Related papers: Velocity Averaging Lemmas: Classical, Quantum and …
We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\hbar$. Going beyond leading order in $\hbar$ we then derive a generalized Boltzmann equation…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
In this work, we study the relativistic quantum kinetic equations in 2+1 dimensions from Wigner function formalism by carrying out a systematic semi-classical expansion up to $\hbar$ order. The derived equations allow us to explore…
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be…
The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting…
We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only in the velocity variable, while the Liouville transport…
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor…
A well known procedure to get quantum hydrodynamical models for charge transport is to resort to the Wigner equations and deduce the hierarchy of the moment equations as in the semiclassical approach. If one truncates the moment hierarchy…
A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further, the hydrodynamic equations of continuity and balance of momentum density have been…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
We tackle the problem of the accelerating universe by reconsidering the most general form of the metric when the speed of light is allowed to evolve with time in a homogeneous and isotropic universe. A new varying speed of light (VSL) model…
In 1983, Wigner outlined a modified Schr\"odinger--von-Neumann equation of motion for macroobjects, to describe their typical coupling to the environment. This equation has become a principal model of environmental decoherence which is…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
The semi-velocity is defined as an exponential function of the rapidity. Physically the semi-velocity is interpreted as the relativistic analogue of the phase velocity, a geometrical interpretation done within the framework of…
We prove averaging theorems for ordinary differential equations and retarded functional differential equations. Our assumptions are weaker than those required in the results of the existing literature. Usually, we require that the…
The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…
We employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum…