Related papers: A kinetic eikonal equation
We discuss the calculation of the linear conductance through a Coulomb-blockade quantum dot in the presence of interactions beyond the charging energy. In the limit where the temperature is large compared with a typical tunneling width, we…
It is shown that any function $G(q_{i}, p_{i}, t)$, defined on the extended phase space, defines a one-parameter group of canonical transformations which act on any function $f(q_{i}, t)$, in such a way that if $G$ is a constant of motion…
We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the…
In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the…
We give a meaning to the Hamilton--Jacobi equation arising from mean-field spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defined on the set of monotone probability measures, these…
We study the limit of a kinetic evolution equation involving a small parameter and perturbed by a smooth random term which also involves the small parameter. Generalizing the classical method of perturbed test functions, we show the…
We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of integro-differential type. We consider the case when the fractional diffusion has the same order as the…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.
In this paper, we show the additive separation of the Hamilton-Jacobi equation, present the 4-velocity of the test particles, and attempt to find the equatorial circular photon orbit (ECPO) in the Kerr-Sen-Taub-NUT (KSTN) solution of the…
We study the large time behaviour of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a BSDE in finite horizon $T$ taken at initial time behaves like a…
The present paper first aims to study the BV-type regularity for viscosity solutions of the Hamilton-Jacobi equation \[ u_t(t,x)+H\big(D_{x} u(t,x)\big)~=~0\qquad\forall (t,x)\in ]0,\infty[\times\mathbb{R}^d \] with a coercive and uniformly…
We study the Hamilton-Jacobi equation f - lambda Hf = h, where H f = e^{-f}Ae^f and where A is an operator that corresponds to a well-posed martingale problem. We identify an operator that gives viscosity solutions to the Hamilton-Jacobi…
The BBGKY formalism is revisited in the framework of plasma spectroscopy. We address the issue of Stark line shape modeling by using kinetic transport equations. In the most simplified treatment of these equations, triple correlations…
We consider the following evolutionary Hamilton-Jacobi equation with initial condition: \begin{equation*} \begin{cases} \partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=\phi(x), \end{cases} \end{equation*} where $\phi(x)\in…
Motivated by Open Problem 17 in Damanik-Fillman's manuscript , we study the decay rate of limit-periodic approximation such that ballistic transport persists in the limit-periodic setting. We show an exponential decay rate, roughly…
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…
Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is…