Kadanoff-Baym approach to bound states in open quantum systems

TL;DR

This paper extends the Kadanoff-Baym equations to study bound state formation in open quantum systems across various dimensions and bath types, analyzing thermodynamics, dynamics, and wave function effects.

Contribution

It introduces a generalized approach for applying Kadanoff-Baym equations to diverse open quantum systems, including different dimensions and bath interactions, with detailed numerical solutions.

Findings

Bound states form and decay depending on temperature and coupling.

System equilibrates perfectly with the heat bath.

Wave functions are significantly influenced by bath interactions.

Abstract

In this paper, we extend the method of Kadanoff-Baym equations for open quantum systems to arbitrary kinds of systems and heat baths, either fermionic or bosonic. This includes three spacial dimensions and different potentials for the system-bath interaction or external traps. We study the quantum-mechanical formation of bound states in one and also in three dimensions with the full Kadanoff-Baym equations and compare them to more simplified approaches with and without memory effects. An in-depth examination of the thermodynamics of open systems is performed, showing perfect equilibration of the system's degrees of freedom along with a comprehensive investigation of the influence of the heat bath on the system's wave functions. The formation time, decay time and regeneration of bound states and their dependence on the temperature and coupling strength is explored We evaluate the non-equilibrium Kadanoff-Baym equations for the system particles, assuming that interactions are elastic two-particle collisions with the heat-bath particles. Finally, we describe in detail the method used to numerically solve the corresponding spatially heterogeneous integro-differential equations for the set of one-particle Green's functions.