Dissipation can enhance quantum effects

TL;DR

This paper demonstrates that momentum dissipation can enhance quantum effects such as tunneling and fluctuations, contrary to the typical classicalizing influence of dissipation.

Contribution

It introduces a model of momentum coupling to a heat bath and shows how this form of dissipation increases quantum fluctuations and tunneling rates.

Findings

Momentum coupling increases position fluctuations at low temperatures.

It raises the barrier frequency, enhancing quantum tunneling.

Quantum effects become significant at higher temperatures with momentum dissipation.

Abstract

Usually one finds that dissipation tends to make a quantum system more classical in nature. In this paper we study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bilinearly to the momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we find that the position and momentum variances for momentum coupling are respectively identical to momentum and position variances for spatial friction. This implies that momentum coupling leads to an increase in the fluctuations in position as the temperature is lowered, exactly the opposite of the classical like localization of the oscillator, found with spatial friction. For a parabolic barrier, momentum coupling causes an {\it increase} in the unstable normal mode barrier frequency, as compared to the lowering of the barrier frequency in the presence of purely spatial coupling. This increase in the frequency leads to an enhancement of the thermal tunneling flux, which below the crossover temperature becomes exponentially large. The crossover temperature between tunneling and thermal activation {\it increases} with momentum friction so that quantum effects in the escape are relevant at higher temperatures.