposed channel entanglement resource framework, here we study a further task of resource detection—witnessing entanglement of quantum channels. We first introduce the general framework and show how channel entanglement detection is related to the Choi state of the channel, enabling channel entanglement detection via conventional state entanglement detection methods. We also consider entanglement of multipartite quantum channels and use the stabilizer formalism to construct entanglement witnesses for circuits consisting of controlled-Z gates. We study the effectiveness of the proposed detection methods and compare their performance for several typical channels. Our work paves the way for systematic theoretical studies of channel entanglement and practical benchmarking of noisy intermediate scaled quantum devices.

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Transport of Jeffrey fluid in a rectangular slit of the microchannel under the effect of uniform reabsorption and a porous medium
H Mehboob,K Maqbool,R Ellahi,Sadiq M Sait
Communications in Theoretical Physics    2021, 73 (11): 115003-.   DOI: 10.1088/1572-9494/ac2054
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This research explores the transport of a Jeffrey fluid through a permeable slit of microchannel under the effect of a porous medium and constant reabsorption. Physical laws of fluid mechanics are used to study the flow in a cross-sectional area of a narrow slit which generates a highly nonlinear system of partial differential equation with nonhomogeneous boundary conditions. To solve the complex boundary value problem; a recursive (Langlois) approach is used and explicit expressions for velocity, pressure, stream function, flux, shear stress and fractional reabsorption are calculated. It is noticed that the flow rate at the centre line of slit and shear stress on the walls of slit decay due to the presence of porous medium and viscoelastic fluid parameters. It is also quantitatively observed that more pressure is required for the fluid flow when the slit is filled with a porous medium and reabsorption on the walls is constant. The mathematical results of the present research have significant importance in the field of biofluid mechanics and medical industry, therefore the application of a diseased rat kidney is also included in this research: and reabsorption velocities in the case of a diseased and a healthy rat kidney are calculated with the effects of a porous medium and constant re-absorption.

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Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations
Sachin Kumar,Monika Niwas,M S Osman,M A Abdou
Communications in Theoretical Physics    2021, 73 (10): 105007-.   DOI: 10.1088/1572-9494/ac11ee
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The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and (2+1)-dimensional breaking soliton equations via a generalized exponential rational function (GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons, double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons, elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.

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The continuous wavelet derived by smoothing function and its application in cosmology
Yun Wang,Ping He
Communications in Theoretical Physics    2021, 73 (9): 95402-.   DOI: 10.1088/1572-9494/ac10be
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The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet functions are obtained by taking the first derivative of smoothing functions with respect to the scale parameter. Due to this wavelet constructing scheme, the inverse transforms are only one-dimensional integrations with respect to the scale parameter, and hence the continuous wavelet transforms (CWTs) constructed in this way are more ready to use than the usual scheme. We then apply the Gaussian-derived wavelet constructed by our scheme to computations of the density power spectrum for dark matter, the velocity power spectrum and the kinetic energy spectrum for baryonic fluid. These computations exhibit the convenience and strength of the CWTs. The transforms are very easy to perform, and we believe that the simplicity of our wavelet scheme will make CWTs very useful in practice.

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Electronic structure and optical properties of non-metallic modified graphene: a first-principles study
Jing-tao Huang,Yong Liu,Zhong-hong Lai,Jin Hu,Fei Zhou,Jing-chuan Zhu
Communications in Theoretical Physics    2022, 74 (3): 35501-.   DOI: 10.1088/1572-9494/ac539f
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In this paper, the electronic structure and stability of the intrinsic, B-, N-, Si-, S-doped graphene are studied based on first-principles calculations of density functional theory. Firstly, the intrinsic, B-, N-, Si-, S-doped graphene structures are optimized, and then the forming energy, band structure, density of states, differential charge density are analyzed and calculated. The results show that B- and Si-doped systems are p-type doping, while N is n-type doping. By comparing the forming energy, it is found that N atoms are more easily doped in graphene. In addition, for B-, N-, Si-doped systems, it is found that the doping atoms will open the band gap, leading to a great change in the band structure of the doping system. Finally, we systematically study the optical properties of the different configurations. By comparison, it is found that the order of light sensitivity in the visible region is as follows: S-doped> Si-doped> pure > B-doped > N-doped. Our results will provide theoretical guidance for the stability and electronic structure of non-metallic doped graphene.

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A classical density functional approach to depletion interaction of Lennard-Jones binary mixtures
Yue Chen,Wei Chen,Xiaosong Chen
Communications in Theoretical Physics    2022, 74 (3): 35602-.   DOI: 10.1088/1572-9494/ac4511
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In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First, to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions using a theoretical approach and compare them with results obtained by molecular dynamics simulation. Then, this approach is applied to two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of the solvent and the temperature of the binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of the repulsive barrier is related to the parameters of the LJ potential and bulk density. Moreover, the depletion force may exhibit attractive wells if the bulk density of the solvent is low. The attractive well tends to appear when the surface–surface distance of colloids is half of the size of the polymer and deepens with temperature lowering in a fixed bulk density. In contrast with the hard-sphere system, no oscillation of depletion potential around zero is observed.

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Entanglement witnesses of four-qubit tripartite separable quantum states
Miao Xu(徐淼),Wei-Feng Zhou(周伟峰),Feng Chen(陈峰),Li-Zhen Jiang(蒋丽珍),Xiao-Yu Chen(陈小余)
Communications in Theoretical Physics    2022, 74 (3): 35102-.   DOI: 10.1088/1572-9494/ac3fb1
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A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.

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Enhancement of feasibility of macroscopic quantum superposition state with the quantum Rabi-Stark model
Jing-Jing Wang,Ming-Song Ding,Li Xiong,Li Zheng
Communications in Theoretical Physics    2022, 74 (3): 35105-.   DOI: 10.1088/1572-9494/ac531b
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We propose an efficient scheme to generate a macroscopical quantum superposition state with a cavity optomechanical system, which is composed of a quantum Rabi-Stark model coupling to a mechanical oscillator. In a low-energy subspace of the Rabi-Stark model, the dressed states and then the effective Hamiltonian of the system are given. Due to the coupling of the mechanical oscillator and the atom-cavity system, if the initial state of the atom-cavity system is one of the dressed states, the mechanical oscillator will evolve into a corresponding coherent state. Thus, if the initial state of the atom-cavity system is a superposition of two dressed states, a coherent state superposition of the mechanical oscillator can be generated. The quantum coherence and their distinguishable properties of the two coherent states are exhibited by Wigner distribution. We show that the Stark term can enhance significantly the feasibility and quantum coherence of the generated macroscopic quantum superposition state of the oscillator.

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The collision frequency of electron-neutral-particle in weakly ionized plasmas with non-Maxwellian velocity distributions
Hong Wang,Jiulin Du,Rui Huo
Communications in Theoretical Physics    2021, 73 (9): 95501-.   DOI: 10.1088/1572-9494/ac0a6f
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The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in plasmas are accurately derived. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in plasmas. Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.

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Ability of the radial basis function approach to extrapolate nuclear mass
Tao Li,Haiwan Wei,Min Liu,Ning Wang
Communications in Theoretical Physics    2021, 73 (9): 95301-.   DOI: 10.1088/1572-9494/ac08fa
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The ability of the radial basis function (RBF) approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker (DZ31), Hartree–Fock-Bogoliubov (HFB27), finite-range droplet model (FRDM12) and Weizsäcker-Skyrme (WS4) mass models. It is found that when the RBF approach is employed with a simple linear basis function, different mass models have different performances in extrapolating nuclear masses in the same region, and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions. The WS4 and FRDM12 models (two macroscopic–microscopic mass models), combined with the RBF approach, may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.

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Three-dimensional massive Kiselev AdS black hole and its thermodynamics
Yuan-Zhang Cui,Wei Xu
Communications in Theoretical Physics    2021, 73 (10): 105401-.   DOI: 10.1088/1572-9494/ac0ed8
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We present an exact three-dimensional massive Kiselev AdS black hole solution. This Kiselev black hole is neither perfectly fluid, nor is it the quintessential solution, but the BTZ black hole modified by the anisotropic matter. This black hole possesses an essential singularity at its radial origin and a single horizon whose radius will increase monotonically when the parameter of the anisotropic matter field ω decreases. We calculate all thermodynamic quantities and find that the first law of thermodynamics of this massive Kiselev AdS black hole can be protected, while the consistent Smarr formula is only held in the extended thermodynamic phase space. After examining the sign of free energy, we conclude that there is no Hawking-Page transition since the massive Kiselev AdS black hole phase is always thermodynamically favored. Moreover, we study the phase transition between the Kiselev AdS black hole and BTZ black hole by considering the matchings for their temperature. We find that the Kiselev AdS black hole is still a thermodynamically more preferred phase, because it always has a smaller amount of free energy than the BTZ black hole, which seems to indicate that the anisotropic matter field may emerge naturally in BTZ black hole spacetime under some thermal fluctuations. We also show a first order phase transition between the Kiselev AdS black hole phase with $-1\lt \omega \lt -\tfrac{1}{2}$ and the black hole phase with $-\tfrac{1}{2}\lt \omega \lt 0$. As the Kiselev AdS black hole has some notable features on the phase transition of black holes in three dimensions, it provides important clues to further investigate these both surprising and similar behaviors in four and higher dimensions.

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Soliton solutions, travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics
Chaudry Masood Khalique,Oke Davies Adeyemo
Communications in Theoretical Physics    2021, 73 (12): 125003-.   DOI: 10.1088/1572-9494/ac27a1
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Many physical systems can be successfully modelled using equations that admit the soliton solutions. In addition, equations with soliton solutions have a significant mathematical structure. In this paper, we study and analyze a three-dimensional soliton equation, which has applications in plasma physics and other nonlinear sciences such as fluid mechanics, atomic physics, biophysics, nonlinear optics, classical and quantum fields theories. Indeed, solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour. We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time. Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function, elliptic functions, elementary trigonometric and hyperbolic functions solutions of the equation. Besides, various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique. These solutions comprise dark soliton, doubly-periodic soliton, trigonometric soliton, explosive/blowup and singular solitons. We further exhibit the dynamics of the solutions with pictorial representations and discuss them. In conclusion, we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula. We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.

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Uncertainty relation of successive measurements based on Wigner–Yanase skew information
Jun Zhang,Jia-Ning Wei,Zhou-Bo Duan,Kan He,Chang-Shui Yu
Communications in Theoretical Physics    2022, 74 (1): 15101-.   DOI: 10.1088/1572-9494/ac3646
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Wigner–Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity. We present the uncertainty principle for two successive projective measurements in terms of Wigner–Yanase skew information based on a single quantum system. It could capture the incompatibility of the observables, i.e. the lower bound can be nontrivial for the observables that are incompatible with the state of the quantum system. Furthermore, the lower bound is also constrained by the quantum Fisher information. In addition, we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state, respectively.

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A spin-less particle on a rotating curved surface in Minkowski space
Run Cheng,Li Wang,Hao Zhao,Cui-Bai Luo,Yong-Long Wang,Jun Wang
Communications in Theoretical Physics    2021, 73 (12): 125004-.   DOI: 10.1088/1572-9494/ac2e6a
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In Minkowski space ${ \mathcal M }$, we derive the effective Schrödinger equation describing a spin-less particle confined to a rotating curved surface ${ \mathcal S }$. Using the thin-layer quantization formalism to constrain the particle on ${ \mathcal S }$, we obtain the relativity-corrected geometric potential ${V}_{g}^{{\prime} }$, and a novel effective potential ${\tilde{V}}_{g}$ related to both the Gaussian curvature and the geodesic curvature of the rotating surface. The Coriolis effect and the centrifugal potential also appear in the equation. Subsequently, we apply the surface Schrödinger equation to a rotating cylinder, sphere and torus surfaces, in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.

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