Renormalization in the Theory of Open Quantum Systems via the Self-Consistency Condition

TL;DR

This paper addresses the renormalization process in open quantum systems, proposing a self-consistency condition to ensure thermodynamic consistency and clarifying the physical interpretation of the Lamb-Stark shift.

Contribution

It introduces a self-consistency condition for renormalization in open quantum systems, ensuring thermodynamic consistency and providing a simplified scheme for common dynamical equations.

Findings

The self-consistency condition restores thermodynamic consistency.

Comparison shows discrepancies between dynamical and static corrections.

A simplified renormalization scheme applicable to standard equations.

Abstract

We investigate the topic of renormalization in the theory of weakly interacting open quantum systems. Our starting point is an open quantum system interacting with a single heat bath. For a given setup, we discuss that the stationary state of the Davies-GKSL equation is thermodynamically inconsistent with the presence of the Lamb-Stark shift term. For this reason, we postulate the self-consistency condition for the dynamical equations. The condition fixes the renormalization procedure and recovers the thermodynamical consistency. In this way, we rederive the cumulant equation to illustrate how the self-consistency condition enters the derivation of the dynamical equations. The physical interpretation of the renormalization procedure is discussed in terms of the Born approximation. Furthermore, we compare the Lamb-Stark shift term (dynamical correction) with the second-order (static) correction to the so-called mean-force (Gibbs state) Hamiltonian. The discrepancy between the static and the dynamical correction questions the physical meaning of the latter one. Finally, we formulate a simplified renormalization scheme that can be directly applied to Davies-GKSL or Bloch-Redfield equations.