相关论文: Equivalent Semigroup Properties for Curvature-Dime…

The general covariance of the Dirac equation is exploited in order to explore the curvature effects appearing in the electronic properties of graphene. Two physical situations are then considered: the weak curvature regime, with…

For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and…

Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from the Heisenberg Uncertainty Principle. A simple example of this is expected to…

Thermal transport is less appreciated in probing quantum materials in comparison to electrical transport. This article aims to show the pivotal role that thermal transport may play in understanding quantum materials: the longitudinal…

Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at…

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension…

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…

Let $L=\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process…

This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…

Symmetric kernel matrices are a well-researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly…

An issue which has attracted increasing attention in contemporary researches are Kirkwood--Dirac quasiprobabilities. List of their use includes many questions of quantum physics. Applications of complex tight frames in quantum information…

In this short note, we hope to give a rapid induction for non-experts into the world of Differential Harnack inequalities, which have been so influential in geometric analysis and probability theory over the past few decades. At the…

We consider metric graphs with Kirchhoff boundary conditions. We study the intrinsic metric, volume doubling and a Poincar\'e inequality. This enables us to prove a parabolic Harnack inequality. The proof involves various techniques from…

We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…

Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of…

Given a symmetric diffusion process and a jump process on the same underlying space, is there a subordinator such that the jump process and the subordinated diffusion processes are comparable? We address this question when the diffusion…

Quark-Gluon plasmas produced in relativistic heavy-ion collisions quickly expand and cool, entering a phase consisting of multiple interacting hadronic resonances just below the QCD deconfinement temperature, $T\sim 155$ MeV. Numerical…

A transport theory which is not restricted to the gradient and quasi-particle approximations is presented which is formulated in terms of the energy moments, or equivalently the equal-time derivatives of the one-particle Green functions. A…

We review recent results on electronic and thermal transport in two different quasi one-dimensional systems: Silicon nanowires (SiNW) and atomic gold chains. For SiNW's we compute the ballistic electronic and thermal transport properties on…

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities…