Related papers: Almost automorphic functions on the quantum time s…
This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…
We study various asymptotic approximations of Good's special functions arising in atomic physics. These special functions are situated beyond Anger's functions to which they are closely related. Our major tool is the method of the…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…
Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…
We consider quantum dynamics for which the strict adiabatic approximation fails but which do not escape too far from the adiabatic limit. To treat these systems we introduce a generalisation of the time dependent wave operator theory which…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
Regarded as one of the most fundamental concepts of classical mechanics and thermodynamics, work has received well-grounded definitions within the quantum framework since the 1970s, having being successfully applied to many contexts. Recent…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the…
Conventional functional/path integrals used in physics are most often defined and understood, either explicitly or implicitly, as the infinite-dimensional analog of Fourier transform. In this paper, the infinite-dimensional analog of Mellin…
We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the…
The unipolar and bipolar macroscopic quantum models derived recently for instance in the area of charge transport are considered in spatial one-dimensional whole space in the present paper. These models consist of nonlinear fourth-order…
The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…
We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of…
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with…
The paper introduces and studies the class of (asymptotically) Stepanov almost automorphic functions with variable exponents. Any function belonging this class needs to be (asymptotically) Stepanov almost automorphic. A few relevant…
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…
We investigate the possibility of defining states on timelike hypersurfaces in quantum field theory. To this end we consider hyperplanes in the real massive Klein-Gordon theory using the Schroedinger representation. We find a well defined…