We study the level spacing statistics $P(s)$ in many-body Fermi systems and determine a critical two-body interaction strength ${U}_{c}$ at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature ${T}_{\mathrm{ch}}$ above which quantum chaos and thermalization set in.We study the level spacing statistics $P(s)$ in many-body Fermi systems and determine a critical two-body interaction strength ${U}_{c}$ at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature ${T}_{\mathrm{ch}}$ above which quantum chaos and thermalization set in.

arXiv:cond-mat/9706040Physical Review LettersSep 8, 1997215 citations

Dynamical Chaos and Many-Body Quantum Systems

Pierre Gaspard

Springer eBooksJan 1, 199210 citations

Quantum chaos: an introduction via chains of spins-1/2

Aviva Gubin, Léa Ferreira dos Santos

We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels. This is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels. This is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.

Jun 28, 20110 citations

Quantum Chaos as Basis for Statistical Mechanics

N. G. van Kampen

NATO ASI series. Series B : PhysicsJan 1, 19857 citations

Many-Body Level Statistics of Single-Particle Quantum Chaos

Yunxiang Liao, Amit Vikram, Victor M. Galitski

We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model)-a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model)-a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

arXiv:2005.08991Physical Review LettersDec 18, 202072 citations

We study the level spacing statistics

P(s)

in many-body Fermi systems and determine a critical two-body interaction strength

{U}_{c}

at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature

{T}_{\mathrm{ch}}

above which quantum chaos and thermalization set in.