Tunneling with the Lorentz Force and the Friction

TL;DR

This paper investigates how magnetic fields and dissipation influence quantum tunneling, revealing effects like suppression, enhancement, and spectral function mapping, with implications for experimental systems such as Hall bar edge states.

Contribution

It introduces a semiclassical framework that maps tunneling with magnetic fields and dissipation onto an effective one-dimensional problem, uncovering dual symmetries and novel effects.

Findings

Magnetic fields can suppress or enhance tunneling rates.

The spectral function can be mapped between different regimes via magnetic field variation.

Explicit expressions for tunneling rates at finite temperatures are provided.

Abstract

We present a semiclassical study of a transport process, the tunneling, in the presence of a magnetic field and a dissipative environment. We have found that the problem can be mapped onto an effective one-dimensional one, and the tunneling rate is strongly affected by the magnetic field, such as a complete suppression by a large parallel magnetic field, an example of the dynamical localization. In such case a small perpendicular component of the field, or the dissipation, can enhance the tunneling rate. In the small parallel field and finite temperatures the tunneling rate is finite. Explicit expressions will be presented in those cases. If viewing the tunneling in the presence of a magnetic field as a dissipative tunneling process, by varying the magnetic field and the potential one can obtain the dissipative spectral function between the subohmic $s =0$ and the superohmic $s = \infty$. In combination with a real dissipative spectral function, the effect of the magnetic field can map the spectral function from $s $ to $2-s$, with $s>2$ mapping to $ s = 0$, revealing a dual symmetry between the friction and the Lorentz force. Two cases relevant to experiments, the edge state tunneling in a Hall bar and the tunneling near the dynamical localization will be discussed in detail.