Complexity of quantum states in the two-dimensional pairing model

J. R. Armstrong, S. Åberg, S. M. Reimann, V. G. Zelevinsky

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish (US)
Article number066204
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number6
DOIs
StatePublished - Dec 5 2012

Fingerprint

Quantum State
two dimensional models
Pairing
Quantum Chaos
Signature
signatures
Fermions
chaos
fermions
Random Matrix Theory
matrix theory
Correlator
correlators
Trap
regularity
Nucleus
Spacing
Correlation Function
regression analysis
eigenvectors

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 86, No. 6, 066204, 05.12.2012.

Research output: Contribution to journalArticle

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