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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, Prof.Dr. A. Knorr**