Influence of damping on quantum interference: An exactly soluble model

Decoherence at absolute zero

“…classical) limit for the environment. In the short time regime (γt ≪ 1) studied by Caldeira and Leggett [9] one finds that dephasing occurs over a time scale of the order of the time for spontaneous emission of one quantum of energy from the system to the environment at absolute zero.…”

“…This is a conceptually important point which sets the present work apart from most earlier attempts towards understanding the measurement aspect of quantum mechanics via environment induced decoherence. Unruh and Zurek [7], Paz, Habib and Zurek [8] and Caldeira and Leggett [9] have addressed similar questions in the past. However, the work of Unruh and Zurek [7] is based on an incorrect regularization procedure which is in conflict with the fluctuation-dissipation theorem.…”

Invitation to Quantum Dynamical Semigroups

“…One can easily find in the literature the models of dephasing based on the linear coupling to bosonic field which are essentially variations of the so-called Caldeira-Leggett model [45][46][47]. To explain this apparent contradiction with our "no-go theorem" consider the simplest version of the spin -boson model defined by the Hamiltonian (here H S ≡ 0)…”

“…For simplicity, we discuss first the case of Brownian motion in one-dimensional space. The most frequently used MME for this case is the so-called Caldeira-Leggett equation [47] of the form…”

“…The index j for A j can correspond both to different parts of the reservoir and to different time instants . The limit theorem (47) reflects the physical picture of influence from R on S which can be decomposed into a sum of many almost independent small contributions. Such case is usually called diffusive regime and due to quantum central limit theorem (47) is well described by the harmonic oscillators bath with a weak linear coupling in the interaction Hamiltonian…”