Abstract
In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional is exactly the effective action of Caldeira-Leggett model but, in our approach, it is derived without the assumption that the particle is weakly coupled to a bath of infinite harmonic oscillators.
Highlights
The number of different systems and physical variables displaying damped dynamics is vast
Integrating out the degrees of freedom of the harmonic oscillators, they found an effective action for the particle with dissipation and they used it to calculate the effect of the damping coefficient on the quantum tunneling rate of the particle [14,15,16]
We show that the Caldeira-Leggett effective action can be obtained, without the assumption of an environmental bath, directly from the dissipative equation of motion through a modification which makes the new dissipative equation of motion invariant for time reversal symmetry
Summary
The number of different systems and physical variables displaying damped dynamics is vast. Integrating out the degrees of freedom of the harmonic oscillators, they found an effective action for the particle with dissipation and they used it to calculate the effect of the damping coefficient on the quantum tunneling rate of the particle [14,15,16] This framework started a deep theoretical effort devoted to understand quantum dynamics in a dissipative environment with its related features such as the localization transition [17] and the diffusion in periodic potential [18,19,20].
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