Reports on Mathematical Physics最新文献

It has been shown that a positive semi-definite Hamiltonian H, that has a tridiagonal matrix representation in a given basis$\left\{|{\varphi }_n〉\right\}$, can be represented in the form H = A^†A, where A is a forward shift operator satisfying$A|{\varphi }_n〉=c_n|{\varphi }_n〉+d_n|{\varphi }_n-1〉$ playing the role of an annihilation operator. Here, the coherent states |z) are defined as eigenstates of A. We also exhibit a complete set of coherent states {|c_n)}, labeled by the discrete points c_n, which we may also use as a basis. We find a solution of the coherent state |z), indexed by the continuous parameter z as a series expansion in terms of the {|c_n)}. We further show how to compute the time development of the coherent state |z) and we illustrate this with examples. As a major result, we find the explicit closed form solution |z) for the Morse oscillator.

Various types of functions, their generalizations and extentions have been widely explored, especially for their applications in various fields of research. In this article, we show that the use of methods of an operational nature, such as umbral calculus, allows us to acquire the hybrid form of the Bessel and Tricomi functions in terms of Mittag-Leffler functions. Certain novel identities such as generating functions, series representations, differential equations, derivative formulae, summation formula and Jacobi-Anger expansion for Mittag-Leffler-Bessel functions are obtained. Some integral formulae for the Oth-order Mittag-Leffler-Bessel functions are established. In addition, the Mittag-Leffler-Tricomi functions are constructed and some captivating properties of these polynomials are explored. The natural transforms of the Mittag-Leffler-Bessel functions and Mittag-Leffler-Tricomi functions are investigated and Laplace and Sumudu transforms are obtained as special cases. The graphical representations of these hybrid functions are given for special values of the parameters.

Two simultaneous nonlocal group constraints of the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems are discussed, of which one constraint changes the eigenvalue parameter into its negative of the complex conjugate and the other constraint does not change the eigenvalue parameter. Under those two constraints, mixed-type nonlocal integrable nonlinear Schrödinger hierarchies are generated. Further, based on specific distributions of eigenvalues and adjoint eigenvalues, a formulation of soliton solutions is established via the corresponding reflection-less generalized Riemann-Hilbert problems, where eigenvalues and adjoint eigenvalues could be equal.

The exact solutions of fractional order (2+1)-dimensional Burgers system are determined by using symmetry approach and power series technique. Also, the graphical behaviour of the obtained solutions is provided for better interpretation. The conservation laws for the system are reported by using the new conservation theorem.

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.