INVARIANT CORRELATIONAL ENTROPY AND COMPLEXITY OF QUANTUM STATES

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.