Vv. Sokolov et al., INVARIANT CORRELATIONAL ENTROPY AND COMPLEXITY OF QUANTUM STATES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(1), 1998, pp. 56-68
We define correlational (von Neumann) entropy for an individual quantu
m stale of a system whose time-independent Hamiltonian contains random
parameters and is treated as a member of a statistical ensemble. This
entropy is representation independent, and can be calculated as a tra
ce functional of the density matrix which describes the system in its
interaction with the noise source. We analyze perturbation theory in o
rder to show the evolution from the pure state to the mixed one. Exact
ly solvable examples illustrate the use of correlational entropy as a
measure of the degree of complexity in comparison with other available
suggestions such as basis-dependent information entropy. It is shown
in particular that a harmonic oscillator in a uniform field of random
strength comes to a quasithermal equilibrium; we discuss the relation
between effective temperature and canonical equilibrium temperature. T
he notion of correlational entropy is applied to a realistic numerical
calculation in the framework of the nuclear shell model. in this syst
em, which reveals generic signatures of quantum chaos, correlational e
ntropy and information entropy calculated in the mean field basis disp
lay similar qualitative behavior.