TY - JOUR
T1 - Quantum chaos and thermalization in isolated systems of interacting particles
AU - Borgonovi, Fausto
AU - Izrailev, F. M.
AU - Izrailev, Felix
AU - Santos, L. F.
AU - Ferreira Dos Santos, Lea
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
SN - 0370-1573
VL - 626
SP - 1
EP - 58
JO - Physics Reports
JF - Physics Reports
ER -