Divergences in open quantum systems

TL;DR

This paper investigates divergences in the quantum master equations of open quantum systems, revealing their role in operator renormalization and the persistence of initial singularities, with implications for effective dynamics.

Contribution

It demonstrates that divergences in the master equation ensure closure on renormalized operators and explores how initial state choices affect singularities.

Findings

Divergences appear in non-Hamiltonian terms of the master equation.

Initial singularities persist for quadratic operators but can be mitigated.

Proper initial state projection removes jolt singularities.

Abstract

We show that for cubic scalar field theories in five and more spacetime dimensions, and for the $T = 0$ limit of the Caldeira-Leggett model, the quantum master equation for long-wavelength modes initially unentangled from short-distance modes, and at second order in perturbation theory, contains divergences in the non-Hamiltonian terms. These divergences ensure that the equations of motion for expectation values of composite operators closes on expectation values of renormalized operators. Along the way we show that initial "jolt" singularities which occur in the equations of motion for operators linear in the fundamental variables persist for quadratic operators, and are removed if one chooses an initial state projected onto low energies, following the Born-Oppenheimer approximation.