Theoretical and Mathematical Physics最新文献

We study the problem of reconstructing a solenoidal vector field from a vortex function with a no-slip condition on the boundary of an external two-dimensional domain. A solvability criterion is obtained as a condition for the orthogonality of the vortex function to harmonic functions. We also obtain some estimates of the solution in the spaces (L_2) and (H_1).

We study a nonlocal abstract Ginzburg–Landau type equation. The equation includes variable coefficients with convolution terms and an abstract linear operator function (A) in a Fourier-type Banach space (E). For sufficiently smooth initial data, assuming growth conditions for the operator (A) and the coefficient (a), the existence and uniqueness of the solution and the (L^p) -regularity properties are established. We obtain the existence and uniqueness of the solution, and the regularity of different classes of nonlocal Ginzburg–Landau-type equations by choosing the space (E) and operator (A) that occur in a wide variety of physical systems.

We present the binary Bargmann symmetry constraint and algebro-geometric solutions for a semidiscrete integrable hierarchy with a bi-Hamiltonian structure. First, we derive a hierarchy associated with a discrete spectral problem by applying the zero-curvature equation and study its bi-Hamiltonian structure. Then, resorting to the binary Bargmann symmetry constraint for the potentials and eigenfunctions, we decompose the hierarchy into an integrable symplectic map and finite-dimensional integrable Hamiltonian systems. Moreover, with the help of the characteristic polynomial of the Lax matrix, we propose a trigonal curve encompassing two infinite points. On this trigonal curve, we introduce a stationary Baker–Akhiezer function and a meromorphic function, and analyze their asymptotic properties and divisors. Based on these preparations, we obtain algebro-geometric solutions for the hierarchy in terms of the Riemann theta function.

It is important to distinguish between classical information and quantum information in quantum information theory. In this paper, we first extend the concept of metric-adjusted correlation measure and some related measures to non-Hermitian operators, and establish several relations between the metric-adjusted skew information with different operator monotone functions. By employing operator monotone functions, we next introduce three uncertainty matrices generated by channels: the total uncertainty matrix, the classical uncertainty matrix, and the quantum uncertainty matrix. We establish a decomposition of the total uncertainty matrix into classical and quantum parts and further investigate their basic properties. As applications, we employ uncertainty matrices to quantify the decoherence caused by the action of quantum channels on quantum states, and calculate the uncertainty matrices of some typical channels to reveal certain intrinsic features of the corresponding channels. Moreover, we establish several uncertainty relations that improve the traditional Heisenberg uncertainty relations involving variance.

We consider an (XYZ) spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to singlet states in the free-fermion limit. We obtain explicit representations for these form factors.

We study the (3)D-consistency property for negative symmetries of KdV-type equations. Its connection with the (3)D consistency of discrete equations is explained.

We present dynamical equations that are valid in the vicinity of a phase transition to the superconducting state. In writing the equations, we take the possible influence of the magnetic interaction between charge carriers and temperature fluctuations into account. We discuss the type of the phase transition under study. We argue in favor of the applicability of stochastic dynamical model A according to the standard classification (the stochastic model with one two-component field without a conservation law) to describe the dynamics of this phase transition.

We investigate the gauge transformations of the noncommutative modified KP hierarchy and the noncommutative constrained modified KP hierarchy in the Kupershmidt–Kiso version. By introducing the Orlov–Schulman operator, which depends on time variables and dressing operators, we construct the quantum torus symmetry for the noncommutative modified KP hierarchy. We also give a recursion operator for the noncommutative constrained modified KP hierarchy. We present an extended noncommutative modified KP hierarchy. The compatibility equations between the noncommutative modified KP flows and the extended noncommutative modified KP flows are constructed.

Two novel extended semidiscrete KP-type systems, namely, partial differential–difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the plane wave factor allows implementing extended integrable systems within the Cauchy matrix approach. We introduce the bilinear (DDelta^2)KP system, the extended (DDelta^2)pKP, (DDelta^2)pmKP, and (DDelta^2)SKP systems, all of which are based on the Cauchy matrix approach. This results in a diversity of solutions for these extended systems as contrasted to the usual multiple soliton solutions.

We discuss the process of Yang–Baxterization in representations of the braid group. We discuss the role played by (n)-CB algebras in Yang–Baxterization. We present diagrams depicting the defining relations for the (4)-CB algebras. These relations are illustrated using the isomorphism between the general free algebra generated by ({1}), ({E_i}), and ({G_i}) (the generators of the Birman–Murakami–Wenzl algebra) and Kauffman’s tangle algebra.