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:1905.07493 · Physical Review A

Interference in the time domain of a decaying particle with itself as the physical mechanism for the exponential-nonexponential transition in quantum decay

Gastón García‐Calderón, Roberto Romo

Published Sep 25, 2019• 5 citations
arXivHTMLPDF

Abstract

By using an exact analytical non-Hermitian approach in terms of resonance states, we show that the exponential-nonexponential transition of decay at long times physically represents a process of interference in the time domain of the decaying particle with itself. We also show that actually the regeneration mechanism proposed by Fonda and Ghirardi [L. Fonda and G. C. Ghirardi, Nuovo Cimento A 7, 180 (1972)] is not the relevant mechanism for nonexponential decay.

DOI
10.1103/physreva.100.032121

Related papers

Probing the nonexponential decay regime in open quantum systems

S. M. Wang, Witold Nazarewicz, Alexander Volya +1 more

The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for nonexponential behavior at long times. Yet such long-term nonexponentiality is expected theoretically to probe the nonresonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of nonexponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.

arXiv:2211.11619•Physical Review Research•Jun 23, 2023•28 citations

Exact analytical non-Hermitian formulation of the time evolution of decay of one and two identical quantum particles

Gastón García-Calderón

An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and nonescape probabilities for the initial state of a single particle and entangled symmetric and antisymmetric initial states of two identical particles evolve in a distinctive form along the exponential and long-time nonexponential decaying regimes. In particular, for the last regime, they exhibit different inverse power of time behaviors.

arXiv:1702.04035•Journal of Physics Conference Series•Jul 3, 2015•1 citation

Full-time nonexponential decay in double-barrier quantum structures

Gastón García‐Calderón, Jorge Villavicencio

We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and nonexponential terms of the survival amplitude modifies the usual exponential decay regime in systems where the ratio of the resonance energy to the decay width is less than 0.3. We suggest that such a regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.

arXiv:quant-ph/0605109•Physical Review A•Jun 28, 2006•34 citations

Quantum tunneling decay due to interference of a bound and an antibound state

Gastón García‐Calderón, Roberto Romo

We consider an exact analytical formulation of the wave function for quantum tunneling decay, given as an expansion in terms of the bound, antibound, and resonant states, for the time-honored problem of a particle initially confined by a potential. We find that the interference term between a bound state and its corresponding antibound state may favor a decay process in which the probability density spreads throughout space in a nonexponential fashion.

Physical Review A•May 23, 2024•0 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

Exponential and nonexponential buildup in resonant tunneling

Roberto Romo, Alberto Hernández-Maldonado, Jorge Villavicencio

The exponential and nonexponential regimes of the buildup process in resonant tunneling structures are analyzed by considering an analytic solution of the time-dependent Schr\"odinger equation. It is found that the buildup exhibits a purely exponential behavior in a finite time interval followed by a clear transition to a nonexponential regime. The buildup of the probability amplitude in the nonexponential regime follows a ${t}^{\ensuremath{-}3/2}$ time dependence, in the same fashion as the survival amplitude in quantum decay. For incidence energies at higher isolated resonances, $E={\ensuremath{\varepsilon}}_{n}$ with $n>1$, it is found that the exponential regime is split into two exponential subregimes: the first one is governed by the width ${\ensuremath{\Gamma}}_{n}$ of the resonance chosen for the incidence energy, and the second one is dominated by the width ${\ensuremath{\Gamma}}_{1}$ of the lowest resonance. The transition occurs directly from $n$ to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and nonexponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances play an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form $|E\ensuremath{-}{\ensuremath{\varepsilon}}_{n}|/\ensuremath{\hbar}$, where ${\ensuremath{\varepsilon}}_{n}$ are the nearest resonances around the incidence energy $E$.

Physical Review A•Feb 27, 2013•5 citations
By using an exact analytical non-Hermitian approach in terms of resonance states, we show that the exponential-nonexponential transition of decay at long times physically represents a process of interference in the time domain of the decaying particle with itself. We also show that actually the regeneration mechanism proposed by Fonda and Ghirardi [L. Fonda and G. C. Ghirardi, Nuovo Cimento A 7, 180 (1972)] is not the relevant mechanism for nonexponential decay.
The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for nonexponential behavior at long times. Yet such long-term nonexponentiality is expected theoretically to probe the nonresonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of nonexponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and nonescape probabilities for the initial state of a single particle and entangled symmetric and antisymmetric initial states of two identical particles evolve in a distinctive form along the exponential and long-time nonexponential decaying regimes. In particular, for the last regime, they exhibit different inverse power of time behaviors.
We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and nonexponential terms of the survival amplitude modifies the usual exponential decay regime in systems where the ratio of the resonance energy to the decay width is less than 0.3. We suggest that such a regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.
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.
The exponential and nonexponential regimes of the buildup process in resonant tunneling structures are analyzed by considering an analytic solution of the time-dependent Schr\"odinger equation. It is found that the buildup exhibits a purely exponential behavior in a finite time interval followed by a clear transition to a nonexponential regime. The buildup of the probability amplitude in the nonexponential regime follows a ${t}^{\ensuremath{-}3/2}$ time dependence, in the same fashion as the survival amplitude in quantum decay. For incidence energies at higher isolated resonances, $E={\ensuremath{\varepsilon}}_{n}$ with n>1n>1n>1, it is found that the exponential regime is split into two exponential subregimes: the first one is governed by the width ${\ensuremath{\Gamma}}_{n}$ of the resonance chosen for the incidence energy, and the second one is dominated by the width ${\ensuremath{\Gamma}}_{1}$ of the lowest resonance. The transition occurs directly from nnn to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and nonexponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances play an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form $|E\ensuremath{-}{\ensuremath{\varepsilon}}_{n}|/\ensuremath{\hbar}$, where ${\ensuremath{\varepsilon}}_{n}$ are the nearest resonances around the incidence energy EEE.