Survival Probability of a Local Excitation in a Non-Markovian Environment: Survival Collapse, Zeno and Anti-Zeno effects

Abstract

The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial-state survival probability, up to a spreading time $t_S$, (ii) exponential decay described by a self-consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes and leading to an inverse power law decay. At this last cross-over time $t_R$ a survival collapse becomes possible. This could reduce the survival probability by several orders of magnitude. The cross-overs times $t_S$ and $t_R$ allow to assess the range of applicability of the Fermi Golden Rule and give the conditions for the observation of the Zeno and Anti-Zeno effect.

References in corpus (5)

• Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect
• Simulations of Information Transport in Spin Chains
• Non-Markovian decay beyond the Fermi Golden Rule: Survival Collapse of the polarization in spin chains
• Effective one-body dynamics in multiple-quantum NMR experiments
• Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule

Cited by in corpus (5)

• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Realistic many-body quantum systems vs full random matrices: static and dynamical properties
• The Loschmidt Echo as a robust decoherence quantifier for many-body systems
• Non-Markovian decay and dynamics of decoherence in private and public environments