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 Theoretical
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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3590140
- author
- Karlström, Olov
LU
; Emary, C.
; Zedler, P.
; Pedersen, Jonas
LU
; Bergenfeldt, Christian
LU
; Samuelsson, Peter
LU
; Brandes, T.
and Wacker, Andreas
LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics A: Mathematical and Theoretical
- volume
- 46
- issue
- 6
- article number
- 065301
- 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
- 2016-04-01 13:49:46
- date last changed
- 2023-09-03 05:42:22
@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.}},
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 Theoretical}},
title = {{A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach}},
url = {{https://lup.lub.lu.se/search/files/3614226/3706268.pdf}},
doi = {{10.1088/1751-8113/46/6/065301}},
volume = {{46}},
year = {{2013}},
}