Related papers: New method to evaluate divergent series via the Wi…
The Wigner function is a well-known phase space distribution function with many applications in quantum mechanics. In this article, we consider an open quantum system consisting of a non-relativistic single particle interacting with a…
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
In this paper, we introduced the theory of the sieve function transformation. Using the principle of sieve function transformation, we improved sieve method, and obtained the difference range of similar sieve function values. For this, we…
A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
The measurement problem is seen as an ambiguity of quantum mechanics, or, beyond that, as a contradiction within the theory: Quantum mechanics offers two conflicting descriptions of the Wigner's-friend experiment. As we argue in this note…
We provide numerical procedures for possibly best evaluating the sum of positive series. Our procedures are based on the application of a generalized version of Kummer's test.
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…
We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator…
The exact solution of the Dirac equation for fermions coupled to an external periodic chiral condensate (chiral spiral) is used to obtain the exact formula for the Wigner function (up to the quantum loop corrections). We find that the…
Let $k\in\mathbb{N}$. Wigert's divisor function $d^{\left(\frac{1}{k}\right)}(j)$ counts the number of representations of $j$ of the form $m^k+mn$ with $m\geq1 , n\geq0$. Let $\mathcal{F}_k(s)$ denote the Dirichlet series of…
A remarkable discrete counterpart of the Gaussian function of one continuous variable can be defined by using a Jacobi theta function, that is, as the sum of a convergent series. We extend this approach to Gaussian functions of two…
The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner…
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…
The Wigner d function, which is the essential part of an irreducible representation of SU(2) and SO(3) parameterized with Euler angles, has been know to suffer from a serious numerical errors at high spins, if it is calculated by means of…