相关论文: Trace forms for the generalized Wigner functions
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
CConsider a bipartite quantum system consisting of two subsystems A and B. The reduced density matrix ofA a is obtained by taking the partial trace with respect to B. In this work, we will show that the Wigner distribution of this reduced…
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is…
This article has to do with the derivation and solution of the Fokker--Planck equation associated to the momentum-independent Wigner function, of a particle subjected to a harmonic external field and immersed in a ohmic thermal bath of…
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…
Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the longitudinal and transversal optical and acoustic phonons are deduced. The equations are valid for any solid,…
In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions with deterministic terms are…
We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and…
The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…
The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging however; a…
Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…
We provide a simple analytic relation which connects the density operator of the radiation field with the number probabilities. The problem of experimentally "sampling" a general matrix elements is studied, and the deleterious effects of…
We derive a compact expression for the second-order correlation function $g^{(2)} (0)$ of a quantum state in terms of its Wigner function, thereby establishing a direct link between $g^{(2)} (0)$ and the state's shape in phase space. We…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
One of the main open problems of mathematical physics is to consistently quantize Yang-Mills gauge theory. If such a consistent quantization were to exist, it is reasonable to expect a ``Wightman reconstruction theorem,'' by which a Hilbert…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
A new reconstruction method for Wigner function is reported for quantum tomography based on compressed sensing. By analogy with computed tomography, Wigner functions for some quantum states can be reconstructed with less measurements…