Operator differential equation approach to the dissipative two-state system

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We consider a two-state system linearly coupled to a collection of harmonic oscillators, the spin-boson Hamiltonian. Expanding the density matrix in terms of Pauli spin matrices, a set of coupled operator differential equations of motion is obtained by solving the Heisenberg equation. Using the cumulant expansion methods, the expectation values of the Pauli spin matrices are obtained and found to be valid for both coherent and incoherent regimes. The results are compared with other approaches.

Original languageEnglish
Pages (from-to)593-605
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Issue number3-4
Publication statusPublished - 1997 Jul 15


  • Population inversion
  • Spin-boson Hamiltonian
  • Two-state system

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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