Long-time behavior of many-particle quantum decay
Open accessAbstract
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.
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Under quite general conditions, a power-law decay holds.
“Under quite general conditions, a power-law decay holds, as has been demonstrated in single-particle [23], few-body [30] and many-body systems [25, 31-33].”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [30]
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Martínez-Tibaduiza, D., Pires, L. B., & Farina, C. (2021) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/ac36ba · Cited by 1 · see citing works
Sasmal, N., & del Campo, A. (2026) · Physical review. B./Physical review. B · doi:10.1103/g7hk-tlq1 · Cited by 1 · see citing works
García-Calderón, G. (2015) · Journal of Physics Conference Series · doi:10.1088/1742-6596/626/1/012064 · Cited by 1 · see citing works
Escape dynamics of many hard disks
Taniguchi, T., Murata, H., & Sawada, S. (2014) · Physical Review E · doi:10.1103/physreve.90.052923 · Cited by 1 · see citing works
Non-adiabatic effects in quantum escapes with a time-dependent potential
Taniguchi, T., & Sawada, S. (2013) · The European Physical Journal B · doi:10.1140/epjb/e2013-40519-y · Cited by 1 · see citing works
Saad, A., & Kocak, F. (2020) · Acta Physica Polonica B · doi:10.5506/aphyspolb.51.2097 · Cited by 1 · see citing works
Bagger–Lambert–Gustavsson Membrane Model as a Constrained System and Dirac Quantization
de Aguiar, A. M., Mendes, A. C. R., Abreu, É. M. C., & Neto, J. A. (2020) · Acta Physica Polonica B · doi:10.5506/aphyspolb.51.2083 · Cited by 1 · see citing works
Lin, Q.-G. (2014) · The European Physical Journal D · doi:10.1140/epjd/e2014-40497-8
Dynamic analysis of shortcut to adiabaticity based on physical information neural network
Ming, L., Zhang, S., & Li, H. (2025) · Acta Physica Sinica · doi:10.7498/aps.74.20250147
Longhi, S. (2026) · Laser & Photonics Review · doi:10.1002/lpor.202501986
Dynamics of shortcut to adiabaticity for Bose-Einstein condensates in a double-well potential
Pengyu, L., & Shengchang, L. (2026) · Acta Physica Sinica · doi:10.7498/aps.75.20251747
- Authors
- del Campo, A.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2011-07-22
- Volume
- 84
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2118233490
- Cited by
- 82
- References
- 42
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 1 · 2023: 2 · 2022: 5 · 2021: 2 · 2020: 9 · 2019: 5 · 2018: 6 · 2017: 5 · 2016: 10 · 2015: 9 · 2014: 6 · 2013: 4 · 2012: 9
- FWCI
- 3.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- quantum decay, non-exponential decay, long-time behavior, many-body systems, tunneling, survival probability, power-law decay, contact interaction, quantum statistics, bosons, fermions, hard-core interactions, resonant states
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