Born-Oppenheimer approximation in open systems

TL;DR

This paper extends the Born-Oppenheimer approximation to open quantum systems, analyzing its validity under different dissipation types and providing a specific example involving a two-level system.

Contribution

It introduces a generalized Born-Oppenheimer approximation for open systems and establishes conditions for its validity with dissipative processes.

Findings

Validity conditions depend on dissipation type

Approximation works for certain regimes of spin relaxation

Effective Hamiltonian can be diagonalized with fixed variables

Abstract

We generalize the standard Born-Oppenheimer approximation to the case of open quantum systems. We define the zeroth order Born-Oppenheimer approximation of an open quantum system as the regime in which its effective Hamiltonian can be diagonalized with fixed slowly changing variables. We then establish validity and invalidity conditions for this approximation for two kinds of dissipations--the spin relaxation and the dissipation of center-of-mass motion. As an example, the Born-Oppenheimer approximation of a two-level open system is analyzed.