Reports on Mathematical Physics最新文献

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.

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.

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

Exact quadratic in momenta complex invariants are investigated for both time independent and time dependent one-dimensional Hamiltonian systems possessing higher order nonlinearities within the framework of the rationalization method. The extended complex phase space approach is utilized to map a real system into complex space. Such invariants are expected to play a role in the analysis of complex trajectories and help to understand some new phenomena associated with complex potentials.

A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.

In this work, some of the present scenarios for the generalized uncertainty principle are reviewed and it is shown that all of them could be derived through a unified approach that guarantees the existence of both, minimal measurable length and maximal available momentum. Then, a new proposal is introduced that compensates for the defects of previous models. We also studied the effects of this modification on the energy levels and the wave function of a simple harmonic oscillator. It is shown that for the case of a harmonic oscillator, generalized uncertainty relation results in an uncertainty relation between the frequency and the mass of the oscillator.

In this paper, we study different solitons on multiply warped product manifolds and realize the geometry of base manifold and fiber manifolds. We also study the base manifolds and fiber manifolds when the multiply warped product manifold is either concircularly flat or conharmonically flat.