Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation

TL;DR

This paper investigates how the decay of Dirac particles in an environment with specific spectral features deviates from exponential behavior, revealing conditions under which decay becomes Markovian or non-Markovian.

Contribution

It demonstrates that high-energy spectral cutoffs and low-energy gaps critically influence decay dynamics, and shows that massless Dirac particles can exhibit Markovian decay without approximations.

Findings

Short-time decay is driven by spectral cutoff L.

Long-time decay is influenced by Dirac gap m.

Massless Dirac particles can decay Markovian without approximations.

Abstract

The decay rate of quantum particles in open quantum systems has traditionally been known as exponential, based on empirical predictions from experiments and theoretical predictions from the Markovian dynamics of the corresponding quantum states. However, both theoretical predictions and experimental observations suggest deviations from this exponential decay, particularly in the short and long time regimes. In this study, we explore the spontaneous emission of a single Dirac particle within an environment characterized by an energy spectrum with a gap $m$ and an energy cutoff $L$. Our results reveal that high-energy structures, such as the spectral cutoff $L$, play a critical role in driving the short-time non-exponential decay. In contrast, the long-time decay is predominantly influenced by low-energy structures, such as the Dirac gap $m$. Surprisingly, we find that in the limits where the energy cutoff $L$ is infinite and the energy gap $m$ is zero, the decay dynamics of massless Dirac particles exhibit Markovian behavior without the need for conventional approximations like the Born-Markov approximation. This work underscores the complex interplay between particle energy properties and decay dynamics, providing new insights into quantum decay processes.