Related papers: Velocity Averaging Lemmas: Classical, Quantum and …

This paper discusses the possibility of applying the velocity averaging theorems in [F. Golse, P.-L. Lions, B. Perthame, R. Sentis: J. Funct. Anal. 76(1):110--125, 1988] to the Wigner equation governing the quantum evolution of the Wigner…

This work introduces a new approach to velocity averaging lemmas in kinetic theory. This approach -- based upon the classical energy method -- provides a powerful duality principle in kinetic transport equations which allows for a natural…

We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results, which display, in some cases, a gain of one full derivative.…

We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. This method requires only elementary techniques in Fourier analysis and shows…

We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount of velocity regularity for solutions, we extend our analysis…

We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable…

We consider the semiclassical limit of nonlinear Schr\"odinger equations with wavepacket initial data. We recover the Wigner measure of the problem, a macroscopic phase-space density which controls the propagation of the physical…

In the present work, we adopt the idea of velocity averaging lemma to establish regularity for stationary linearized Boltzmann equations in a bounded convex domain. Considering the incoming data, with three iterations, we establish…

We prove new velocity averaging lemmas for multi-dimensional hyperbolic-parabolic partial differential equations. These theorems may be applied to establish several compactness results for both deterministic and stochastic…

This article addresses the local boundedness and H\"older continuity of weak solutions to kinetic Fokker-Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and…

We show that Wigner-Leggett-Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temerature, Ohmic environment can be identified as a…

A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical…

This paper addresses the problem of the separation of rotational and internal motion. It introduces the concept of average angular velocity as the moment of inertia weighted average of particle angular velocities. It extends and elucidates…

We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic case and as far as we work in $L^2$, the…

This paper examines an averaging technique applied to the transport equations as an alternative to vanishing viscosity. Such techniques have been shown to be valid shock-regularizations of the Burgers equation and the Euler equations, but…

A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…

In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of \hbar can be constructed for them without referring to the…

The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)] for shearing simple liquids and measuring their viscosity is extended to the Vicsek-model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)] and its metric-free…

As is well-known, for plasmas of high density and modest temperature, the classical kinetic theory needs to be extended. Such extensions can be based on the Schr\"odinger Hamiltonian, applying a Wigner transform of the density matrix, in…

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a Brownian system subjected to a Levy stable random force. The corresponding classical transport equations for the Wigner function are…