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# Project A2: Linking electron and photon statistics in dissipative mesoscopic structures.

The goal of this project is
to develop a theory for FCS and its coupling to light

emission
within the equation-of-motion method (EoM) of the density matrix

formalism for current driven quantum dots. By doing so, we expect to
be able

to calculate quantum light statistics and FCS within a
formalism that is

complementary to usual approaches, i.e.
Born-Markov Master equations (ME)

or non-equilibrium Green
functions.

In practice, the EoM hierarchy is terminated by using
a factorisation (decoupling)

procedure, leading to a closed set
of non-linear equations, such as the equation

for the
*average* photon density, or higher order photon correlations.
Here, the

nonlinearity results from Pauli-blocking,
Coulomb-blockade, multiple electron-phonon

scattering and
further many-particle interactions. This will be extended by either

time-dependent boundary conditions such as fluctuating couplings
to electronic

reservoirs, or by introducing time-dependent
counting fields that describe single

charge/photon events right
at the level of the microscopic equations and that lead to

(cumulant) generating functions for the photon
*distribution*. For the stationary case

(e.g., in biased
quantum dots), this has to coincide with the corresponding ME result

in lowest order dot-lead coupling. The general case requires
higher order numerical

derivatives with respect to the counting
fields, which can turn out to be a delicate task,

as the EoM
method usually amounts to solving huge sets of coupled differential
equations.

The reward will be a systematic theory of the
combined electron-hole-photon statistics

within a
non-perturbative approach that allows one to describe non-Markovian
effects in

phonon-induced dissipation (in principle up to very
high orders) which is important in order

to realistically
describe non-equilibrium heating effects in the environment and
dephasing

of the electronic coherence.**Project leaders: Prof.Dr. T. Brandes [1], Prof.Dr.
A. Knorr [2]**

homepage/parameter/en/

e_ag_knorr/parameter/en/