Decoherence and thermalization in a simple bosonic system.

Properties of a parameter-dependent quantum system with the Hamiltonian H(lambda) randomized by fluctuations of the parameter lambda in a narrow range are investigated. The model employed (the interacting boson model-1) exhibits a crossover behavior at a critical parameter value. Due to the fluctuations, individual eigenstates /psi(alpha)(lambda)> of the Hamiltonian become statistical ensembles of states [density matrices rho(alpha)(lambda)], which allows us to study effects related to the decoherence and thermalization. In the decoherence part, we evaluate von Neumann and information entropies of the density matrices rho(alpha)(lambda) and the overlaps of the eigenstates of the density matrix with various physically relevant bases. An increased decoherence at the " phase transitional" point and an exceptional role of the dynamic-symmetry U(5) basis are discovered. In the part devoted to the thermalization, we develop a method of how a given density matrix rho(alpha)(lambda) can be represented by an equivalent canonical (thermal) ensemble. Thermodynamic consequences of the quantum "phase transition" (related, in particular, to the specific heat of the thermal equivalent) are discussed.