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

Europhysics Letters (EPL)

Persistence of exponential decay for metastable quantum states at long times

Robert E. Parrott, Jay Lawrence

Published Mar 1, 2002• 17 citations
Publisher

Abstract

Quantum dynamics predicts that a metastable state should decay exponentially except at very early and very late times. We show through an exactly soluble model that if the decay products can interact weakly with their environment, then the exponential decay regime is prolonged to later times, while the exponential decay constant itself remains essentially unaffected . As the number of environmental degrees of freedom is increased, the asymptotic late-time decay follows higher powers of 1/ t and the exponential decay regime is extended without limit.

DOI
10.1209/epl/i2002-00509-0

Related papers

Nonexponential decay at late times and a different Zeno paradox

Jay Lawrence

The decay profile of a metastable quantum state decaying in isolation is predicted to depart from exponential behaviour after many lifetimes, and in typical cases to adopt algebraic behaviour as the late-time limit. The effect of environmental interactions, including measurement, is quite different from that of the familiar Zeno (and anti-Zeno) effects that have been observed at very early times. Instead of arresting the decay (or hastening it), the late-time interactions tend to enforce the exponential decay law, without substantially changing the decay constant intrinsic to the isolated system. The experimental challenge is to prevent these interactions and observe the crossover to the nonexponential regime.

Journal of Optics B Quantum and Semiclassical Optics•Aug 1, 2002•11 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

Long-time behavior of many-particle quantum decay

Adolfo del Campo

While exponential decay is ubiquitous in nature, deviations at both short and long times are dictated by quantum mechanics. Nonexponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time nonexponential behavior of the nonescape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that, whereas for noninteracting bosons the long-time decay follows a power law with an exponent linear in the number of particles $N$, the exponent becomes quadratic in $N$ in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial antibunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.

arXiv:1104.4318•Physical Review A•Jul 22, 2011•81 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

Nonexponential Quantum Decay under Environmental Decoherence

Mathieu Beau, Jukka Kiukas, I. L. Egusquiza +1 more

A system prepared in an unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from exponential decay in open quantum systems under very general conditions. Our results are illustrated with the exact dynamics under quantum Brownian motion and suggest an explanation of recent experimental observations.

arXiv:1706.06943•Physical Review Letters•Sep 27, 2017•67 citations

Operational approach to metastability

Katarzyna Macieszczak

In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how the averages of system observables change with time and quantifies how non-stationary the system is during a given time regime. By drawing an analogy with the exponential decay, we are able to further investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system is approximately stationary. While this is always the case within the initial and final regimes of the dynamics, with the system respectively approximated by its initial and asymptotic states, we show that a distinct regime of approximate stationarity may arise. In turn, we establish a quantitative description of the phenomenon of metastability in open quantum systems. The initial relaxation occurring before the corresponding metastable regime and of the long-time dynamics taking place afterwards are also characterised. Furthermore, we explain how metastability relates to the separation in the real part of the master equation spectrum and connect our approach to the spectral theory of metastability, clarifying when the latter follows. All of our general results directly translate to Markovian dynamics of classical stochastic systems.

arXiv:2104.05095•Apr 11, 2021•1 citation
Quantum dynamics predicts that a metastable state should decay exponentially except at very early and very late times. We show through an exactly soluble model that if the decay products can interact weakly with their environment, then the exponential decay regime is prolonged to later times, while the exponential decay constant itself remains essentially unaffected . As the number of environmental degrees of freedom is increased, the asymptotic late-time decay follows higher powers of 1/ t and the exponential decay regime is extended without limit.
The decay profile of a metastable quantum state decaying in isolation is predicted to depart from exponential behaviour after many lifetimes, and in typical cases to adopt algebraic behaviour as the late-time limit. The effect of environmental interactions, including measurement, is quite different from that of the familiar Zeno (and anti-Zeno) effects that have been observed at very early times. Instead of arresting the decay (or hastening it), the late-time interactions tend to enforce the exponential decay law, without substantially changing the decay constant intrinsic to the isolated system. The experimental challenge is to prevent these interactions and observe the crossover to the nonexponential regime.
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.
While exponential decay is ubiquitous in nature, deviations at both short and long times are dictated by quantum mechanics. Nonexponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time nonexponential behavior of the nonescape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that, whereas for noninteracting bosons the long-time decay follows a power law with an exponent linear in the number of particles NNN, the exponent becomes quadratic in NNN in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial antibunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.
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 ).
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how the averages of system observables change with time and quantifies how non-stationary the system is during a given time regime. By drawing an analogy with the exponential decay, we are able to further investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system is approximately stationary. While this is always the case within the initial and final regimes of the dynamics, with the system respectively approximated by its initial and asymptotic states, we show that a distinct regime of approximate stationarity may arise. In turn, we establish a quantitative description of the phenomenon of metastability in open quantum systems. The initial relaxation occurring before the corresponding metastable regime and of the long-time dynamics taking place afterwards are also characterised. Furthermore, we explain how metastability relates to the separation in the real part of the master equation spectrum and connect our approach to the spectral theory of metastability, clarifying when the latter follows. All of our general results directly translate to Markovian dynamics of classical stochastic systems.