Canonical quantization of the dissipative hofstadter model

초록

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 the oscillator operators so that the algebra of the string coordinate operators at the boundary becomes noncommutative. 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.

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