This paper proposes an innovative form of group reduction or similarity transformation involving off-diagonal block matrices. The proposed method is applied to the Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problem, leading to the generation of reduced matrix AKNS integrable hierarchies. As a result, a variety of reduced multiple-component integrable nonlinear Schrödinger and modified Korteweg–de Vries models are derived from the analysis of the reduced AKNS matrix spectral problem.
We investigate the entanglement entropy in quantum states featuring repeated sequential excitations of unit patterns in momentum space. In the scaling limit, each unit pattern contributes independently and universally to the entanglement entropy, leading to a characteristic volume-law scaling. Crucially, this universal contribution remains identical for both free and interacting models, enabling decomposition of the total entanglement into pattern-specific components. Numerical verification in fermionic and bosonic chains confirms this volume-law fragmentation phenomenon. For fermionic systems, we derive analytical expressions where many-body entanglement becomes expressible through few-body entanglement components. Notably, this analytical framework extends to spin-1/2 XXZ chains through appropriate identifications.
The paper considers applications of Rota–Baxter algebras to renormalization in quantum field theory and quantum integrability to obtain new solutions for the Yang–Baxter equations which can be studied by the method of Renormalization Group.
This study investigates the dimensionless quasi-geostrophic potential vorticity (QG-PV) equation with external sources. Employing the Gardner–Morikawa transformation and weakly nonlinear perturbation expansion, we derive the nonlinear Boussinesq equation with external sources. We demonstrate the existence of explicit zero-order and first-order Wronskian solutions for the model equation when α4 = 0. Furthermore, using a modified Jacobi elliptic function method, we obtain soliton-like solutions for both α4 = 0 and α4 ≠ 0. Analysis of these solutions reveals that the generalized β-plane approximation and shear flow are significant factors in inducing nonlinear Rossby waves, and that external sources play a crucial role in influencing Rossby wave behavior.
In this paper, we investigate data-driven bright soliton solutions of the nonlocal reverse-time nonlinear Schrödinger (NLS) equation and the parameter identification using the physically informed neural networks (PINNs) algorithm. Accurate simulations and comparative analyses of relative and absolute errors are performed for two-soliton and four-soliton solutions including linear solitary waves and periodic waves. In the training process, the standard PINNs scheme is employed for linear solitary wave solutions, while the prior information is added at local sharp regions for periodic wave solutions due to the complicated collision behaviors. For the parameter identification, we accurately recognize the nonlinear coefficients of the nonlocal NLS equation from known solutions with different noises. These results reinforce the application of deep learning with the PINNs framework to successfully study nonlocal integrable systems.
In this article, we introduce a new theoretical approach to improve the accuracy of two-dimensional (2D) atomic localization within a tripod-type, four-level atomic system by analyzing its transmission spectrum. In this method, the atom interacts with two orthogonal standing-wave fields and a weak probe field. By examining how the weak probe field passes through the system, we can determine the atom position. Our analysis reveals the presence of both double and sharply defined single localized peaks in the transmission spectrum, which correspond to specific positions of the atom. Importantly, we achieve ultra-high-resolution atomic localization with accuracy confined to a region smaller than λ/32 × λ/32. This level of precision is a significant improvement compared to earlier methods, which had lower localization accuracy. The increased precision is due to the complex interaction between the atom and the carefully controlled standing-wave and probe fields, which allows for precise control over the atom’s position. The implications of this work are significant, especially for applications like nano-lithography, where precise atomic placement is essential, and for laser cooling technologies, where better atomic localization could lead to more effective cooling processes and improved manipulation of atomic states.
Shor’s algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor’s algorithm, showing that the coherence in each step relies on the dimension of register or the order, and discuss the relations between geometric coherence and geometric entanglement. We investigate how unitary operators induce variations in coherence and entanglement, and analyze the variations of coherence and entanglement within the entire algorithm, demonstrating that the overall effect of Shor’s algorithm tends to deplete coherence and produce entanglement. Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.
For loops with UV divergences, assuming that the physical contributions of loops from UV regions are insignificant, a UV-free scheme method described by an equation is introduced to derive loop results without UV divergences in the calculations, i.e., a route of the analytic continuation ${{ \mathcal T }}_{{\rm{F}}}\to {{ \mathcal T }}_{{\rm{P}}}$ besides the traditional route ∞ − ∞ in the mathematical structure. This scheme provides a new perspective to an open question of the hierarchy problem of Higgs mass, i.e., an alternative interpretation without fine-tuning within the standard model.
We construct and study numerical solutions corresponding to generalized electrically charged half-monopole in Weinberg–Salam theory, denoted as Type I and Type II solutions. These solutions possess magnetic charge qm = +2nπ/e (−2nπ/e) that is situated along the negative z-axis (positive z-axis) and electric charge qe that depends on the electric charge parameter η, as well as net zero neutral charge. Other properties of this half-dyon configurations such as magnetic dipole moment and angular moment are studied. These solutions are closely related to the Cho–Maison monopole–antimonopole pair reported earlier but possess some distinctive features. Our results also show important implication that a full Cho–Maison monopole can undergo distortion and possesses an axially symmetric tear-drop shape.
In this work, we investigate the strong decays for P-wave excited states of doubly charmed and bottom baryons in the constituent quark model. Our results indicate that some λ-mode Ξcc/bb(1P) and Ωcc/bb(1P) states are relatively narrow, which are very likely to be discovered by future experiments. The light meson emissions for the low-lying ρ-mode states are highly suppressed due to the orthogonality of wave functions between initial and final states. Moreover, the strong decay behaviors for doubly charmed and bottom baryons preserve the heavy superflavor symmetry well, where the small violation originates from the finite heavy quark masses. We hope that present theoretical results for undiscovered doubly charmed and bottom baryons can provide helpful information for future experiments and help us to better understand the heavy quark symmetry.
A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic, and its Lyapunov exponent saturates the chaos bound proposed by Maldacena, Shenker, and Stanford, with the temperature being the Hawking temperature. Motivated by this, we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction. Numerically, we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field. They are mainly contributed by the bound states near the horizon and lie below the chaos bound.
Based on the idea of treating the anti de Sitter (AdS) radius as a fixed parameter, we study the thermodynamics and topology of d-dimensional charged AdS black holes in the restricted phase space utilizing Visser’s holographic approach. For the charged black hole with a cloud of strings and quintessence in the higher-dimensional spacetimes with d = (4, 5, 6), we demonstrate that the topological number remains invariant within the same canonical ensemble; however, a distinct topological number emerges in the grand canonical ensemble for the same black hole system. Notably, these results are independent of the dimension d and other related parameters. The formalism known as restricted phase space thermodynamics is checked in detail and some interesting thermodynamic behavior is revealed in the example case of d-dimensional charged AdS black holes with a cloud of strings and quintessence. This research lays the foundation for establishing a universal framework of restricted phase space thermodynamics and investigating its fundamental thermodynamic properties.
Signal transduction in a cell is mostly mediated with biochemical reactions which are noisy and often modeled with chemical master equations or Langevin type of dynamics. Thus stochastic simulation constitutes a major part of computation in cell signaling. Nevertheless, the presence of a wide span of time scales or molecular numbers in various pathways may lead to trouble in computation efficiency or accuracy. To avoid this problem, the commonly employed variational method evolves the whole probability distribution and reduces the stochastic equations to deterministic ones of only a few parameters. However, the design of the left variational basis is essential for its successful application, especially to large networks. In this paper, we extend the conventional polynomial basis to the Fourier and further the Gaussian basis, much facilitating description of multi-peaked or localized non-Gaussian distributions and at the same time avoiding numerical instability and computational complexity frequently encountered with conventional basis. The extension here is demonstrated in several typical biochemical signaling networks and achieves similar accuracy as the benchmark Gillespie algorithm, but with much less running time, which seems to open new opportunities in the variational approach to efficient analysis of noisy dynamics.
We study Onsager vortex clustered states in a shell-shaped superfluid containing a large number of quantum vortices. In the incompressible limit and at low temperatures, the relevant problem can be boiled down to the statistical mechanics of neutral point vortices confined on a sphere. We analyze rotation-free vortex-clustered states within the mean-field theory in the microcanonical ensemble. We find that the sandwich state, which involves the separating of vortices with opposite circulation and the clustering of vortices with the same circulation around the poles and the equator, is the maximum entropy vortex distribution, subject to a zero angular momentum constraint. The dipole moment vanishes for the sandwich state and the quadrupole tensor serves as an order parameter to characterize the vortex cluster structure. For a given finite angular momentum, the equilibrium vortex distribution forms a dipole structure, i.e., vortices with opposite sign are separated and accumulate around the south and north poles, respectively. The conditions for the onset of clustering and the exponents associated with the quadrupole moment and the dipole moment as functions of energy are obtained within the mean field theory. At large energies, we obtain asymptotically exact vortex density distributions using the stereographic projection method, yielding the parameter bounds for the vortex clustered states. The analytical predictions are in excellent agreement with microcanonical Monte Carlo simulations.
We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width W2(L, t) and the interface height h(x, t) in the (1+1)-dimensional Kardar–Parisi–Zhang (KPZ) growth system within the early growth regime. Through extensive numerical simulations, we find that long-range temporally correlated noise does not significantly impact the distribution form of the interface width. Generally, W2(L, t) approximately obeys a lognormal distribution when the temporal correlation exponent θ ≥ 0. On the other hand, the effects of long-range spatially correlated noise are evidently different from the temporally correlated case. Our results show that, when the spatial correlation exponent ρ ≤ 0.20, the distribution forms of W2(L, t) approach the lognormal distribution, and when ρ > 0.20, the distribution becomes more asymmetric, steep, and fat-tailed, and tends to an unknown distribution form. As a comparison, probability distributions of the interface height are also provided in the temporally and spatially correlated KPZ system, exhibiting quite different characteristics from each other within the whole correlated strengths. For the temporal correlation, the height distributions follow Tracy–Widom Gaussian orthogonal ensemble (TW-GOE) when θ → 0, and with increasing θ, the height distributions crossover continuously to an unknown distribution. However, for the spatial correlation, the height distributions gradually transition from the TW-GOE distribution to the standard Gaussian form.
We developed a model of a quantum Otto engine using two coupled two-level atoms. Based on the platform, we show that frequency detuning and the coupling strength induced by dipole-dipole interactions can lead to decoherence by disrupting coherent energy exchange. We focus on fundamental thermodynamic quantities, including heat absorption, release to heat baths, work done and efficiency. It is noteworthy that the interatomic coupling strength and frequency detuning do not merely affect the shape of the work and the efficiency but ultimately govern its quantitative magnitude. In the field of quantum thermodynamics, we have established an upper bound efficiency that is stricter than the Carnot limit. Moreover, our analysis confirms that quantum coherence enables the system to exceed the efficiency threshold of a classical Otto heat engine. The second law of thermodynamics holds all the while. Our results constitute a step forward in the design of conceptually new quantum thermodynamic devices which take advantage of uniquely quantum resources of quantum coherence.
We numerically investigate the effect of in-plane bending strain on valley-resolved conductance and valley polarization in a graphene nanoribbon with zigzag edges. The central region of the nanoribbon is bent into an arc with central angle φ. We find that the bending strain reduces the conductance but enhances the valley polarization. In the valley-resolved conductance spectra, there exist single-valley plateaus near the Dirac points and distinct Fano-type dips. Accordingly, a plateau of full valley polarization appears, which expands significantly at large φ. At valley-resolved conductance dips, the valley polarization can be much larger than that in the unstrained case. The bending-induced enhancement of valley polarization can be explained by the features of pseudo-Landau levels in the bent region. Strain-induced valley polarization depends nonmonotonously on the nanoribbon width. These findings could be helpful in designing valleytronic devices with flexibility.
Recently, quantum Hall interface has become a popular subject of research; distinct from that of the quantum Hall edge, which is constrained by external background confinement, the interface has the freedom to move, likely towards a string-like state. In disk geometry, it was known that the interface energy has an extra correction due to its curvature which depends on the size of the disk. In this work, we analytically calculate the energy of the integer quantum Hall interface on a cone surface which has the advantage of its curvature being more easily adjustable. By tuning the length and curvature of the interface by the cone angle parameter β, we analyze the dependence of the quantum Hall interface energy on the curvature and verify this geometric correction. Moreover, we find that the tip of the cone geometry has an extra contribution to the energy that reflects on the u2, u4 term.
We compute electronic and thermoelectric properties and density of states of disordered kagome lattice doped with impurity atoms in the context of tight binding model Hamiltonian due to spin–orbit coupling. The effect of scattering by dilute charged impurities is discussed in terms of the self-consistent Born approximation. Green’s function approach has been implemented to find the behavior of density of states and transport properties of kagome lattice. Specially, temperature dependences of electrical and thermal conductivities of kagome structure in the presence of impurity atoms have been analyzed. Also the effects of impurity concentration and scattering potential strength on behaviors of thermoelectric properties of kagome structure have been studied. Specially, the behaviors of Seebeck coefficient, power factor function, figure of merit and Lorenz number of the system have been analyzed in the presence of both impurity atoms and spin–orbit coupling effects. Our results show that impurity concentration leads to reduction of transport properties and thermoelectric factors of the disordered kagome lattice.
Investigations into first-order quantum phase transition (QPT) remain unclear in comparison to those of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and, at the same time, the concepts of universality class and critical scaling can be characterized by critical exponents. Here, we present a comparison study of these two kinds of QPT in the transverse Ising model; the emphasis is on the first-order QPT. In the absence of a longitudinal field, the ground state of the model exhibits a second-order QPT from the paramagnetic phase to the ferromagnetic phase, which is smeared out once the longitudinal field is applied. Surprisingly, the first excited state involves a first-order QPT as the longitudinal field increases, which has not been reported in the literature. Within the framework of the pattern picture, we clearly identify the difference between these two kinds of QPT: for the continuous QPT, only the pattern flavoring the ferromagnetic phase is always dominant over the others. By contrast, there are at least two competitive patterns in the first-order QPT, which is further indicated by the patterns’ occupancies, calculated by pattern projections on the ground- and first excited-state wavefunctions. Our results not only have a fundamental significance in the understanding of the nature of QPTs, but also a practical interest in quantum simulations used to test the present findings.
