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Spin—Boson Systems

  • Luigi Accardi
  • Igor Volovich
  • Yun Gang Lu
Chapter

Abstract

The generalized rotating-wave approximation condition (4.10.2) is too restrictive. In the present chapter we begin to realize the second step of the program described in Sect. 4.9, i.e. we shall generalize the multiplicative Hamiltonian (4.8.1) by dropping this condition and allowing the system operators to be arbitrary [modulo the analytical condition (4.9.3)]. We shall see that this leads to a new phenomenon, namely: even if we start with a single scalar boson Fock field, in the limit we shall have not a single, but an infinity of independent quantum noises — one for each Bohr frequency [see (4.8.4) for this notion] of the system; this is the stochastic resonance principle. In this chapter the stochastic golden rule is applied to the investigation of the stochastic limit for the general spin—boson Hamiltonian, describing a discrete system coupled with a boson field. The spin—boson Hamiltonian is widely used in physics [4], in studying quantum computing [Vol99], in studying stochastic resonance(1) [AcKoVo97, Gam98, Gri98, ImYuOh99] , etc.

Keywords

Master Equation Stochastic Resonance Langevin Equation Markov Semigroup Free Evolution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Luigi Accardi
    • 1
  • Igor Volovich
    • 2
  • Yun Gang Lu
    • 3
  1. 1.Centro Vito Volterra, Facolta di EconomiaUniversità di RomaRomaItaly
  2. 2.Steklov Mathematical InstituteMoscow, GSP-1Russia
  3. 3.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly

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