Double resonances in the dynamics of quantum systems with a dense discrete spectrum
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AL, NONLINEAR, AND SOFT MATTER PHYSICS
Double Resonances in the Dynamics of Quantum Systems with a Dense Discrete Spectrum V. A. Benderskiia,*, L. N. Gaka, and E. I. Katsb,c,** a
Institute of Problems of Chemical Physics, Russian Academy of Sciences, pr. Akademika Semenova 1, Chernogolovka, Moscow oblast, 142432 Russia * email: [email protected] b Landau Institute for Theoretical Physics, Russian Academy of Sciences, pr. Akademika Semenova 1a, Chernogolovka, Moscow oblast, 142432 Russia c Institut Laue–Langevin, Grenoble, Cedex 9, 38000 France ** email: [email protected] Received March 31, 2009
Abstract—The quantum dynamics of a simple model of a nanoparticle has been investigated. This model suggests that the initially prepared state (system) interacts with the other states (reservoir) forming a dense discrete spectrum. In contrast to our previous papers concerned with this problem [1, 2], in which only the dynamics of the system has been studied, the present paper is devoted to the description of the evolution of reservoir states. In the initial recurrence cycles, the reverse transitions from the reservoir to the system gener ate a double resonance (an echo at frequencies of the reservoir states transitions). Since different states of the reservoir are depleted at different instants of time, the Loschmidt echo in the system is inhomogeneously broadened, whereas the double resonances remain narrower and more intense. Apart from the main reso nances, there arise satellites due to the redistribution of the populations between the reservoir states during the cycle. In mixing cycles regime, the regular evolution of the reservoir states (like the system state) trans forms into a stochasticlike evolution. It is noted that the predicted double resonances can be experimentally detected and used in analyzing vibrational relaxation of large molecules and nanoparticles. PACS numbers: 03.65w, 82.20.w, 82.20.Bc DOI: 10.1134/S1063776109090167
1. INTRODUCTION In our recent papers [1, 2], we proposed a method for investigating the evolution of mesoscopic vibra tional systems (i.e., systems with a large but finite number of degrees of freedom that have a dense dis crete spectrum of normal vibrations). The method involves (1) the expansion of nonstationary wave func tions in the basis set of eigenfunctions of a decoupled degree of freedom (system) and the other degrees of freedom (reservoir), (2) the solution to the Heisenberg equations for timedependent amplitudes in the form of trigonometric series in eigenfrequencies, and (3) the representation of the solutions in the form of sums of partial amplitudes of recurrence cycles. In [1, 2], this method was applied to analyzing, most likely, the simplest model among the possible mesoscopic mod els, which was proposed by Zwanzig [3]. The model suggests that the reservoir has an infinite equidistant spectrum and that the coupling matrix elements of the system and all reservoir states are identical. The specific feature revealed in [1, 2] for the sys tems with dense discrete spe
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