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A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach

Karlström, Olov LU ; Emary, C.; Zedler, P.; Pedersen, Jonas LU ; Bergenfeldt, Christian LU ; Samuelsson, Peter LU ; Brandes, T. and Wacker, Andreas LU (2013) In Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00 46(6).
Abstract
We investigate the second-order von Neumann approach from a diagrammatic point of view and demonstrate its equivalence with the resonant tunneling approximation. The investigation of higher order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough comparison sheds light on the validity of all these self-consistent second-order approaches. We analyze the discrepancy between the noise... (More)
We investigate the second-order von Neumann approach from a diagrammatic point of view and demonstrate its equivalence with the resonant tunneling approximation. The investigation of higher order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough comparison sheds light on the validity of all these self-consistent second-order approaches. We analyze the discrepancy between the noise calculated by our method and the exact Levitov formula for a simple non-interacting quantum dot model. Furthermore, we study the noise of the canyon of current suppression in a two-level dot, a phenomenon that requires the inclusion of electron-electron interaction as well as higher order tunneling processes. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00
volume
46
issue
6
publisher
IOP Publishing
external identifiers
  • wos:000314221000009
  • scopus:84873171646
ISSN
1751-8113
DOI
10.1088/1751-8113/46/6/065301
language
English
LU publication?
yes
id
9e380fbe-6374-4345-b177-88c1e4d3d2b0 (old id 3590140)
alternative location
http://arxiv.org/abs/1206.1744
date added to LUP
2013-03-20 08:43:21
date last changed
2019-08-11 03:44:35
@article{9e380fbe-6374-4345-b177-88c1e4d3d2b0,
  abstract     = {We investigate the second-order von Neumann approach from a diagrammatic point of view and demonstrate its equivalence with the resonant tunneling approximation. The investigation of higher order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough comparison sheds light on the validity of all these self-consistent second-order approaches. We analyze the discrepancy between the noise calculated by our method and the exact Levitov formula for a simple non-interacting quantum dot model. Furthermore, we study the noise of the canyon of current suppression in a two-level dot, a phenomenon that requires the inclusion of electron-electron interaction as well as higher order tunneling processes.},
  articleno    = {065301},
  author       = {Karlström, Olov and Emary, C. and Zedler, P. and Pedersen, Jonas and Bergenfeldt, Christian and Samuelsson, Peter and Brandes, T. and Wacker, Andreas},
  issn         = {1751-8113},
  language     = {eng},
  number       = {6},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00},
  title        = {A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach},
  url          = {http://dx.doi.org/10.1088/1751-8113/46/6/065301},
  volume       = {46},
  year         = {2013},
}