Quantum energy decays and decoherence in discrete baths

TL;DR

This paper investigates how the energy and coherence of a quantum particle decay due to interactions with a finite structured bath, revealing different decay regimes and the transition from non-Markovian to Markovian dynamics as the bath size increases.

Contribution

It provides a detailed analysis of energy and decoherence decay in quantum systems coupled to finite discrete baths, highlighting the transition from non-Markovian to Markovian behavior with increasing bath size.

Findings

Decay rates depend on the number of bath constituents N.

Two exponential decay regimes and a power-law decay are observed.

Decoherence occurs at intermediate N, with a transition to Markovian dynamics at large N.

Abstract

The quantum average energy decay and the purity decay are studied for a system particle as a function of the number of constituents of a discrete bath model. The system particle is subjected to two distinct physical situations: the harmonic oscillator (HO) and the Morse potential. The environment (bath) is composed by a {\it finite} number N of uncoupled HOs, characterizing the structured bath, which in the limit $N\to\infty$ is assumed to have an ohmic, sub-ohmic or super-ohmic spectral density. For very low values of N the mean energy and purity remain constant in time but starts to decay for intermediate values (10<N<20), where two distinct time regimes are observed: two exponential decays for relatively short times and a power-law decay for larger times. In this interval of N decoherence occurs for short times and a non-Markovian dynamics is expected for larger times. When $N$ increases, energy and coherence decay very fast and a Markovian dynamics is expected to occur. Wave packet dynamics is used to determine the evolution of the particle inside the system potentials.