Reports on Mathematical Physics最新文献

We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [16] and Rodnianski [18] on the free Schrödinger evolution to the general case regarding potentials.

In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (P, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (P, μ) is chain mixing, then φⁿ is chain transitive for each n ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (P, μ, φ) under suitable conditions. Examples are given to support the theory.

We study singular reduction of contact Hamiltonian systems acted upon properly by a Lie group. The tools we use are the category of differential space.

The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.

This research paper discusses the construction of novel and better quantum codes from the direct product of t-copies of ring R (discussed in Section 2), using cyclic codes over R by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring R. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.

In the present paper, we investigate the 3-dimensional Lie group (ℍ² × ℝ, g) where g is a left-invariant Riemannian metric and we determine the Ricci solitons and Ricci bi-conformal vector fields on it.

The purpose of the presented article is to develop some new global regularity criteria for a magnetohydrodynamic (MHD) fluid flowing in a saturated porous medium. The effect of the porous medium, over the fluid flow, is characterized by a Darcy–Forchheimer law. The fluid, under study, is considered as one-dimensional and flowing in the x–direction with velocity component u. In addition, such a component is assumed to vary with the y–direction, i.e. u(y). Then, given the vorticity function$w=-\frac{\partial u}{\partial y}$, such that${\Vert w\Vert }_{\text{BMO}}^2$ is sufficiently small, we develop the regularity criteria under the scope of the L² space. We extend our results to the spaces L^s, where s > 2. Afterward, we prove the Liouville-type theorem for the MHD Darcy–Forchheimer flow equation. Eventually, we obtain some characterization about the asymptotic behaviour of solutions, particularly, the nonuniform convergence in L² for$t\to \infty$.

The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics.

A twirling channel is a quantum channel induced by a continuous unitary representation$\pi ={\sum }_i^{\oplus }{m}_i{\pi }_i$ on a compact group G, where π_i are inequivalent irreducible representations. Motivated by a recent work [8] on minimal mixed unitary rank of Φ_π, we explore the connections of the independence number, zero-error capacity, quantum codes, orthogonality index and phase retrievability of the quantum channel Φ_π with the irreducible representation multiplicities m_i and the irreducible representation dimensions dim$H_{{\pi }_i}$. In particular, we show that the independence number of Φ_π is the sum of the multiplicities, the orthogonal index of Φ_π is exactly the sum of those representation dimensions, and the zero-error capacity is equal to log$\left({\sum }_{i=1}^d{m}_i\right)$. We also present a lower bound for the phase retrievability in terms of the minimal length of phase retrievable frames for ℂⁿ

In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find solutions of the equations of motion by quadratures.