Time evolution in quantum systems and stochastics
Abstract
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential equations, which naturally emerge when computing the path integral, leads to a universal expression for the associated measure regardless of the form of the differential operators. The discrete non-linear hierarchy (DNLS) is then considered and the corresponding hierarchy of solvable, in principle, SDEs is extracted. The first couple members of the hierarchy correspond to the discrete stochastic transport and heat equations. The discrete stochastic Burgers equation is also obtained through the analogue of the Cole-Hopf transformation. The continuum limit is also discussed.
Cite
@article{arxiv.2001.01637,
title = {Time evolution in quantum systems and stochastics},
author = {Anastasia Doikou and Simon J. A. Malham and Anke Wiese},
journal= {arXiv preprint arXiv:2001.01637},
year = {2021}
}
Comments
8 pages, LaTex. Based on a talk given by AD in "Quantum Theory and Symmetries XI", July 2019, Montreal, Canada. Relevant results can also be found in arXiv:1810.08095