Statistical theory of finite Fermi systems based on the structure of chaotic eigenstates

Flambaum, V. V.; Izrailev, F. M.

doi:10.1103/physreve.56.5144

Cited by 189 publications

(304 citation statements)

References 21 publications

Supporting

Mentioning

289

Contrasting

Order By: Relevance

“…nor small like 1/n!. The appearance of logarithms in the coefficients of wave function was also observed in [19]. Like in Eq.…”

Section: High Order Effective Interactionsupporting

confidence: 53%

Chaos thresholds in finite Fermi systems

Silvestrov

1998

Phys. Rev. E

View full text Add to dashboard Cite

The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple Slaterdeterminant states. Nevertheless, the transition from Poisson to Wigner-Dyson statistics of energy levels is governed by the effective high order interaction between states very distant in the Fock space. The concrete form of the transition depends on the way one chooses to work out the problem of factorial divergency of the number of Feynman diagrams. In the proposed scheme the change of statistics has a form of narrow phase transition and may happen even below the direct interaction threshold.

show abstract

“…nor small like 1/n!. The appearance of logarithms in the coefficients of wave function was also observed in [19]. Like in Eq.…”

Section: High Order Effective Interactionsupporting

confidence: 53%

Chaos thresholds in finite Fermi systems

Silvestrov

1998

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…This equilibrium enables one to develop a statistical theory for finite few-particle quantum systems with strong interaction between the particles [14,15]. This theory should allow one to introduce temperature, entropy, etc., and calculate various properties of the system, e.g., the occupation numbers, or the rms values of matrix elements of an external perturbation between the chaotic many-body states.…”

Section: Equilibrium Brought By the Interaction Between Particlesmentioning

confidence: 99%

“…The properties of the chaotic eigenstates can be used to develop a statistical theory of finite few-particle quantum systems [13][14][15]. The specific equilibrium that emerges in the system due to the residual twobody interaction enables one to introduce thermodynamic temperature-based description in the isolated few-body system [9,16] and use it, e.g., to calculate average occupation numbers of the single-particle states.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos in many-body systems: what can we learn from the Ce atom?

Flambaum

Gribakina

Gribakin

et al. 1999

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Results of an extensive study of a real quantum chaotic many-body system -the Ce atom -are presented. We discuss the origins of the quantum chaotic behaviour of the system, analyse statistical and dynamical properties of the multi-particle chaotic eigenstates and consider matrix elements or transition amplitudes between them. We show that based on the universal properties of the chaotic eigenstates a statistical theory of finite few-particle systems with strong interaction can be developed. We also discuss such important physical effects as enhancement of weak perturbations in many-body quantum chaotic systems, distribution of single-particle occupation numbers and its deviations from the standard Fermi-Dirac shape, and ways of introducing statistical temperature-based description in such systems.

show abstract

“…This was understood in application to nuclear reactions from the early times of nuclear physics [16,29,30]. The detailed analysis of atomic [31,32] and nuclear [6,33] chaotic states supported an old idea [34] of thermalization in a closed system driven by the interactions between the constituents, with no heat bath: the average over a generic chaotic wave function in a chaotic region is equivalent to the average over a standard equilibrium thermal ensemble [35]. Currently this idea, sometimes called the "eigenfunction thermalization hypothesis", is extensively discussed in the many-body physics community [36].…”

Section: Introductionmentioning

confidence: 99%

Nuclear level density: Shell-model approach

Sen'kov

Zelevinsky

2016

Phys. Rev. C

View full text Add to dashboard Cite

The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally used parameters are also compared with standard phenomenological approaches.

show abstract

Statistical theory of finite Fermi systems based on the structure of chaotic eigenstates

Cited by 189 publications

References 21 publications

Chaos thresholds in finite Fermi systems

Chaos thresholds in finite Fermi systems

Quantum chaos in many-body systems: what can we learn from the Ce atom?

Nuclear level density: Shell-model approach

Contact Info

Product

Resources

About