Decoherence and thermalization in a simple bosonic system

Properties of a parameter-dependent quantum system with the Hamiltonian (H) over cap(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>)over cap>(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>)over cap>(alpha)(lambda) and the overlaps of the eigenstates of the density matrix with various physically relevant bases. An increased decoherence at the r 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>)over cap>(alpha)(lambda) can be represented by on equivalent canonical (thermal) ensemble. Thermodynamic consequences of the quantum "phase transition" (related, in particular, to the specific heat of the thermal equivalent) are discussed.