Reports on Mathematical Physics最新文献

Umbral operational techniques offer sturdy mechanism in the studies of special functions and special polynomials. The techniques of umbral calculus are employed to derive properties of families of exponential-like functions and their hyperbolic forms. The generalized forms of Mittag-Leffler functions are used to solve technical problems concerning transport of a charged beam in a solenoid magnet. The proposed method is flexible and has many advantages over standard computational techniques.

The discrete modified KP hierarchies are compatible with generalized k-constraints. By means of the gauge transformation, a large class of solutions can be represented by the Wronskian determinants of functions satisfying a set of linear equations. In this paper, we give a sufficient and necessary condition to reduce the discrete mKP hierarchies obtained by the Wronskian solutions to the discrete k-constrained mKP hierarchies.

The present paper introduces a new definition of entropy on sequential effect algebras. Unlike the logarithmic behaviour of the entropy defined in the literature, the entropy considered here is of exponential nature. Conditional entropy and entropy on the dynamical system are also introduced and studied. It is also proved that entropy of the dynamical system is invariant under isomorphism.

The Hilbert space is the space which is usually chosen as the space of state vectors. In addition, the operators of quantum mechanics act on that space. However, the Hilbert space cannot provide a proper mathematical structure to define Dirac formulation. In particular, the use of Dirac formalism on the domain of definition of an observable leads to some physical contradictions. One example arises from the Infinite Potential Well System (IPWS) which is one of the most fundamental systems of quantum mechanics. Our aim in this paper is the explicit construction of the Gel'fand triplet for the IPWS.

A rigorous relationship between local quantum uncertainty and local quantum Fisher information as recent quantifiers of nonclassical correlations is investigated. It consists of analysing the quantum correlation rate ingrained in a bipartite quantum system interacting with its surrounding environment under the Markovian regime. Indeed, we quantify the separability between two qubits where each qubit interacts with its own environment. Furthermore, a common reservoir is also taken into consideration, which allows us to solve exactly the Markovian master equation of this system. Pointing out that the degrees of freedom that belong to the environment, act only implicitly. We study the local quantum uncertainty and local quantum Fisher information quantifiers of the open system. By controlling several parameters encoded in the reduced density operator of the open system, it is shown that the nonclassical measures fluctuate similarly between their maximum and minimum amplitudes. In particular, the high values of the damping rates related to each reservoir and some special values of the initial phase parameter allow for robust values of local quantum uncertainty and local quantum Fisher information. In particular, it is shown that in the non-resonance case, it is possible to enhance the quantum correlation of the proposed system.

We write the electromagnetic self-force of a non-Lorentz-contractible uniformly charged shell of radius a as a series in powers of a, and we calculate the first three terms of this expansion. The method of calculation presented here allows the exact consideration of all linear and nonlinear terms in velocity and its derivatives corresponding to a given power of a. Our calculation is entirely done in the laboratory frame of reference.

We consider the factor υ of the characteristic polynomial w^H (x) of the Heisenberg Hamiltonian Ĥ of the XXX model, corresponding to the generic star [k = ±1, ±3] of quasimomentum k for octagonal (N = 8) magnetic ring in the two-magnon sector. This factor is recognized as the fourth-degree polynomial with integer coefficients, indecomposable over the prime number field ℚ of rationals. We demonstrate the physical meaning of the corresponding Galois group as the group of permutations of eigenenergies between the quasimomenta entering the generic star of the Brillouin zone of octagon. In particular, we point out the role of intersection of this group with Galois group of the cyclotomic field, responsible for the translational symmetry of octagon. Bound and scattered two-magnon eigenstates are identified by their spectra. Some general remarks are made on Galois symmetries within the XXX integrable model.

This article concerns the study of perfect fluid spacetimes equipped with different types of gradient solitons. It is shown that if a perfect fluid spacetime with Killing velocity vector admits a τ-Einstein soliton of gradient type, then the spacetime represents phantom regime, or ψ remains invariant under the velocity vector field ρ. Besides, we establish that in a perfect fluid spacetime with constant scalar curvature, if the Lorentzian metric is the gradient τ-Einstein soliton, then either the τ-Einstein gradient potential function is pointwise collinear with ρ, or the spacetime represents stiff matter fluid. Furthermore, we prove that under certain conditions, a perfect fluid spacetime turns into a generalized Robertson–Walker spacetime, as well as a static spacetime and such a spacetime is of Petrov type I, D or O. We also characterize perfect fluid spacetimes whose Lorentzian metric is equipped with gradient m-quasi Einstein solitons and that the perfect fluid spacetime has vanishing expansion scalar, or it represents dark energy era under certain restriction on the potential function.

It is shown that in presence of certain external fields a well-defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational fields with nonrelativistic and relativistic Hamiltonians. The physical intepretation of these operators is proposed in terms of time of arrival in the momentum space.