Canonical Quantization of The Dissipative Hofstadter Model

TL;DR

This paper performs canonical quantization of the dissipative Hofstadter model, exploring its dualities and non-commutative structures, and develops a boundary state formulation relevant to condensed matter and string theory.

Contribution

It introduces a novel canonical quantization approach for the dissipative Hofstadter model, linking target space duality with non-commutative algebra and boundary state formulation.

Findings

Target space duality removes magnetic field interaction.

Dual transformation induces non-commutative algebra at the boundary.

Boundary state formulation for the model is developed.

Abstract

We perform canonical quantization of the dissipative Hofstadter model, which has a wide range of applications in condensed matter physics and string theory. The target space duality and the non-commutative algebra developed in string theory are discussed for the model. We show that the target space duality transformation of closed string theory, $O(2,2;R)$, removes the interaction with a uniform magnetic field. The $O(2,2;R)$ dual transformation changes the basis of oscillator operators so that the algebra of the string coordinate operators at the boundary become non-commutative. In the zero temperature limit, the non-commutative algebra of open string theory emerges. We also developed the boundary state formulation for the dissipative Hofstadter model.