Full density matrix dynamics for large quantum systems: Interactions, Decoherence and Inelastic effects

TL;DR

This paper introduces analytical and numerical methods to simulate the full density matrix dynamics of large quantum systems, specifically the Anderson model, including interactions, decoherence, and inelastic effects, advancing understanding of nonequilibrium quantum phenomena.

Contribution

It develops and extends three computational techniques to accurately model the global density matrix dynamics of interacting quantum systems with decoherence and inelastic effects.

Findings

Exact path integral simulations reveal electron-electron interactions significantly influence system dynamics.

Quantum Langevin equations provide a mean-field approximation compared to exact methods.

Probe techniques effectively mimic decoherence and thermalization in large quantum systems.

Abstract

We develop analytical tools and numerical methods for time evolving the total density matrix of the finite-size Anderson model. The model is composed of two finite metal grains, each prepared in canonical states of differing chemical potential and connected through a single electronic level (quantum dot or impurity). Coulomb interactions are either excluded all together, or allowed on the dot only. We extend this basic model to emulate decoherring and inelastic scattering processes for the dot electrons with the probe technique. Three methods, originally developed to treat impurity dynamics, are augmented to yield global system dynamics: the quantum Langevin equation method, the well known fermionic trace formula, and an iterative path integral approach. The latter accommodates interactions on the dot in a numerically exact fashion. We apply the developed techniques to two open topics in nonequilibrium many-body physics: (i) We explore the role of many-body electron-electron repulsion effects on the dynamics of the system. Results, obtained using exact path integral simulations, are compared to mean-field quantum Langevin equation predictions. (ii) We analyze aspects of quantum equilibration and thermalization in large quantum systems using the probe technique, mimicking elastic-dephasing effects and inelastic interactions on the dot. Here, unitary simulations based on the fermionic trace formula are accompanied by quantum Langevin equation calculations.