# Long-time behavior of many-particle quantum decay

## Abstract

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.

- Authors:

- Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, D-30167 Hannover (Germany)

- Publication Date:

- OSTI Identifier:
- 22038596

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSONS; FERMIONS; MANY-BODY PROBLEM; PARTICLES; QUANTUM MECHANICS; TRAPS; TUNNEL EFFECT

### Citation Formats

```
Campo, A. del.
```*Long-time behavior of many-particle quantum decay*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.012113.

```
Campo, A. del.
```*Long-time behavior of many-particle quantum decay*. United States. doi:10.1103/PHYSREVA.84.012113.

```
Campo, A. del. Fri .
"Long-time behavior of many-particle quantum decay". United States. doi:10.1103/PHYSREVA.84.012113.
```

```
@article{osti_22038596,
```

title = {Long-time behavior of many-particle quantum decay},

author = {Campo, A. del},

abstractNote = {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.},

doi = {10.1103/PHYSREVA.84.012113},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}