Reservoir fermionic

Open quantum systems have attracted much attention over the last decades. While most of the studies dealt with systems coupled to bosonic heat baths, recently systems coupled to fermionic reservoirs describing for example molecular wires have been in the focus of many investigations. This chapter will not try to give a concise overview of the available literature but will focus on a particular approach time-local (TL) quantum master equations (QMEs) and in particular their combination with specific forms of the spectral density. 

Similar to the case of the bosonic bath, one may also define correlation functions in the case of fermionic reservoirs. In contrast to the former case, two different correlation functions will be introduced since there are also two different parts of the system-reservoir interaction one creates and one annihilates an electron in the wire. The correlation functions are given by... 

After discussing the properties of the environments, let us now turn to the dynamics of a system in a dissipative environment, i.e. a system coupled to a bosonic bath. The case of fermionic reservoirs will be treated in the next section. 

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