Journal Article

FZJ-2019-01048

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Duality for open fermion systems: Energy-dependent weak coupling and quantum master equations

Schulenborg, J. ; Splettstoesser, J. ; Wegewijs, M. R. (Corresponding author)FZJ*

2018
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/21510  doi:10.1103/PhysRevB.98.235405

Abstract: Open fermion systems with energy-independent bilinear coupling to a fermionic environment have been shown to obey a general duality relation [J. Schulenborg et al., Phys. Rev. B 93, 081411 (2016)] which allows for a drastic simplification of time-evolution calculations. In the weak-coupling limit, such a system can be associated with a unique dual physical system in which all energies are inverted, in particular the internal interaction. This paper generalizes this fermionic duality in two ways: we allow for weak coupling with arbitrary energy dependence and describe both occupations and coherences coupled by a quantum master equation for the density operator. We also show that whenever generalized detailed balance holds (Kolmogorov criterion), the stationary probabilities for the dual system can be expressed explicitly in terms of the stationary recurrence times of the original system, even at large bias. We illustrate the generalized duality by a detailed analysis of the rate equation for a quantum dot with strong onsite Coulomb repulsion, going beyond the commonly assumed wide-band limit. We present predictions for (i) the decay rates for transient charge and heat currents after a gate-voltage quench and (ii) the thermoelectric linear-response coefficients in the stationary limit. We show that even for pronouncedly energy-dependent coupling, all nontrivial parameter dependence in these problems is entirely captured by just two well-understood stationary variables, the average charge of the system and of the dual system. Remarkably, it is the latter that often dictates the most striking features of the measurable quantities (e.g., positions of resonances), underscoring the importance of the dual system for understanding the actual one.

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Contributing Institute(s):

1. Theoretische Nanoelektronik (PGI-2)
2. JARA-FIT (JARA-FIT)

Research Program(s):

1. 141 - Controlling Electron Charge-Based Phenomena (POF3-141) (POF3-141)

Appears in the scientific report 2018

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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