Thermal Reservoir coupled to External Field and Quantum Dissipation

In the framework of the Caldeira -Leggett model of dissipative quantum mechanics, we investigate the effects of the interaction of the thermal reservoir with an external field. In particular, we discuss how the interaction modifies the conservative dynamics of the central particle, and the mechanism of dissipation. We briefly comment on possible observable consequencies. PACS numbers: 05.30.-d, 05.40+j, 03.65.Db DFPD 92/TH/27 May 1992 Bitnet address: [email protected] Bitnet address: [email protected] 1 1.Introduction. By quantum dissipation we conventionally denote the problem of the quantum mechanics of a particle in contact with a dissipative environment. After pioneering work by Feynman and Vernon [1], an exactly solvable lagrangian was put forward by Ullersma [2] in the slightly different context of quantum brownian motion. Ullersma introduced a mechanical model for the thermal reservoir as a set of independent harmonic oscillators; he then showed that in the limit of an infinite number of oscillators and of continously distributed frequencies the dynamics of the particle is governed by the damped Langevin equation. Caldeira and Leggett [3] addressed the problem of the effect of dissipation on quantum tunnelling by applying the formalism of the effective action in the framework of the Feynman path integral quantization. In their analysis they considered systems subject to both dissipative and “true” external forces, thereby ruled in the quasiclassical region by the damped equation of motion Mq̈ + ηq̇ + dV dq = Fext(t). (1) They studied in detail the problem of the modification of tunnelling rates in the presence of dissipation and pioneered a new broad field of research, mesoscopic physics, where one is considering situations when both thermal and quantum fluctuations are important. For recent comprehensive reviews on quantum brownian motion, dissipative quantum tunnelling, and mesoscopic physics see references [4]-[7]. The problem of quantum brownian motion and the Ullersma -Caldeira -Leggett model of quantum dissipation have also been recently reformulated [8] in the framework of stochastic mechanics at finite temperature [9]. In this letter we address the question of how the coupling of an external field with the thermal reservoir affects the dynamics of a dissipative quantum system. 2.The model without field-reservoir coupling. We will handle the problem following the effective action approach of Caldeira and