相关论文: Doubly Damped Stochastic Parallel Translations and…

We study the Neumann problem for special Lagrangian type equations with critical and supercritical phases. These equations naturally generalize the special Lagrangian equation and the k-Hessian equation. By establishing uniform a priori…

We derive a non-linear version of the Feynman-Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence (global in time) and uniqueness for a stochastic terminal…

The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrodinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite difference…

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…

There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…

We study a random matching problem on closed compact $2$-dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume…

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems…

We consider the time-dependent Schr\"odinger equation on a Riemannian manifold $\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\mathcal{C}$. When we scale the potential in the directions…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

In the recent years the Schr\"odinger problem has gained a lot of attention because of the connection, in the small-noise regime, with the Monge-Kantorovich optimal transport problem. Its optimal value, the \emph{entropic cost}…

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…

We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…

The Karman-Howarth-Monin-Hill (KHMH) equation has been widely applied to scale-by-scale turbulent energy cascade studies in recent years, however, the forms and interpretations are not consistent. The present work generalizes to considering…

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…

A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of…

The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the…

This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…

This paper considers a family of second-order periodic parabolic equations with highly oscillating potentials, which have been considered many times for the time-varying potentials in stochastic homogenization. Following a standard…

We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states.…

We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and…