Phase Diagram of the Dissipative Hofstadter Model

TL;DR

This paper explores the phase diagram of a dissipative quantum system with a magnetic field and periodic potential, revealing a fractal structure that connects to the Hofstadter model in the zero dissipation limit.

Contribution

It provides a detailed analysis of the phase diagram of the dissipative Hofstadter model, uncovering a fractal structure linking dissipation effects to quantum energy levels.

Findings

Identified a fractal phase structure in the dissipative Hofstadter model.

Showed the phase diagram converges to the Hofstadter energy spectrum as dissipation approaches zero.

Mapped critical points for delocalization in the system.

Abstract

The dissipative quantum mechanics of a charged particle in a uniform magnetic field and periodic potential has delocalization critical points which correspond to backgrounds for the open string. We study the phase diagram of this system (in the magnetic field/dissipation constant plane) and find a fractal structure which, in the limit of zero dissipation, matches the fractal energy level structure of the pure quantum mechanical version of this problem (Hofstadter model).