TY - JOUR

T1 - Quantum chaos and thermalization in isolated systems of interacting particles

AU - Borgonovi, Fausto

AU - Izrailev, Felix

AU - Ferreira Dos Santos, Lea

AU - Izrailev, F. M.

AU - Santos, L. F.

AU - Zelevinsky, V. G.

PY - 2016

Y1 - 2016

N2 - This review is devoted to the problem of thermalization in a small isolated conglomerate
of interacting constituents. A variety of physically important systems of intensive
current interest belong to this category: complex atoms, molecules (including biological
molecules), nuclei, small devices of condensed matter and quantum optics on nano-
and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of
quantum computers, where there are many interacting qubits, also fall into this group.
Statistical regularities come into play through inter-particle interactions, which have two
fundamental components: mean field, that along with external conditions, forms the
regular component of the dynamics, and residual interactions responsible for the complex
structure of the actual stationary states. At sufficiently high level density, the stationary
states become exceedingly complicated superpositions of simple quasiparticle excitations.
At this stage, regularities typical of quantum chaos emerge and bring in signatures of
thermalization. We describe all the stages and the results of the processes leading to
thermalization, using analytical and massive numerical examples for realistic atomic,
nuclear, and spin systems, as well as for models with random parameters. The structure
of stationary states, strength functions of simple configurations, and concepts of entropy
and temperature in application to isolated mesoscopic systems are discussed in detail. We
conclude with a schematic discussion of the time evolution of such systems to equilibrium.

AB - This review is devoted to the problem of thermalization in a small isolated conglomerate
of interacting constituents. A variety of physically important systems of intensive
current interest belong to this category: complex atoms, molecules (including biological
molecules), nuclei, small devices of condensed matter and quantum optics on nano-
and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of
quantum computers, where there are many interacting qubits, also fall into this group.
Statistical regularities come into play through inter-particle interactions, which have two
fundamental components: mean field, that along with external conditions, forms the
regular component of the dynamics, and residual interactions responsible for the complex
structure of the actual stationary states. At sufficiently high level density, the stationary
states become exceedingly complicated superpositions of simple quasiparticle excitations.
At this stage, regularities typical of quantum chaos emerge and bring in signatures of
thermalization. We describe all the stages and the results of the processes leading to
thermalization, using analytical and massive numerical examples for realistic atomic,
nuclear, and spin systems, as well as for models with random parameters. The structure
of stationary states, strength functions of simple configurations, and concepts of entropy
and temperature in application to isolated mesoscopic systems are discussed in detail. We
conclude with a schematic discussion of the time evolution of such systems to equilibrium.

KW - quantum chaos

KW - statistical mechanics

KW - thermalization in isolated systems

KW - quantum chaos

KW - statistical mechanics

KW - thermalization in isolated systems

UR - http://hdl.handle.net/10807/76537

U2 - 10.1016/j.physrep.2016.02.005

DO - 10.1016/j.physrep.2016.02.005

M3 - Article

VL - 626

SP - 1

EP - 58

JO - Physics Reports

JF - Physics Reports

SN - 0370-1573

ER -