Related papers: Geometric approach to the discrete Wigner function
We propose a methodology to design Wigner representations in phase spaces with nontrivial topology having evolution equations with desired mathematical properties. As an illustration, two representations of molecular rotations are developed…
In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined on an infinite rooted tree. We discuss, through its connection with composition operators, the boundedness and…
We are using the finite-gap approach for the construction of the Schr\"{o}dinger operator discretization on a quad graph. The latter is represented by a two-dimensional integer sublattice in a $d$-dimensional space. The Green's function of…
In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space is developed. By taking advantage of the refined…
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The…
We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a…
The Green's function of the discrete Sch\"odinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting appropriate potentials. We show two ways of the expression for the Green's…
We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a…
We discuss a discrete analogue of the Dirac-K\"{a}hler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of…
The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact,…
We use discrete analogs of Riemann-Hilbert problem's methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define discrete analogs of a Riemann-Hilbert problem…
A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the…
We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…
We present an application of variational-wavelet analysis to quasiclassical calculations of solutions of Wigner equations related to nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, multiresolution…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We compute the covariant Wigner function for spin-1/2 fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set…
In this work we consider the inverse problem of determining the properties of a Wigner function from the set of its zeros (the nodal set). The previous state of the art of the problem is Hudson's theorem, which shows that an empty nodal set…
The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner…
We study the values of the zeta-function of the root system of type $G_2$ at positive integer points. In our previous work we considered the case when all integers are even, but in the present paper we prove several theorems which include…
This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize…