Dynamic and spectral mixing in nanosystems |
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Authors: | V A Benderskii and E I Kats |
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Institution: | 1.Institute of Problems of Chemical Physics,Russian Academy of Sciences,Chernogolovka, Moscow region,Russia;2.Laue-Langevin Institute,Grenoble,France;3.Landau Institute for Theoretical Physics,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | In the framework of a simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like
behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir
states are formed by three sequences with rationally independent periodicities 1; 1 ± δ typical for vibrational states in
many nanosize systems (e.g., large molecules containing CH2 fragment chains, or carbon nanotubes). We show that quantum evolution of the system is determined by a dimensionless parameter
δΓ, where Γ is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. When δΓ
> 1 spectral chaos destroys recurrence cycles and the system state evolution is stochastic-like. In the opposite limit δΓ
< 1 dynamics is regular up to the critical recurrence cycle k
c
and for larger k > k
c
dynamic mixing leads to quasi-stochastic time evolution. Our semi-quantitative analytic results are confirmed by numerical
solution of the equation of motion. We anticipate that both kinds of stochastic-like behavior (namely, due to spectral mixing
and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems in the spectral window
1011–1013 s−1 |
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Keywords: | |
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