Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices

Abstract

We have recently calculated exact non-equilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact $I(V)$ characteristic and conductance out of equilibrium as a function of driving voltage $V$ and temperature $T$. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and $V/T$. The differential-conductance curve as a function of the interaction strength broadens significantly as $V/T$ is increased, and develops a pronounced maximum at a (universal) critical value $(eV/k_{B}T)=\mathrm{7.18868...}$. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.

38 pages (22 in little format); uses harvmac macros. Two uuencoded figures are appended. Revised version corrects many typos

References in corpus (8)

• Exact Conductance through Point Contacts in the $\nu =1/3$ Fractional Quantum Hall Effect
• Exact solution of a massless scalar field with a relevant boundary interaction
• Free Fermion Representation of a Boundary Conformal Field Theory
• The Fermi Edge Singularity and Boundary Condition Changing Operators
• Solving 1d plasmas and 2d boundary problems using Jack polynomials and functional relations
• Luttinger States at the Edge
• Asymptotic tunneling conductance in Luttinger liquids
• Low-temperature nonequilibrium transport in a Luttinger liquid

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