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Junctions of three quantum wires and the dissipative Hofstadter model

Claudio Chamon·Masaki Oshikawa·Ian Affleck
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Abstract

We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a non-trivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find non-trivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.

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Claudio Chamon, Masaki Oshikawa, Ian Affleck. 2003-05-07. Junctions of three quantum wires and the dissipative Hofstadter model. https://doi.org/10.1103/physrevlett.91.206403

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