Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0905.4934 · Journal of Physics A Mathematical and Theoretical

Quantum decay into a non-flat continuum

James Aisenberg, Itamar Sela, Tsampikos Kottos, Doron Cohen, Alexander Elgart

Published Feb 9, 2010• 1 citation
arXivHTMLPDF

Abstract

We study the decay of a prepared state into non-flat continuum. We find that the survival probability P ( t ) might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time t 0 that does not depend on the functional form. It is only for a flat 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 local density of states, and the nonlinear dependence of 1/ t 0 on the strength of the coupling.

DOI
10.1088/1751-8113/43/9/095301

Related papers

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

Itamar Sela, James Aisenberg, Tsampikos Kottos +2 more

We study the decay of a prepared state E0 into a continuum {Ek} in the case of non-Ohmic models. This means that the coupling is Vk,|proportional|Ek-E0s-1 with s not equal 1. We find that irrespective of model details there is a universal generalized Wigner time t0 that characterizes the decay of the survival probability P0(t). The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the band profile. But depending on nonuniversal 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 intracontinuum couplings. The analysis highlights the coexistence of perturbative and nonperturbative features in the dynamics. It turns out that there are special circumstances in which t0 is reflected in the spreading process and not only in the survival probability, contrary to the naive linear-response theory expectation. .

arXiv:1003.1645•Physical Review E•Mar 25, 2010•2 citations

Amplification of non‐Markovian decay due to bound state absorption into continuum

Savannah Sterling Garmon, T. Petrosky, L. Simine +1 more

Abstract It is known that quantum systems yield non‐exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time ‘near zone’ and long time ‘far zone’. In the near zone the survival probability falls off according to a t‐1 power law, and in the far zone i t falls off as t‐3. We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t‐1 power law even on asymptotic scales. Conversely, one could study the case of an anti‐bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t‐1 power law dominates precisely at the point of ejection.

arXiv:1204.6141•Fortschritte der Physik•Jul 5, 2012•45 citations

True quantum face of the “exponential” decay law

K. Urbanowski

Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, “exponential” (or “canonical”) described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the “exponential” regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.

arXiv:1606.07301•The European Physical Journal D•May 1, 2017•9 citations

Nonclassical face of quantum decay processes

K. Urbanowski

A detailed analysis of the quantum decay processes shows the survival probability ( t ) can not take that exponential form at any time interval including times smaller than the lifetime τ . We show that for times t ∼ τ and for the times later than τ the form of ( t ) looks as a composition of an oscillating and exponential functions. The amplitude of these oscillations is very small for t ≪ τ and grows with increasing time and depends on the model considered. We also study the survival probability of moving relativistic unstable particles with definite momentum : It turns out that late time deviations of the survival probability of these particles from the exponential-like form of the decay law should occur much earlier than it follows from the classical standard approach resolving itself into replacing time t by t / γ (where γ is the relativistic Lorentz factor) in the formula for the survival probability ( t ).

Journal of Physics Conference Series•Aug 1, 2017•0 citations

Limited quantum decay

Bernard Gaveau, Lawrence S. Schulman

An isolated level coupled to a continuum of levels need not decay fully into them. Ordinarily one expects exponential decay, module finite-size effects, transients and long-time power-law tails. In the phenomenon we describe the amplitude for remaining in the initial state at first drops, but it then levels off and remains O(1) indefinitely. Because of the available continuum, this is different from certain quantum localization phenomena where there is an absence of on-shell levels. The origin of the effect we describe is the existence of thresholds and band edges. A condition relating the proximity to threshold with the strength of the coupling determines whether the limited decay occurs.

Journal of Physics A Mathematical and General•Dec 21, 1995•45 citations

Limited quantum decay

P M Curie

An isolated level coupled to a continuum of levels need not decay fully into them Ordinarily one expects exponential decay. modulo finite-sire effects. transients and long-time power-law tails. In the phenomenon we describe the amplitude for remaining in the initial state at first drops, but then levels off and remains O(1) indefinitely. Because-of the available continuum, this is different from certain quantum localization phenomena where there is an absence of on-shell levels. The origin of the effect we describe is, the existence af thresiiolds and band edges. A condition relating the proximity to threshold with the strength ofthe coupling determines whether the limited decay occurs.

•Jan 1, 1995•0 citations
We study the decay of a prepared state into non-flat continuum. We find that the survival probability P ( t ) might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time t 0 that does not depend on the functional form. It is only for a flat 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 local density of states, and the nonlinear dependence of 1/ t 0 on the strength of the coupling.
We study the decay of a prepared state E0 into a continuum {Ek} in the case of non-Ohmic models. This means that the coupling is Vk,|proportional|Ek-E0s-1 with s not equal 1. We find that irrespective of model details there is a universal generalized Wigner time t0 that characterizes the decay of the survival probability P0(t). The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the band profile. But depending on nonuniversal 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 intracontinuum couplings. The analysis highlights the coexistence of perturbative and nonperturbative features in the dynamics. It turns out that there are special circumstances in which t0 is reflected in the spreading process and not only in the survival probability, contrary to the naive linear-response theory expectation. .
Abstract It is known that quantum systems yield non‐exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time ‘near zone’ and long time ‘far zone’. In the near zone the survival probability falls off according to a t‐1 power law, and in the far zone i t falls off as t‐3. We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t‐1 power law even on asymptotic scales. Conversely, one could study the case of an anti‐bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t‐1 power law dominates precisely at the point of ejection.
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, “exponential” (or “canonical”) described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the “exponential” regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
A detailed analysis of the quantum decay processes shows the survival probability ( t ) can not take that exponential form at any time interval including times smaller than the lifetime τ . We show that for times t ∼ τ and for the times later than τ the form of ( t ) looks as a composition of an oscillating and exponential functions. The amplitude of these oscillations is very small for t ≪ τ and grows with increasing time and depends on the model considered. We also study the survival probability of moving relativistic unstable particles with definite momentum : It turns out that late time deviations of the survival probability of these particles from the exponential-like form of the decay law should occur much earlier than it follows from the classical standard approach resolving itself into replacing time t by t / γ (where γ is the relativistic Lorentz factor) in the formula for the survival probability ( t ).
An isolated level coupled to a continuum of levels need not decay fully into them. Ordinarily one expects exponential decay, module finite-size effects, transients and long-time power-law tails. In the phenomenon we describe the amplitude for remaining in the initial state at first drops, but it then levels off and remains O(1) indefinitely. Because of the available continuum, this is different from certain quantum localization phenomena where there is an absence of on-shell levels. The origin of the effect we describe is the existence of thresholds and band edges. A condition relating the proximity to threshold with the strength of the coupling determines whether the limited decay occurs.
An isolated level coupled to a continuum of levels need not decay fully into them Ordinarily one expects exponential decay. modulo finite-sire effects. transients and long-time power-law tails. In the phenomenon we describe the amplitude for remaining in the initial state at first drops, but then levels off and remains O(1) indefinitely. Because-of the available continuum, this is different from certain quantum localization phenomena where there is an absence of on-shell levels. The origin of the effect we describe is, the existence af thresiiolds and band edges. A condition relating the proximity to threshold with the strength ofthe coupling determines whether the limited decay occurs.