Non-Markovian Quantum Decay in Complex Environments: A Hyperstatistical Approach

arXiv:2609.22190v1 Announce Type: new Abstract: The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law ``long-time tails.'' In this paper, we apply the recently proposed \textit{hyperstatistics} framework to solve the problem of quantum decay in such complex environments. By considering a $\gamma$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is finite for $q<2$. The convergence of the second moment instead requires the stricter condition $q<3/2$. For $1<q<3/2$ both the mean lifetime and its variance are finite, for $3/2\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad, and for $q\ge2$ the mean lifetime itself diverges. This result provides a physical interpretation linking extreme environmental complexity to Anderson localization and Griffiths-like phases.

Abstract:The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law ``long-time tails.'' In this paper, we apply the recently proposed \textit{hyperstatistics} framework to solve the problem of quantum decay in such complex environments. By considering a $\gamma$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is finite for $q<2$. The convergence of the second moment instead requires the stricter condition $q<3/2$. For $1<q<3/2$ both the mean lifetime and its variance are finite, for $3/2\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad, and for $q\ge2$ the mean lifetime itself diverges. This result provides a physical interpretation linking extreme environmental complexity to Anderson localization and Griffiths-like phases.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.22190 [quant-ph]

(or arXiv:2609.22190v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.22190 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

Non-Markovian Quantum Decay in Complex Environments: A Hyperstatistical Approach

Subiecte conexe