Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states

TL;DR

This paper introduces a Green's function formalism using semicoherent vortex states to unify the understanding of quantization and lifetime effects in high magnetic field electron dynamics within arbitrary potentials.

Contribution

The authors develop an exact Green's function approach for quadratic potentials at high magnetic fields, revealing a unified treatment of quantization and lifetime effects through vortex states.

Findings

Unified description of confining and saddle potentials.

Quantization effects linked to confining potentials.

Lifetime effects arise from quantum tunneling at saddle points.

Abstract

We have developed a Green's function formalism based on the use of an overcomplete semicoherent basis of vortex states, specially devoted to the study of the Hamiltonian quantum dynamics of electrons at high magnetic fields and in an arbitrary potential landscape smooth on the scale of the magnetic length. This formalism is used here to derive the exact Green's function for an arbitrary quadratic potential in the special limit where Landau level mixing becomes negligible. This solution remarkably embraces under a unified form the cases of confining and unconfining quadratic potentials. This property results from the fact that the overcomplete vortex representation provides a more general type of spectral decomposition of the Hamiltonian operator than usually considered. Whereas confining potentials are naturally characterized by quantization effects, lifetime effects emerge instead in the case of saddle-point potentials. Our derivation proves that the appearance of lifetimes has for origin the instability of the dynamics due to quantum tunneling at saddle points of the potential landscape. In fact, the overcompleteness of the vortex representation reveals an intrinsic microscopic irreversibility of the states synonymous with a spontaneous breaking of the time symmetry exhibited by the Hamiltonian dynamics.