Smits, O. and Slingerland, Joost and Simon, S.H.
(2014)
Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect.
Working Paper.
arXiv.
Abstract
We analyse the noise of the edge current of a generic fractional quantum Hall state in a tunnelling
point contact system. We show that the non-symmetrized noise in the edge current for the system
out-of-equilibrium is completely determined by the noise in the tunnelling current and the Nyquist-
Johnson (equilibrium) noise of the edge current. Simply put, the noise in the tunnelling current does
not simply add up the equilibrium noise of the edge current. A correction term arises associated
with the correlation between the tunnelling current and the edge current. We show, using a nonequilibrium
Ward identity, that this correction term is determined by the anti-symmetric part of
the noise in the tunnelling current. This leads to a non-equilibrium fluctuation-dissipation theorem
and related expressions for the excess and shot noise of the noise in the edge current. Our approach
makes use of simple properties of the edge, such as charge conservation and chirality, and applies
to generic constructions of the edge theory which includes edges of non-Abelian states and edges
with multiple charged channels. Two important tools we make use of are the non-equilibrium Kubo
formula and the non-equilibrium Ward identity. We discuss these identities in the appendix.
| Item Type: |
Monograph
(Working Paper)
|
| Keywords: |
Non-equilibrium noise; (non-)Abelian; fractional quantum Hall effect; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematical Physics |
| Item ID: |
6308 |
| Identification Number: |
arXiv:1401.4581 |
| Depositing User: |
Dr. Joost Slingerland
|
| Date Deposited: |
20 Aug 2015 12:12 |
| Publisher: |
arXiv |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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