In the realm of nonlinear integrable systems, the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrability. By focusing on single-component decompositions within the potential BKP hierarchy, it has been observed that specific linear superpositions of decomposition solutions remain consistent with the underlying equations. Moreover, through the implementation of multi-component decompositions within the potential BKP hierarchy, successful endeavors have been undertaken to formulate linear superposition solutions and novel coupled KdV-type systems that resist decoupling via alterations in dependent variables.

In this paper, the physics informed neural network (PINN) deep learning method is applied to solve two-dimensional nonlocal equations, including the partial reverse space y-nonlocal Mel'nikov equation, the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal two-dimensional nonlinear Schrödinger (NLS) equation. By the PINN method, we successfully derive a data-driven two soliton solution, lump solution and rogue wave solution. Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small, which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations. Moreover, the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.

To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other methods that are based on integrable scalar nonlinear partial differential equations. We show that some systems of integrable equations published recently are the ${{ \mathcal M }}_{2}$-extension of integrable such scalar equations. For illustration, we give Korteweg–de Vries, Kaup-Kupershmidt, and Sawada-Kotera equations as examples. By the use of such an extension of integrable scalar equations, we obtain some new integrable systems with recursion operators. We also give the soliton solutions of the systems and integrable standard nonlocal and shifted nonlocal reductions of these systems.

In this paper, we use the Riemann–Hilbert (RH) method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data: q(z, 0) = o(1) as z → −∞ and q(z, 0) = δ + o(1) as z → ∞, where δ is an arbitrary positive constant. We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameter λ. As an example, we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.

Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks. In this study, we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field. The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO. Through the application of multi-target optimal control theory, we strategically design microwave pulses to execute logical operations, including Fourier transform, oracle U_f operation, and inverse Fourier transform within a three-level molecular qutrit structure. The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit, which quantifies the maximum speed of quantum state manipulation. Subsequently, we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule, achieving remarkable fidelity. Consequently, a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation. Therefore, our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.

Our concern is to investigate controlled remote implementation of partially unknown operations with multiple layers. We first propose a scheme to realize the remote implementation of single-qubit operations belonging to the restricted sets. Then, the proposed scheme is extended to the case of single-qudit operations. As long as the controller and the higher-layer senders consent, the receiver can restore the desired state remotely operated by the sender. It is worth mentioning that the recovery operation is deduced by general formulas which clearly reveal the relationship with the measurement outcomes. For the sake of clarity, two specific examples with two levels are given respectively. In addition, we discuss the influence of amplitude-damping noise and utilize weak measurement and measurement reversal to effectively resist noise.

We study single photon scattering in a one-dimensional coupled resonator waveguide, which is dressed by a small and a giant artificial atom simultaneously. Here, we have set the small atom to be a neighbor to one leg of the giant atom, and the giant atom couples to the waveguide via two distant sites. When the small and giant atoms are both resonant with the bare resonator in the waveguide, we observe the perfect reflection of the resonant incident photon. On the other hand, when the small atom is detuned from the giant atom, the single photon reflection is characterized by a wide window and Fano line shape. We hope our work will pave the way for the potential application of small and giant atom hybrid systems in the study of photonic control in the low-dimensional waveguide structure.

The monogamy of entanglement stands as an indispensable feature within multipartite quantum systems. We study monogamy relations with respect to any partitions for the generalized W-class (GW) states based on the unified-(q, s) entanglement (UE). We provide the monogamy relation based on the squared UE for a reduced density matrix of a qudit GW state, as well as tighter monogamy relations based on the αth (α ≥ 2) power of UE. Furthermore, for an n-qudit system ABC₁...C_n−2, a generalized monogamy relation and an upper bound satisfied by the βth (0 ≤ β ≤ 1) power of the UE for the GW states under the partition AB and C₁...C_n−2 are established. In particular, two partition-dependent residual entanglements for the GW states are analyzed in detail.

The circuit quantum electrodynamics (QED) system has brought us into an ultrastrong and deep coupling regime in the light–matter interaction community, in which the quantum effect has attracted significant interest. In this study, we theoretically investigated the photon blockade phenomenon in a double-transmon system operating in an ultrastrong coupling regime. We considered the effect of the counter-rotating wave terms in the interaction Hamiltonian and derived the master equation in the eigenpresentation. We found that photon blockade occurred in only one of the eigenmodes, and the counter-rotating wave terms enhanced the blockade by reducing the minimum value of the second-order correlation function. This study will be beneficial for the design of single-photon devices in circuit QED systems, especially in the ultrastrong coupling regime.

Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated by walks. Quantum walks show promise for faster mixing times than classical methods but lack universal proof, especially in finite group settings. Here, we investigate the continuous-time quantum walks on Cayley graphs of the dihedral group D_2n for odd n, generated by the smallest inverse closed symmetric subset. We present a significant finding that, in contrast to the classical mixing time on these Cayley graphs, which typically takes at least order ${\rm{\Omega }}({n}^{2}\mathrm{log}(1/2\epsilon ))$, the continuous-time quantum walk mixing time on D_2n is of order $O(n{(\mathrm{log}n)}^{5}\mathrm{log}(1/\epsilon ))$, achieving a quadratic improvement over the classical case. Our paper advances the general understanding of quantum walk mixing on Cayley graphs, highlighting the improved mixing time achieved by continuous-time quantum walks on D_2n. This work has potential applications in algorithms for a class of sampling problems based on non-abelian groups.

Quantum information masking (QIM) is a crucial technique for protecting quantum data from being accessed by local subsystems. In this paper, we introduce a novel method for achieving 1-uniform QIM in multipartite systems utilizing a Fourier matrix. We further extend this approach to construct an orthogonal array with the aid of a Hadamard matrix, which is a specific type of Fourier matrix. This allows us to explore the relationship between 2-uniform QIM and orthogonal arrays. Through this framework, we derive two distinct 2-uniform quantum states, enabling the 2-uniform masking of original information within multipartite systems. Furthermore, we prove that the maximum number of quantum bits required for achieving a 2-uniformly masked state is 2ⁿ − 1, and the minimum is 2ⁿ⁻¹ + 3. Moreover, our scheme effectively demonstrates the rich quantum correlations between multipartite systems and has potential application value in quantum secret sharing.

Finding the optimal control is of importance to quantum metrology under a noisy environment. In this paper, we tackle the problem of finding the optimal control to enhance the performance of quantum metrology under an arbitrary non-Markovian bosonic environment. By introducing an equivalent pseudomode model, the non-Markovian dynamic evolution is reduced to a Lindblad master equation, which helps us to calculate the gradient of quantum Fisher information and perform the gradient ascent algorithm to find the optimal control. Our approach is accurate and circumvents the need for the Born–Markovian approximation. As an example, we consider the frequency estimation of a spin with pure dephasing under two types of non-Markovian environments. By maximizing the quantum Fisher information at a fixed evolution time, we obtain the optimal multi-axis control, which results in a notable enhancement in quantum metrology. The advantage of our method lies in its applicability to the arbitrary non-Markovian bosonic environment.

The effects and rules of the dimensionless parameter ξ on neutrino annihilation $\nu +\bar{\nu }\to {e}^{-}+{e}^{+}$ dominated gamma-ray bursts are analysed and investigated within the context of black holes in asymptotic safety. We also computationally model photon orbits around black holes, as photons and neutrinos have the same geodesic equations near black holes. We show that the black hole shadow radius decreases with increasing ξ. Calculations are made to determine the temperature of the accretion disk surrounding the black hole and the ratio $\dot{Q}/{\dot{Q}}_{{Newt}}$ of energy deposition per unit time and compared to that of the Newtonian scenario. The accretion disk temperature peaks at a higher temperature due to quantum gravity corrections, which increases the probability of neutrino emission from the black hole. It is interesting to note that larger quantum gravity effects cause the ratio value to significantly decline. In the neutrino–antineutrino annihilation process, the energy deposition rate is sufficient even while the energy conversion is inhibited because of quantum corrections. Gamma-ray bursts might originate from the corrected annihilation process. Additionally, we examine the derivative ${\rm{d}}\dot{Q}/{\rm{d}}r$ about the star radius r. The findings demonstrate that the ratio is lowered by the black hole's quantum influence. The neutrino pair annihilation grows weaker the more prominent the influence of quantum gravity.

In weak field limits, we compute the deflection angle of a gravitational decoupling extended black hole (BH) solution. We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss–Bonnet theorem (GBT). We also looked into the deflection angle of light by a black hole in weak field limits with the use of the Gibbons–Werner method. We verify the graphical behavior of the black hole after determining the deflection angle of light. Additionally, in the presence of the plasma medium, we also determine the deflection angle of the light and examine its graphical behavior. Furthermore, we compute the Einstein ring via gravitational decoupling extended black hole solution. We also compute the quasi-periodic oscillations and discuss their graphical behavior.

By regarding the Newton constant G_N and cosmological constant Λ as variables, in this paper we study the thermodynamics and phase transition of the Reissner-Nordstr $\ddot{o}{\rm{m}}$ anti-de Sitter (RN-AdS) black hole with a global monopole within the framework of AdS/CFT correspondence. We find interesting critical phenomena and phase behavior in the (grand) canonical ensembles of fixed ($\tilde{Q},{ \mathcal V },C$), ($\tilde{{\rm{\Phi }}},{ \mathcal V },C$) and ($\tilde{Q},{ \mathcal V },\mu $). When the other parameters are fixed, the free energy decreases with the global monopole increases. In the ($\tilde{Q},{ \mathcal V },C$) ensemble, the range of the unstable region decreases with the increase of the global monopole. In the ($\tilde{{\rm{\Phi }}},{ \mathcal V },C$) ensemble, when $\tilde{{\rm{\Phi }}}\lt {{\rm{\Phi }}}_{c}$, the free energy appears as two branches, where the upper and lower branches correspond to low and high entropy, respectively. When ($\tilde{Q},{ \mathcal V },\mu $) is fixed, a new zero-order phase transition occurs in the high-entropy phase and the low-entropy phase at certain μ-dependent temperatures. When μ increases to a certain value, this zero-order phase transition disappears. This certain value is negatively related to the magnitude of the global monopole. Finally, we find that $p-{ \mathcal V }$ criticality does not appear with the change of global monopole. Therefore, it is important to note that the CFT states of charged black holes with global monopoles do not correspond to van der Waals fluids. Finally, we find that charged black holes with global monopoles can better reflect thermodynamic phase transitions and critical phenomena under the AdS/CFT correspondence. By adjusting the change of the global monopole, the thermodynamic phase transition will also change.

We consider a relativistic two-fluid model of superfluidity, in which the superfluid is described by an order parameter that is a complex scalar field satisfying the nonlinear Klein–Gordon equation (NLKG). The coupling to the normal fluid is introduced via a covariant current–current interaction, which results in the addition of an effective potential, whose imaginary part describes particle transfer between superfluid and normal fluid. Quantized vorticity arises in a class of singular solutions and the related vortex dynamics is incorporated in the modified NLKG, facilitating numerical analysis which is usually very complicated in the phenomenology of vortex filaments. The dual transformation to a string theory description (Kalb–Ramond) of quantum vorticity, the Magnus force, and the mutual friction between quantized vortices and normal fluid are also studied.

We study the confinement of a spinless charged particle to a spherical quantum dot under the influence of a linear electric field. The spherical quantum dot is described by a short-range potential given by the power-exponential potential. Then, by analysing the region near the spherical quantum dot centre, we discuss two cases where the energy levels can be obtained for s-waves and how the linear electric field modifies the spectrum of energy of the spherical quantum dot.