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@PHDTHESIS{Eissing:686159,
author = {Eissing, Katharina},
othercontributors = {Meden, Volker and Schoeller, Herbert},
title = {{F}unctional renormalization group in {F}loquet space
applied to periodically driven quantum dots},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2017-02670},
pages = {1 Online-Ressource (vii, 131 Seiten) : Illustrationen,
Diagramme},
year = {2017},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2017},
abstract = {The main goal of the present thesis is to set up a
functional renormalization group formalism in Floquet space
to treat interacting, time periodic quantum dots and to
investigate the consequential renormalization of the
parameters and the transport through the dot. Building upon
the time independent, steady state description in frequency
space (Karrasch 2010, Jakobs 2009) and a time dependent FRG
formulation (Kennes 2014), we tackle the steady state of
periodically driven quantum dots. We focus on the long time
behavior where all transients have died out, and therefore
the entire system is characterized by the same periodicity
as given by the driven external fields. As a consequence, we
can transform the according time dependent flow equation to
Floquet space using Floquet-Green’s functions. It allows
us to study quantum dot systems in the whole range of
driving frequency and amplitude in the presence of a small
Coulomb interaction. We exemplify the potential of our
approach by applying it to the interacting resonant level
model (IRLM), describing an idealized single level quantum
dot dominated only by charge fluctuations.We investigate the
role of the driving frequency Ω in the RG flows of the time
periodic parameters of the IRLM. The small driving amplitude
limit allows to complement our numerical solution by
analytic expressions of the renormalization of all dot
parameters to the leading order of driving amplitude over
mean value. Four different configurations are studied, where
distinct combinations of the hopping and/or onsite energy of
the dot are chosen to be time periodic. The transparent
structure of the renormalization of the parameters in this
limit, allows for an analytic treatment of all higher
harmonics, where the various protocols reveal very different
RG flows. Even beyond the small driving amplitude limit the
RG flow is discussed with the help of an effective reservoir
distribution function which can be defined in this setup and
its form is defined by the ratio of driving amplitude and
frequency (Suzuki 2015). The second focus is directed to the
transport in the time periodic quantum dot systems and how
it is affected by the Coulomb interaction. Based on the well
studied parameter pump in the adiabatic limit (Brouwer
1998), where two parameters are varied periodically and
phase shifted, we like to investigate the pumped charge in
the whole regime of driving frequency and amplitude
including interaction in such a setup. Further a single
parameter pump is realized and the charge susceptibility as
well as the mean current are studied. The latter reveals
power law behavior on the driving frequency. A quantum
master equation calculation in Floquet-Liouville space
complements the FRG results to study the requirements of
such a single parameter quantum pump. Finally, the
conductance and the current are considered for several time
periodic hoppings of non-sinusoidal form.},
cin = {135820 / 130000},
ddc = {530},
cid = {$I:(DE-82)135820_20140620$ / $I:(DE-82)130000_20140620$},
typ = {PUB:(DE-HGF)11},
urn = {urn:nbn:de:hbz:82-rwth-2017-026701},
doi = {10.18154/RWTH-2017-02670},
url = {https://publications.rwth-aachen.de/record/686159},
}
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