Hilbert space decomposition for Coulomb blockade in Fabry--Pérot interferometers

Details Hilbert space decomposition for Coulomb blockade in Fabry--Pérot interferometers Hilbert space decomposition for Coulomb blockade in Fabry--Pérot interferometers

2011-12-27

arxiv.org/abs/1112.5946v1

Physics

Mathematical Physics

11 pages, 2 figures, Proceedings of the 9-th International Workshop "Lie Theory and Its Applications in Physics" (LT-9), 20-26

Scientific paper

We show how to construct the thermodynamic grand potential of a droplet of incompressible fractional quantum Hall liquid, formed inside of an electronic Fabry--P\'erot interferometer, in terms of the conformal field theory disk partition function for the edge states in presence of Aharonov-Bohm flux. To this end we analyze in detail the algebraic structure of the edge states' Hilbert space and identify the effect of the variation of the flux. This allows us to compute, in the linear response approximation, all thermodynamic properties of the conductance in the regime when the Coulomb blockade is softly lifted by the change of the magnetic flux due to the weak coupling between the droplet and the two quantum point contacts.

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