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Progress of Theoretical Physics Supplement

Quantum Langevin Dynamics of a Two State System Coupled to a Bosonic Bath. II : Complex Dynamics in Nonlinear Systems

Toshio Tsuzuki

Published Mar 28, 1990• 0 citations
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The quantum Langevin equation of a two-state system coupled to a bosonic bath is studied on the basis of the bare boson representation. We can realize the role of the reaction field more explicitly in this case than in the case of displaced boson representation studied in I. The characteristic frequency of variable which mediates the interaction between the slow variable of the two-state system and the bath is determined quantum-mechanically by the commutation relation whose non-commutability is governed by the reaction field.
It is pointed out that the simultaneous inclusion of the reaction field in addition to the direct field of the bath is essentially important to describe the dynamics of the two-state system coupled to a bosonic bath. This is formulated in the framework of the quantum Langevin equation where the direct field of the bath is treated as the quantum mechanical random force. We study in detail the quantum-mechanical and statistical-mechanical notions of the reaction field as well as the direct field in the Ohm-Drude case of the spectral intensity of the bath. It is shown that the non-interacting blip approximation of Leggett et al. is equivalent to the approximation of the complete neglect of the reaction field. We propose a fundamental equation of the quantum Langevin dynamics, accompanied by a brief discussion about the feature of the equation.