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Modeling the COVID-19 epidemic and awareness diffusion on multiplex networks
Le He,Linhe Zhu
Communications in Theoretical Physics    2021, 73 (3): 35002-.   DOI: 10.1088/1572-9494/abd84a
Abstract156)   HTML6)    PDF (1089KB)(199)      

The coronavirus disease 2019 (COVID-19) has been widely spread around the world, and the control and behavior dynamics are still one of the important research directions in the world. Based on the characteristics of COVID-19's spread, a coupled disease-awareness model on multiplex networks is proposed in this paper to study and simulate the interaction between the spreading behavior of COVID-19 and related information. In the layer of epidemic spreading, the nodes can be divided into five categories, where the topology of the network represents the physical contact relationship of the population. The topological structure of the upper network shows the information interaction among the nodes, which can be divided into aware and unaware states. Awareness will make people play a positive role in preventing the epidemic diffusion, influencing the spread of the disease. Based on the above model, we have established the state transition equation through the microscopic Markov chain approach (MMCA), and proposed the propagation threshold calculation method under the epidemic model. Furthermore, MMCA iteration and the Monte Carlo method are simulated on the static network and dynamic network, respectively. The current results will be beneficial to the study of COVID-19, and propose a more rational and effective model for future research on epidemics.

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A pedagogical review on solvable irrelevant deformations of 2D quantum field theory
Yunfeng Jiang
Communications in Theoretical Physics    2021, 73 (5): 57201-.   DOI: 10.1088/1572-9494/abe4c9
Abstract150)   HTML2)    PDF (992KB)(142)      

This is a pedagogical review on ${T}\overline{{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to ${T}\overline{{T}}$deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the ${T}\overline{{T}}$/${J}\overline{{T}}$ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of ${T}\overline{{T}}$ deformation are presented, including its relation to random geometry, 2D topological gravity and holography. We summarize more recent developments until January 2021 in the last part.

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Notes on index of quantum integrability
Jia Tian,Jue Hou,Bin Chen
Communications in Theoretical Physics    2021, 73 (5): 55001-.   DOI: 10.1088/1572-9494/abe9aa
Abstract88)   HTML14)    PDF (341KB)(81)      

A quantum integrability index was proposed in Komatsu et al (2019 SciPost Phys. 7 065). It systematizes the Goldschmidt and Witten’s operator counting argument (Goldschmidt and Witten 1980 Phys. Lett. B 91 392) by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models ${SU}(N)/{SO}(N)$ and ${SO}(2N)/{SO}(N)\times {SO}(N)$. The indexes of these theories are all non-positive except for the case of ${SO}(4)/{SO}(2)\times {SO}(2)$. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the ${{\mathbb{CP}}}^{N}$ model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.

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Eigen microstates and their evolutions in complex systems
Yu Sun, Gaoke Hu, Yongwen Zhang, Bo Lu, Zhenghui Lu, Jingfang Fan, Xiaoteng Li, Qimin Deng, Xiaosong Chen
Communications in Theoretical Physics    2021, 73 (6): 65603-.   DOI: 10.1088/1572-9494/abf127
Abstract87)   HTML3)    PDF (7171KB)(82)      

Emergence refers to the existence or formation of collective behaviors in complex systems. Here, we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A, whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as ${\boldsymbol{A}}={\sum }_{I=1}^{r}{\sigma }_{I}{{\boldsymbol{U}}}_{I}\otimes {{\boldsymbol{V}}}_{I}$, where $r={\rm{\min }}(N,M)$, eigenvalue σI behaves as the probability amplitude of the eigen microstate UI so that ${\sum }_{I=1}^{r}{\sigma }_{I}^{2}=1$ and UI evolves following VI. In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σI becomes finite in the thermodynamic limit, there is a condensation of the eigen microstate UI in analogy to the Bose-Einstein condensation of Bose gases. This indicates the emergence of UI and a phase transition in complex system. Our framework has been applied successfully to equilibrium three-dimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown order-parameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.

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Deposition pattern of drying droplets
Xiuyuan Yang,Zechao Jiang,Peihan Lyu,Zhaoyu Ding,Xingkun Man
Communications in Theoretical Physics    2021, 73 (4): 47601-.   DOI: 10.1088/1572-9494/abda21
Abstract83)   HTML3)    PDF (1754KB)(79)      

The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications, ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations, facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.

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A deep learning method for solving third-order nonlinear evolution equations
Jun Li(李军),Yong Chen(陈勇)
Communications in Theoretical Physics    2020, 72 (11): 115003-.   DOI: 10.1088/1572-9494/abb7c8
Abstract68)   HTML3)    PDF (2173KB)(80)      

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.

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Self-consistent tomography of temporally correlated errors
Mingxia Huo,Ying Li
Communications in Theoretical Physics    2021, 73 (7): 75101-.   DOI: 10.1088/1572-9494/abf72f
Abstract66)   HTML10)    PDF (768KB)(41)      

The error model of a quantum computer is essential for optimizing quantum algorithms to minimize the impact of errors using quantum error correction or error mitigation. Noise with temporal correlations, e.g. low-frequency noise and context-dependent noise, is common in quantum computation devices and sometimes even significant. However, conventional tomography methods have not been developed for obtaining an error model describing temporal correlations. In this paper, we propose self-consistent tomography protocols to obtain a model of temporally correlated errors, and we demonstrate that our protocols are efficient for low-frequency noise and context-dependent noise.

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Padé approximant approach to singular properties of quantum gases: the ideal cases
Yuan-Hong Tian(田远鸿), Wen-Du Li(李文都), Yao Shen(沈尧), Wu-Sheng Dai(戴伍圣)
Communications in Theoretical Physics    2021, 73 (6): 65602-.   DOI: 10.1088/1572-9494/abf4b6
Abstract65)   HTML3)    PDF (495KB)(43)      

In this paper, we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padé approximant. The virial expansion is a high-temperature and low-density expansion and in practice, often, only the first several virial coefficients can be obtained. For Bose gases, we determine the BEC phase transition from a truncated virial expansion. For Fermi gases, we recover the low-temperature and high-density result from the virial expansion.

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A physics-constrained deep residual network for solving the sine-Gordon equation
Jun Li(李军),Yong Chen(陈勇)
Communications in Theoretical Physics    2021, 73 (1): 15001-.   DOI: 10.1088/1572-9494/abc3ad
Abstract51)   HTML3)    PDF (847KB)(123)      

Despite some empirical successes for solving nonlinear evolution equations using deep learning, there are several unresolved issues. First, it could not uncover the dynamical behaviors of some equations where highly nonlinear source terms are included very well. Second, the gradient exploding and vanishing problems often occur for the traditional feedforward neural networks. In this paper, we propose a new architecture that combines the deep residual neural network with some underlying physical laws. Using the sine-Gordon equation as an example, we show that the numerical result is in good agreement with the exact soliton solution. In addition, a lot of numerical experiments show that the model is robust under small perturbations to a certain extent.

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Effects of rebinding rate and asymmetry in unbinding rate on cargo transport by multiple kinesin motors
Yao Wang,Yu-Ying Liu,Jian Liang,Peng-Ye Wang,Ping Xie
Communications in Theoretical Physics    2021, 73 (1): 15603-.   DOI: 10.1088/1572-9494/abc46e
Abstract49)   HTML3)    PDF (1637KB)(58)      

Many intracellular transports are performed by multiple molecular motors in a cooperative manner. Here, we use stochastic simulations to study the cooperative transport by multiple kinesin motors, focusing mainly on effects of the form of unbinding rate versus force and the rebinding rate of single motors on the cooperative transport. We consider two forms of the unbinding rate. One is the symmetric form with respect to the force direction, which is obtained according to Kramers theory. The other is the asymmetric form, which is obtained from the prior studies for the single kinesin motor. With the asymmetric form the simulated results of both velocity and run length of the cooperative transport by two identical motors and those by a kinesin-1 motor and a kinesin-2 motor are in quantitative agreement with the available experimental data, whereas with the symmetric form the simulated results are inconsistent with the experimental data. For the cooperative transport by a faster motor and a much slower motor, the asymmetric form can give both larger velocity and longer run length than the symmetric form, giving an explanation for why kinesin adopts the asymmetric form of the unbinding rate rather than the symmetric form. For the cooperative transport by two identical motors, while the velocity is nearly independent of the rebinding rate, the run length increases linearly with the rebinding rate. For the cooperative transport by two different motors, the increase of the rebinding rate of one motor also enhances the run length of the cooperative transport. The dynamics of transport by N (N = 3, 4, 5, 6, 7 and 8) motors is also studied.

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Interface water-induced hydrophobic carbon chain unfolding in water
Zhang Xie,Zheng Li,Gang Lou,Qing Liang,Jiang-Xing Chen,Jianlong Kou,Gui-Na Wei
Communications in Theoretical Physics    2021, 73 (5): 55602-.   DOI: 10.1088/1572-9494/abe84e
Abstract48)   HTML2)    PDF (6398KB)(38)      

The folding and unfolding of the carbon chain, which is the basic constitutional unit of polymers, are important to the performance of the material. However, it is difficult to regulate conformational transition of the carbon chain, especially in an aqueous environment. In this paper, we propose a strategy to regulate the conformational transition of the carbon chain in water based on the all-atom molecular dynamics simulations. It is shown that the unfolded carbon chain will spontaneously collapse into the folded state, while the folded carbon chain will unfold with an external electric field. The regulation ability of the electric field is attributed to the electric field-induced redistribution of interface water molecules near the carbon chain. The demonstrated method of regulating conformational transition of the carbon chain in water in this study provides an insight into regulating hydrophobic molecules in water, and has great potential in drug molecule design and new polymer material development.

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The explicit symmetry breaking solutions of the Kadomtsev–Petviashvili equation
Zheng-Yi Ma(马正义),Jin-Xi Fei(费金喜),Quan-Yong Zhu(朱泉涌),Wei-Ping Cao(曹伟平)
Communications in Theoretical Physics    2020, 72 (11): 115001-.   DOI: 10.1088/1572-9494/aba260
Abstract44)   HTML8)    PDF (1163KB)(78)      

To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.

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Understanding sequence effect in DNA bending elasticity by molecular dynamic simulations
Xiao-Wei Qiang,Hai-Long Dong,Kai-Xin Xiong,Wenbing Zhang,Zhi-Jie Tan
Communications in Theoretical Physics    2021, 73 (7): 75601-.   DOI: 10.1088/1572-9494/abf825
Abstract39)   HTML4)    PDF (1870KB)(28)      

Structural elasticity of double-strand DNAs is very important for their biological functions such as DNA-ligand binding and DNA-protein recognition. By all-atom molecular dynamics simulations, we investigated the bending elasticity of DNA with three typical sequences including poly(A)-poly(T) (AA-TT), poly(AT)-poly(TA) (AT-TA), and a generic sequence (GENE). Our calculations indicate that, AA-TT has an apparently larger bending persistence length (P ∼63 nm) than GENE (P ∼49 nm) and AT-TA (P ∼48 nm) while the persistence length of AT-TA is only very slightly smaller than that of GENE, which agrees well with those from existing works. Moreover, through extensive electrostatic calculations, we found that the sequence-dependent bending elasticity is attributed to the sequence-dependent electrostatic bending energy for AA-TT, AT-TA and GENE, which is coupled to their backbone structures. Particularly, the apparently stronger bending stiffness of AA-TT is attributed to its narrower minor groove. Interestingly, for the three DNAs, we predicted the non-electrostatic persistence length of ∼17 nm, thus electrostatic interaction makes the major contribution to DNA bending elasticity. The mechanism of electrostatic energy dominating sequence effect in DNA bending elasticity is furtherly illustrated through the electrostatic calculations for a grooved coarse-grained DNA model where minor groove width and other microscopic structural parameters can be artificially adjusted.

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On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method
Kang-Jia Wang
Communications in Theoretical Physics    2021, 73 (4): 45001-.   DOI: 10.1088/1572-9494/abdea1
Abstract38)   HTML8)    PDF (713KB)(69)      

In this paper, we mainly study the time-space fractional strain wave equation in microstructured solids. He’s variational method, combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation. The main advantage of the variational method is that it can reduce the order of the differential equation, thus simplifying the equation, making the solving process more intuitive and avoiding the tedious solving process. Finally, the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method. The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics.

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Linear superposition of Wronskian rational solutions to the KdV equation
Wen-Xiu Ma
Communications in Theoretical Physics    2021, 73 (6): 65001-.   DOI: 10.1088/1572-9494/abeb5f
Abstract38)   HTML7)    PDF (218KB)(22)      

A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear KdV equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

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Dust acoustic rogue waves of fractional-order model in dusty plasma
Jun-Chao Sun,Zong-Guo Zhang,Huan-He Dong,Hong-Wei Yang
Communications in Theoretical Physics    2020, 72 (12): 125001-.   DOI: 10.1088/1572-9494/abb7d7
Abstract37)   HTML4)    PDF (1068KB)(58)      

In this paper, the fractional-order model is used to study dust acoustic rogue waves in dusty plasma. Firstly, based on control equations, the multi-scale analysis and reduced perturbation method are used to derive the (3+1)-dimensional modified Kadomtsev-Petviashvili (MKP) equation. Secondly, using the semi-inverse method and the fractional variation principle, the (3+1)-dimensional time-fractional modified Kadomtsev-Petviashvili (TF-MKP) equation is derived. Then, the Riemann-Liouville fractional derivative is used to study the symmetric property and conservation laws of the (3+1)-dimensional TF-MKP equation. Finally, the exact solution of the (3+1)-dimensional TF-MKP equation is obtained by using fractional order transformations and the definition and properties of Bell polynomials. Based on the obtained solution, we analyze and discuss dust acoustic rogue waves in dusty plasma.

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Quantum key distribution system against the probabilistic faint after-gate attack
Meng Ye,Jian-Hui Li,Yong Wang,Peng Gao,Xin-Xin Lu,Yong-Jun Qian
Communications in Theoretical Physics    2020, 72 (11): 115102-.   DOI: 10.1088/1572-9494/abb7d8
Abstract37)   HTML2)    PDF (488KB)(35)      

In practical quantum key distribution (QKD) systems, a single photon-detector (SPD) is one of the most vulnerable components. Faint after-gate attack is a universal attack against the detector. However, the original faint after-gate attack can be discovered by monitoring the photocurrent. This paper presents a probabilistic generalization of the attack, which we refer to as probabilistic faint after-gate attack, by introducing probability control modules. Previous countermeasures for photocurrent monitoring may fail in detecting the eavesdropper under some specific probabilities. To mitigate this threat, we provide a method to determine the detectable boundary in the limitation of precision of photocurrent monitoring, and investigate the security of QKD systems under such boundaries using the weak randomness model.

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High-order breather, M-kink lump and semi-rational solutions of potential Kadomtsev–Petviashvili equation
Yulei Cao,Yi Cheng,Jingsong He,Yiren Chen
Communications in Theoretical Physics    2021, 73 (3): 35004-.   DOI: 10.1088/1572-9494/abdaa6
Abstract37)   HTML5)    PDF (910KB)(88)      

N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev–Petviashvili equation are derived by means of the Hirota bilinear method, and the limit process of high-order synchronized breathers are shown. Furthermore, M-lump solutions are also presented by taking the long wave limit. Additionally, a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions, their interaction behaviors are shown by three-dimensional plots and contour plots.

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Modulation instability, rogue waves and conservation laws in higher-order nonlinear Schrödinger equation
Min-Jie Dong,Li-Xin Tian
Communications in Theoretical Physics    2021, 73 (2): 25001-.   DOI: 10.1088/1572-9494/abcfb6
Abstract36)   HTML3)    PDF (1098KB)(107)      

In this paper, the modulation instability (MI), rogue waves (RWs) and conservation laws of the coupled higher-order nonlinear Schrödinger equation are investigated. According to MI and the 2 × 2 Lax pair, Darboux-dressing transformation with an asymptotic expansion method, the existence and properties of the one-, second-, and third-order RWs for the higher-order nonlinear Schrödinger equation are constructed. In addition, the main characteristics of these solutions are discussed through some graphics, which are draw widespread attention in a variety of complex systems such as optics, Bose-Einstein condensates, capillary flow, superfluidity, fluid dynamics, and finance. In addition, infinitely-many conservation laws are established.

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Exploring the influence of microRNA miR-34 on p53 dynamics: a numerical study*
Nan Liu(刘楠),Hongli Yang(杨红丽),Liangui Yang(杨联贵)
Communications in Theoretical Physics    2021, 73 (3): 35601-.   DOI: 10.1088/1572-9494/abd84c
Abstract36)   HTML4)    PDF (716KB)(41)      

The tumor suppressor p53 is at the hub of the cellular DNA damage response network. P53-dependent cell fate decision is inseparable from p53 dynamics. A type of non-coding microRNA miR-34 has the function of enhancing p53 content. An intriguing question arises: How does miR-34 affect p53 kinetics? To address this question, we reconstruct a p53 signal transduction network model containing miR-34. Some experimental phenomena of p53 pulses are reproduced to explain the rationality of the model. The method of numerical bifurcation is used to investigate the effect of miR-34 on p53 kinetics. We point out that appropriate or higher miR-34 transcription rates can prevent DNA-damaged cell proliferation by causing p53 oscillation or high steady-state kinetic behavior, respectively. However, the lack of miR-34 synthesis ability will induce p53 to remain at a low level, and cells cannot respond correctly to DNA damage. These results are well in line with the anti-cancer role of miR-34. Our work sheds light on how miR-34 carries out its tumor-suppressive function from tuning p53 dynamic aspect.

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Numerical studies on the boundary entanglement in an optomechanical phonon laser system
Qing-Xia Meng,Zhi-Jiao Deng,Shi-Wei Cui
Communications in Theoretical Physics    2020, 72 (11): 115101-.   DOI: 10.1088/1572-9494/abb7db
Abstract35)   HTML1)    PDF (524KB)(39)      

In our previous work (Meng et al 2020 Phys. Rev. A 101 023838), we discover the phenomenon that the quantum entanglement on the driving threshold line remains a constant in a three-mode optomechanical phonon laser system. In this paper, to find the conditions under which the constant boundary entanglement shows up, we explicitly study how this boundary entanglement depends on various parameters through numerical integrations. The results show that the necessary and sufficient condition is a resonant frequency match between the optical frequency difference and the mechanical vibrational frequency, and this constant value is proportional to the multiplication of the square of the optomechanical coupling strength and the resonant driving threshold power.

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Statistical mechanics of a nonequilibrium steady-state classical particle system driven by a constant external force
Jie Yao(姚婕),Yanting Wang(王延颋)
Communications in Theoretical Physics    2020, 72 (11): 115601-.   DOI: 10.1088/1572-9494/abb7d2
Abstract35)   HTML1)    PDF (386KB)(26)      

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. In this work, the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles, free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium hypothesis. The momentum space distribution is determined by a random walk argument, and the position space distribution is determined by employing the equiprobability and ergodicity principles. The expressions for energy, entropy, free energy, and pressures are then deduced, and the relation among external force, drift velocity, and temperature is also established. Moreover, the relaxation towards its equilibrium is found to be an exponentially decaying process obeying the minimum entropy production theorem.

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Dynamics of a D’Alembert wave and a soliton molecule for an extended BLMP equation
Bo Ren
Communications in Theoretical Physics    2021, 73 (3): 35003-.   DOI: 10.1088/1572-9494/abda17
Abstract35)   HTML7)    PDF (2336KB)(80)      

The D’Alembert solution of the wave motion equation is an important basic formula in linear partial differential theory. The study of the D’Alembert wave is worthy of deep consideration in nonlinear partial differential systems. In this paper, we construct a (2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli (eBLMP) equation which fails to pass the Painlevé property. The D’Alembert-type wave of the eBLMP equation is still obtained by introducing one arbitrary function of the traveling-wave variable. The multi-solitary wave which should satisfy the velocity resonance condition is obtained by solving the Hirota bilinear form of the eBLMP equation. The dynamics of the three-soliton molecule, the three-kink soliton molecule, the soliton molecule bound by an asymmetry soliton and a one-soliton, and the interaction between the half periodic wave and a kink soliton molecule from the eBLMP equation are investigated by selecting appropriate parameters.

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Exact solution of an anisotropic J1J2 model with the Dzyloshinsky–Moriya interactions at boundaries
Yusong Cao,Jian Wang,Yi Qiao,Junpeng Cao,Wen-Li Yang
Communications in Theoretical Physics    2021, 73 (7): 75001-.   DOI: 10.1088/1572-9494/abf551
Abstract35)   HTML6)    PDF (293KB)(41)      

We propose a method to construct new quantum integrable models. As an example, we construct an integrable anisotropic quantum spin chain which includes the nearest-neighbor, next-nearest-neighbor and chiral three-spin couplings. It is shown that the boundary fields can enhance the anisotropy of the first and last bonds, and can induce the Dzyloshinsky–Moriya interactions along the z-direction at the boundaries. By using the algebraic Bethe ansatz, we obtain the exact solution of the system. The energy spectrum of the system and the associated Bethe ansatz equations are given explicitly. The method provided in this paper is universal and can be applied to constructing other exactly solvable models with certain interesting interactions.

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New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves
Md Nur Alam,M S Osman
Communications in Theoretical Physics    2021, 73 (3): 35001-.   DOI: 10.1088/1572-9494/abd849
Abstract34)   HTML11)    PDF (2878KB)(71)      

This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves. The modified $(G^{\prime} /G)$-expansion procedure is utilized to raise new closed-form wave solutions. Those solutions are investigated through hyperbolic, trigonometric and rational function. The graphical design makes the dynamics of the equations noticeable. It provides the mathematical foundation in diverse sectors of underwater acoustics, electromagnetic wave propagation, design of specific optoelectronic devices and physics quantum mechanics. Herein, we concluded that the studied approach is advanced, meaningful and significant in implementing many solutions of several nonlinear partial differential equations occurring in applied sciences.

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Polarization state and image rotation via spontaneously generated coherence in a spinning fast light medium
Habibur Rahman,Mansoor Khan,Shabir Ahmad,Muhammad Tayyab,Haseena Bibi,Hazrat Ali
Communications in Theoretical Physics    2020, 72 (11): 115502-.   DOI: 10.1088/1572-9494/abb7dc
Abstract33)   HTML2)    PDF (449KB)(47)      

In this article we propose a four-level rubidium (Rb87 ) atomic system for observing interesting features of polarization state rotation in a fast light medium. We investigate spontaneously generated coherence (SGC) for a spinning medium. We show how SGC can affect different spectral profiles of the polarization state and images in this suggested model. We observe a 0.5 radian rotation and 2.5 microsecond time advancement in our proposed system. Our precise results will provide a new platform for researchers in quantum optics due to its applications in image coding, telecommunications and cloaking technology.

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A modification of Faddeev-Popov approach free from Gribov ambiguity
Chong-yao Chen,Fei Gao,Yu-Xin Liu
Communications in Theoretical Physics    2020, 72 (12): 125201-.   DOI: 10.1088/1572-9494/abb7cb
Abstract33)   HTML1)    PDF (280KB)(26)      

We propose a modified version of the Faddeev-Popov (FP) quantization approach for non-Abelian gauge field theory to avoid Gribov ambiguity. We show that by means of introducing a new method of inserting the correct identity into the Yang-Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group, the problem of Gribov ambiguity can be removed naturally. Meanwhile by handling the absolute value of the FP determinant with the method introduced by Williams and collaborators, we lift the Jacobian determinant together with the absolute value and obtain a local Lagrangian. The new Lagrangian will have a nilpotent symmetry which can be viewed as an analog of the Becchi-Rouet-Stora-Tyutin symmetry.

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Efficient two-dimensional atom localization in a five-level conductive chiral atomic medium via birefringence beam absorption spectrum
Sajid Ali,Muhammad Idrees,Bakth Amin Bacha,Arif Ullah,Muhammad Haneef
Communications in Theoretical Physics    2021, 73 (1): 15102-.   DOI: 10.1088/1572-9494/abc46c
Abstract32)   HTML1)    PDF (1184KB)(103)      

We have theoretically investigated two-dimensional atom localization using the absorption spectra of birefringence beams of light in a single wavelength domain. The atom localization is controlled and modified through tunneling effect in a conductive chiral atomic medium with absorption spectra of birefringent beams. The significant localization peaks are investigated in the left and right circularly polarized beam. Single and double localized peaks are observed in different quadrants with minimum uncertainty and significant probability. The localized probability is modified by controlling birefringence and tunneling conditions. These results may be useful for the capability of optical microscopy and atom imaging.

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Joule-Thomson expansion of higher dimensional nonlinearly AdS black hole with power Maxwell invariant source
Zhong-Wen Feng, Xia Zhou, Guansheng He, Shi-Qi Zhou, Shu-Zheng Yang
Communications in Theoretical Physics    2021, 73 (6): 65401-.   DOI: 10.1088/1572-9494/abecd9
Abstract32)   HTML10)    PDF (808KB)(10)      

In this paper, the Joule-Thomson expansion of the higher dimensional nonlinearly anti-de Sitter (AdS) black hole with power Maxwell invariant source is investigated. The results show the Joule-Thomson coefficient has a zero point and a divergent point, which coincide with the inversion temperature Ti and the zero point of the Hawking temperature, respectively. The inversion temperature increases monotonously with inversion pressure. For the high-pressure region, the inversion temperature decreases with the dimensionality D and the nonlinearity parameter s, whereas it increases with the charge Q. However, Ti for the low-pressure region increase with D and s, while it decreases with Q. The ratio $\eta$BH between the minimum inversion temperature and the critical temperature does not depend on Q, it recovers the higher dimensional Reissner-Nördstrom AdS black hole case when s = 1. However, for s > 1, it becomes smaller and smaller as D increases and approaches a constant when D → ∞ . Finally, we found that an increase of mass M and s, or reducing the charge Q and D can enhance the isenthalpic curve, and the effect of s on the isenthalpic curve is much greater than other parameters.

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On the Riemann-Hilbert problem of a generalized derivative nonlinear Schrödinger equation
Bei-Bei Hu,Ling Zhang,Tie-Cheng Xia
Communications in Theoretical Physics    2021, 73 (1): 15002-.   DOI: 10.1088/1572-9494/abc3ac
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In this work, we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger (DNLS) equation. By establishing a matrix Riemann–Hilbert problem and reconstructing potential function q(x, t) from eigenfunctions ${\{{G}_{j}(x,t,\eta )\}}_{1}^{3}$ in the inverse problem, the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed. Moreover, we also obtain that the spectral functions f(η), s(η), F(η), S(η) are not independent of each other, but meet an important global relation. As applications, the generalized DNLS equation can be reduced to the Kaup–Newell equation and Chen–Lee–Liu equation on the half-line.

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Bouncing scenario of general relativistic hydrodynamics in extended gravity
A Y Shaikh,B Mishra
Communications in Theoretical Physics    2021, 73 (2): 25401-.   DOI: 10.1088/1572-9494/abcfb2
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In this paper, we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity. The metric assumed here is the flat Friedmann-Robertson-Walker space-time and the stress energy tensor is of perfect fluid. Since general relativity (GR) has certain issues with late time cosmic speed up phenomena, here we have introduced an additional matter geometry coupling that described the extended gravity to GR. The dynamical parameters are derived and analyzed. The dynamical behavior of the equation of state parameter has been analyzed. We have observed that the bouncing behavior is mostly controlled by the coupling parameter.

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Lump and new interaction solutions to the (3+1)-dimensional nonlinear evolution equation
Asma Issasfa,Ji Lin
Communications in Theoretical Physics    2020, 72 (12): 125003-.   DOI: 10.1088/1572-9494/abb7d3
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In this paper, a new (3+1)-dimensional nonlinear evolution equation is introduced, through the generalized bilinear operators based on prime number p = 3. By Maple symbolic calculation, one-, two-lump, and breather-type periodic soliton solutions are obtained, where the condition of positiveness and analyticity of the lump solution are considered. The interaction solutions between the lump and multi-kink soliton, and the interaction between the lump and breather-type periodic soliton are derived, by combining multi-exponential function or trigonometric sine and cosine functions with a quadratic one. In addition, new interaction solutions between a lump, periodic-solitary waves, and one-, two- or even three-kink solitons are constructed by using the ansatz technique. Finally, the characteristics of these various solutions are exhibited and illustrated graphically.

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Dynamics of momentum distribution and structure factor in a weakly interacting Bose gas with a periodical modulation
Ning Liu(刘宁), Z C Tu(涂展春)
Communications in Theoretical Physics    2020, 72 (12): 125501-.   DOI: 10.1088/1572-9494/abb7f0
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The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated. The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated. An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived, which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose-Einstein condensates. It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior. For stable dynamics, some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously, which is consistent with the derivative relation.

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How machine learning conquers the unitary limit
Bastian Kaspschak,Ulf-G Meißner
Communications in Theoretical Physics    2021, 73 (3): 35101-.   DOI: 10.1088/1572-9494/abd84d
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Machine learning has become a premier tool in physics and other fields of science. It has been shown that the quantum mechanical scattering problem cannot only be solved with such techniques, but it was argued that the underlying neural network develops the Born series for shallow potentials. However, classical machine learning algorithms fail in the unitary limit of an infinite scattering length. The unitary limit plays an important role in our understanding of bound strongly interacting fermionic systems and can be realized in cold atom experiments. Here, we develop a formalism that explains the unitary limit in terms of what we define as unitary limit surfaces. This not only allows to investigate the unitary limit geometrically in potential space, but also provides a numerically simple approach towards unnaturally large scattering lengths with standard multilayer perceptrons. Its scope is therefore not limited to applications in nuclear and atomic physics, but includes all systems that exhibit an unnaturally large scale.

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Balanced biosynthesis and trigger threshold resulting in a double adder mechanism of cell size control
Leilei Li
Communications in Theoretical Physics    2021, 73 (8): 85601-.   DOI: 10.1088/1572-9494/ac0135
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How cells accomplish cell size homeostasis is a fascinating topic, and several cell size regulation mechanisms were proposed: timer, sizer, and adder. Recently the adder model has received a great deal of attention. Adder property was also found in the DNA replication cycle. This paper aims to explain the adder phenomenon both in the division-centric picture and replication-centric picture at the molecular level. We established a self-replication model, and the system reached a steady state quickly based on evolution rules. We collected tens of thousands of cells in the same trajectory and calculated the Pearson correlation coefficient between biological variables to decide which regulatory mechanism was adopted by cells. Our simulation results confirmed the double-adder mechanism. Chromosome replication initiation and cell division control are independent and regulated by respective proteins. Cell size homeostasis originates from division control and has nothing to do with replication initiation control. At a slow growth rate, the deviation from adder toward sizer comes from a significant division protein degradation rate when division protein is auto-inhibited. Our results indicated the two necessary conditions in the double-adder mechanism: one is balanced biosynthesis, and the other is that there is a protein trigger threshold to inspire DNA replication initiation and cell division. Our results give insight to the regulatory mechanism of cell size and instructive to synthetic biology.

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Photon polarization tensor in a magnetized plasma system
Jingyi Chao,Mei Huang
Communications in Theoretical Physics    2020, 72 (11): 115301-.   DOI: 10.1088/1572-9494/aba25e
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We investigate the photon polarization tensor at finite temperatures in the presence of a static and homogeneous external magnetic field. In our scheme, the summing of the Matsubara frequency is performed after Poisson resummation, which is easily completed and converges quickly. Moreover, the behaviors of finite Landau levels are presented explicitly. It shows a convergence while summing infinite Landau levels. Consequently, there is no necessity to truncate the Landau level in a numerical estimation. At zero temperature, the lowest Landau level (LLL) approximation is analytically satisfied for the vacuum photon polarization tensor. However, we examine that the LLL approximation is not enough for the thermal polarization tensor. The thermal tensor obtains non-trivial contributions from the finite-n Landau levels. And, photon spectra gains a large imaginary contribution in thermal medium, which is the so-called Landau damping. Finally, it is argued that the summation of Matsubara frequency is not commuted with Landau level ones, such conjecture is excluded in our calculations.

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Multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas-Lenells equation
Rong Fan,Zhao Zhang,Biao Li
Communications in Theoretical Physics    2020, 72 (12): 125007-.   DOI: 10.1088/1572-9494/abb7cf
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In this letter, we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas-Lenells equation over a nonzero background. First, we obtain 2n-soliton solutions with a nonzero background via n-fold Darboux transformation, and find that these soliton solutions will appear in pairs. Particularly, 2n-soliton solutions consist of n ‘bright' solitons and n ‘dark' solitons. This phenomenon implies a new form of integrability: even integrability. Then interactions between solitons with even numbers and breathers are studied in detail. To our best knowledge, a novel nonlinear superposition between a kink and 2n-soliton is also generated for the first time. Finally, interactions between some different smooth positons with a nonzero background are derived.

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Localization of nonlocal symmetries and interaction solutions of the Sawada-Kotera equation
Jian-wen Wu, Yue-jin Cai, Ji Lin
Communications in Theoretical Physics    2021, 73 (6): 65002-.   DOI: 10.1088/1572-9494/abf552
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The nonlocal symmetry of the Sawada-Kotera (SK) equation is constructed with the known Lax pair. By introducing suitable and simple auxiliary variables, the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further. On the other hand, the group invariant solutions of the SK equation are constructed with the classic Lie group method. In particular, by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.

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Influences of magnetic field on the coexistence of diquark and chiral condensates in the Nambu–Jona–Lasinio model with axial anomaly
Xiao-Bing Zhang(张小兵),Fu-Ping Peng(彭富平),Yun-Ben Wu(吴云奔),Yi Zhang(张一)
Communications in Theoretical Physics    2020, 72 (11): 115302-.   DOI: 10.1088/1572-9494/aba25b
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In this paper, we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu–Jona–Lasinio model with QCD axial anomaly, as it relates to color-flavor-locked quark matter. Due to the coupling of rotated-charged quarks to magnetic fields, diquark condensates become split, and the coexistence region is thus superseded in favor of a specific diquark Bose–Einstein condensation (BEC), denoted as the BECI phase. For strong magnetic fields, we find that the BECI transition is pushed to larger quark chemical potentials. The effect of magnetic catalysis tends to disrupt the BEC–BCS (Bardeen–Cooper–Schrieffer) crossover predicted in previous works. For intermediate fields, the effect of inverse magnetic catalysis is observed, and the axial-anomaly-induced phase structure is essentially unchanged.

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Numerical simulation of the soliton solutions for a complex modified Korteweg-de Vries equation by a finite difference method
Tao Xu,Guowei Zhang,Liqun Wang,Xiangmin Xu,Min Li
Communications in Theoretical Physics    2021, 73 (2): 25005-.   DOI: 10.1088/1572-9494/abd0e5
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In this paper, a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modified Korteweg-de Vries (MKdV) equation (which is equivalent to the Sasa-Satsuma equation) with the vanishing boundary condition. It is proved that such a numerical scheme has the second-order accuracy both in space and time, and conserves the mass in the discrete level. Meanwhile, the resulting scheme is shown to be unconditionally stable via the von Nuemann analysis. In addition, an iterative method and the Thomas algorithm are used together to enhance the computational efficiency. In numerical experiments, this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation. The numerical accuracy, mass conservation and linear stability are tested to assess the scheme’s performance.

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