Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum

Abstract

We study the decay of a prepared state $E_0$ into a continuum {E_k} in the case of non-Ohmic models. This means that the coupling is $|V_{k,0}|\propto |E_k-E_0{|}^{s-1}$ with $s\ne 1$. We find that irrespective of model details there is a universal generalized Wigner time $t_0$ that characterizes the evolution of the survival probability $P_0(t)$. The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the bandprofile. But depending on non-universal features of the model a power-law decay might take over: it is only for an Ohmic coupling to the continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the dynamics. It turns out that there are special circumstances in which $t_0$ is reflected in the spreading process and not only in the survival probability, contrary to the naive linear response theory expectation.

arXiv comment13 pages, 11 figures

References in corpus (15)

• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Observation of resonance trapping in an open microwave cavity
• Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
• Excited Eigenstates and Strength Functions for Isolated Systems of Interacting Particles
• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• Unconventional decay law for excited states in closed many-body systems
• Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates
• Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence
• Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates
• Return probability: Exponential versus Gaussian decay
• Wavepacket dynamics in energy space, RMT and quantum-classical correspondence
• Wavepacket Dynamics, Quantum Reversibility and Random Matrix Theory
• Stretched Exponential Decay of a Quasiparticle in a Quantum Dot
• Quantum Irreversibility of Energy Spreading
• Decays in Quantum Hierarchical Models

Cited by in corpus (1)

• Quantum anomalies and linear response theory