Dissipative Hofstadter Model at the Magic Points and Critical Boundary Sine-Gordon Model

TL;DR

This paper explores the dissipative Hofstadter model at specific parameter points, establishing its equivalence to the critical boundary sine-Gordon model using boundary state formulation and fermion representation.

Contribution

It provides an exact boundary state construction for the model at magic points and demonstrates its equivalence to the boundary sine-Gordon model.

Findings

Exact boundary states constructed at magic points.

Equivalence established with boundary sine-Gordon model.

Framework connects quantum dissipative systems with string theory.

Abstract

The dissipative Hofstadter model describes quantum particles moving in two dimensions subject to a uniform magnetic field, a periodic potential and a dissipative force. We discuss the dissipative Hofstadter model in the framework of the boundary state formulation in string theory and construct exact boundary states for the model at the magic points by using the fermion representation. The dissipative Hofstadter model at magic points is shown to be equivalent to the critical boundary sine-Gordon model.