2017/12/10 by Viviana Letizia, Letizia, Viviana
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1712.03590
openalex publication_date 2017/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the one-dimensional discrete linear Schrodinger (DLS) equation perturbed by a conservative stochastic dynamics, that changes the phase of each particles, conserving the total norm (or number of particles). The resulting total dynamics is a degenerate hypoelliptic diffusion with a smooth stationary state. We will show that the system has a hydrodynamical limit given by the solution of the heat equation. When it is coupled at the boundaries to two Langevin thermostats at two different chemical potentials, we prove that the stationary state, in the limit as N ! 1, satisfies the Fourier's law.