Fluctuation-dissipation theorem and quantum tunneling with dissipation

TL;DR

This paper uses the fluctuation-dissipation theorem to analyze quantum dissipative phenomena like tunneling, deriving key effects from fundamental principles without relying on specific models.

Contribution

It demonstrates that essential features of quantum dissipation and tunneling can be derived from general principles such as the fluctuation-dissipation theorem, unitarity, and causality, bypassing explicit model assumptions.

Findings

Quantum coherence is suppressed by Ohmic dissipation.

The fluctuation-dissipation theorem underpins quantum dissipative phenomena.

Connection established between quantum tunneling with dissipation and Anderson's orthogonality theorem.

Abstract

We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian. An interesting connection between quantum tunneling with Ohmic dissipation and the Anderson's orthogonality theorem is also noted.