### Abstract

It is known that many-fermion systems, such as complex atoms and nuclei, reveal (at some level of excitation energy) local signatures of quantum chaos similar to the predictions of random matrix theory. Here, we study the gradual development of such signatures in a model system of up to 16 fermions interacting through short-range pairing-type forces in a two-dimensional harmonic trap. We proceed from the simplest characteristics of the level spacing distribution to the complexity of eigenstates, strength, and correlation functions. For increasing pairing strength, at first, chaotic signatures gradually appear. However, when the pairing force dominates the Hamiltonian, we see a regression towards regularity. We introduce a "phase correlator" that allows us to distinguish the complexity of a quantum state that originates from its collective nature, from the complexity originating from quantum chaos.

Original language | English (US) |
---|---|

Article number | 066204 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 86 |

Issue number | 6 |

DOIs | |

State | Published - Dec 5 2012 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*86*(6), [066204]. https://doi.org/10.1103/PhysRevE.86.066204

**Complexity of quantum states in the two-dimensional pairing model.** / Armstrong, J. R.; Åberg, S.; Reimann, S. M.; Zelevinsky, V. G.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 86, no. 6, 066204. https://doi.org/10.1103/PhysRevE.86.066204

}

TY - JOUR

T1 - Complexity of quantum states in the two-dimensional pairing model

AU - Armstrong, J. R.

AU - Åberg, S.

AU - Reimann, S. M.

AU - Zelevinsky, V. G.

PY - 2012/12/5

Y1 - 2012/12/5

N2 - It is known that many-fermion systems, such as complex atoms and nuclei, reveal (at some level of excitation energy) local signatures of quantum chaos similar to the predictions of random matrix theory. Here, we study the gradual development of such signatures in a model system of up to 16 fermions interacting through short-range pairing-type forces in a two-dimensional harmonic trap. We proceed from the simplest characteristics of the level spacing distribution to the complexity of eigenstates, strength, and correlation functions. For increasing pairing strength, at first, chaotic signatures gradually appear. However, when the pairing force dominates the Hamiltonian, we see a regression towards regularity. We introduce a "phase correlator" that allows us to distinguish the complexity of a quantum state that originates from its collective nature, from the complexity originating from quantum chaos.

AB - It is known that many-fermion systems, such as complex atoms and nuclei, reveal (at some level of excitation energy) local signatures of quantum chaos similar to the predictions of random matrix theory. Here, we study the gradual development of such signatures in a model system of up to 16 fermions interacting through short-range pairing-type forces in a two-dimensional harmonic trap. We proceed from the simplest characteristics of the level spacing distribution to the complexity of eigenstates, strength, and correlation functions. For increasing pairing strength, at first, chaotic signatures gradually appear. However, when the pairing force dominates the Hamiltonian, we see a regression towards regularity. We introduce a "phase correlator" that allows us to distinguish the complexity of a quantum state that originates from its collective nature, from the complexity originating from quantum chaos.

UR - http://www.scopus.com/inward/record.url?scp=84871427763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871427763&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.86.066204

DO - 10.1103/PhysRevE.86.066204

M3 - Article

C2 - 23368021

AN - SCOPUS:84871427763

VL - 86

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 6

M1 - 066204

ER -