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JETP Letters

, Volume 92, Issue 6, pp 370–374 | Cite as

Dynamic and spectral mixing in nanosystems

  • V. A. Benderskii
  • E. I. Kats
Article

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

Keywords

JETP Letter Reservoir State Reservoir Level Triplet Structure Spin Boson 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • V. A. Benderskii
    • 1
  • E. I. Kats
    • 2
    • 3
  1. 1.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Laue-Langevin InstituteGrenobleFrance
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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