Non-Markovian character and irreversibility of real-time quantum many-body dynamics

TL;DR

This paper investigates the non-Markovian behavior and irreversibility in real-time quantum many-body dynamics, emphasizing the role of pairing correlations, canonical orbitals, and entropy measures in nuclear systems.

Contribution

It introduces a framework using canonical wave functions and natural orbitals to analyze memory effects and irreversibility in quantum many-body dynamics, highlighting limitations of truncation in time-dependent scenarios.

Findings

Canonical basis effectively describes static properties.

Truncation of orbitals is valid for static but not for dynamic calculations.

Natural orbitals provide insight into non-equilibrium quantum behavior.

Abstract

The presence of pairing correlations within the time-dependent density functional theory (TDDFT) extension to superfluid systems, is tantamount to the presence of a quantum collision integral in the evolution equations, which leads to an obviously non-Markovian behavior of the single-particle occupation probabilities, unexpected in a traditional quantum extension of kinetic equations. The quantum generalization of the Boltzmann equation, based on a collision integral in terms of phase-space occupation probabilities, is the most used approach to describe nuclear dynamics and which by construction has a Markovian character. By contrast, the extension of TDDFT to superfluid systems has similarities with the Baym and Kadanoff kinetic formalism, which however is formulated with much more complicated evolution equations with long-time memory terms and non-local interactions. The irreversibility of quantum dynamics is properly characterized using the canonical wave functions/natural orbitals, and the associated canonical occupation probabilities, which provide the smallest possible representation of any fermionic many-body wave function. In this basis, one can evaluate the orbital entanglement entropy, which is an excellent measure of the non-equilibrium dynamics of an isolated system. To explore the phenomena of memory effects and irreversibility, we investigate the use of canonical wave functions/natural orbitals in nuclear many-body calculations, assessing their utility for static calculations, dynamics, and symmetry restoration. As the number of single-particle states is generally quite large, it is highly desirable to work in the canonical basis whenever possible, preferably with a cutoff. We show that truncating the number of canonical wave functions can be a valid approach in the case of static calculations, but that such a truncation is not valid for time-dependent calculations...