  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.
