6533b82ffe1ef96bd1295c6a

RESEARCH PRODUCT

Nonequilibrium dynamics of nonconservative diffusion processes

subject

description

Fokker-Planck operators of diffusion processes with nonconservative drift fields, in dimension $N\geq 2$, can be directly related with non-Hermitian electromagnetic-type Hamiltonian generators of motion. The induced nonequilibrium dynamics of probability densities points towards an issue of path integral solutions of the Fokker-Planck equation, and calls for revisiting links between known exact path integral formulas for quantum propagators in real and Euclidean time, with these for Fokker-Planck-induced transition probability density functions. In below we shall follow the $N=3$ "magnetic thread", within which one encounters formally and conceptually distinct implementations of the magnetic (or magnetic-looking) impact on the dynamics of stochastic diffusion processes. That includes the "magnetic affinity" of nonconservative diffusion processes, the classic Brownian motion of charged particles in the (electro)magnetic field, so-called Euclidean quantum mechanics involving non-Hermitian magnetic-type Hamiltonians, and path integral evaluation of integral kernels of Schr\"{o}dinger semigroups with a minimal electromagnetic coupling (encoded in their Hermitian generators). Our main objective is to go beyond the lore of magnetic analogies/affinities. We aim at detecting deeper interrelations between "magnetically affine" approaches, while clearly discriminating between the classic Lorentz or magnetic forcing in the Brownian motion of charged particles, quantum methods of incorporating electromagnetism, and potentially useful electromagnetic analogies ("surrogate magnetism") in the dynamics of diffusion processes.