# Quantum chaos in nuclear physics

## Abstract

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

- Authors:

- St. Petersburg State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22612640

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 79; Journal Issue: 4; Other Information: Copyright (c) 2016 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; CHAOS THEORY; DEGREES OF FREEDOM; HAMILTONIANS; LYAPUNOV METHOD; NUCLEAR PHYSICS; QUANTUM NUMBERS; QUANTUM SYSTEMS; SYMMETRY

### Citation Formats

```
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu.
```*Quantum chaos in nuclear physics*. United States: N. p., 2016.
Web. doi:10.1134/S1063778816040062.

```
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu.
```*Quantum chaos in nuclear physics*. United States. doi:10.1134/S1063778816040062.

```
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu. Fri .
"Quantum chaos in nuclear physics". United States.
doi:10.1134/S1063778816040062.
```

```
@article{osti_22612640,
```

title = {Quantum chaos in nuclear physics},

author = {Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu},

abstractNote = {A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.},

doi = {10.1134/S1063778816040062},

journal = {Physics of Atomic Nuclei},

number = 4,

volume = 79,

place = {United States},

year = {Fri Jul 15 00:00:00 EDT 2016},

month = {Fri Jul 15 00:00:00 EDT 2016}

}

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