Two-dimensional tunnel correlations with dissipation

TL;DR

This paper investigates two-dimensional quantum tunneling of particles under dissipation, identifying bifurcation phenomena, critical temperature effects, and the influence of heat bath modes, with implications for experimental observations in molecular systems.

Contribution

It introduces a theoretical framework for understanding bifurcations and phase transition-like behavior in dissipative two-particle tunneling, explaining experimental quantum fluctuation data.

Findings

Critical temperature T_c marks bifurcation of tunneling trajectories.

Heat bath local modes significantly affect tunneling probabilities.

Parallel and antiparallel tunneling exhibit different phase transition behaviors.

Abstract

Tunneling of two particles in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. The critical temperature T_c corresponding to a bifurcation of the underbarrier trajectory is determined. The effect of a heat bath local mode on the probability of two-dimensional tunneling transfer is also investigated. At certain values of the parameters, the degeneracy of antiparallel tunneling trajectories is important. Thus, four, six, twelve, etc., pairs of the trajectories should be taken into account (a cascade of bifurcations). For the parallel particle tunneling the bifurcation resembles phase transition of a first kind, while for the antiparallel transfer it behaves as second order phase transition. The proposed theory allows for the explanation of experimental data on quantum fluctuations in two-proton tunneling in porphyrins near the critical temperature.