Construction of quantum systems with soluble ground-state properties

Abstract

The authors propose a transformation of the Langevin equation into an eigenvalue problem as a method to construct systems with soluble ground-state properties. As examples, they discuss quantum systems resulting from the Toda and sine-Gordon chains evolving according to the Langevin equation. Some ground-state properties are then evaluated with methods originally devised to calculate the partition function of one-dimensional classical systems. They also present numerical results for the two-phonon bound-state frequency and its coupling constant dependence by simulating a generalised quantum sine-Gordon system.