Reservoir bosonic

Hereafter we put /ig = 1. Below we express our results in terms of the statistical properties (correlators) of the environment s noise, X(t). Depending on the physical situation at hand, one can choose to model the environment via a bath of harmonic oscillators [6, 3]. In this case the generalized coordinate of the reservoir is defined as X = ]T)Awhere xi are the coordinate operators of the oscillators and Aj are the respective couplings. Eq. 2 is then referred to as the spin-boson Hamiltonian [8]. Another example of a reservoir could be a spin bath [11] 5. However, in our analysis below we do not specify the type of the environment. We will only assume that the reservoir gives rise to markovian evolution on the time scales of interest. More specifically, the evolution is markovian at time scales longer than a certain characteristic time rc, determined by the environment 6. We assume that rc is shorter than the dissipative time scales introduced by the environment, such as the dephasing or relaxation times and the inverse Lamb shift (the scale of the shortest of which we denote as Tdiss, tc [Pg.14]

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. 

As for the case of a bosonic bath, the Hamiltonian describing the molecular junction is separated into the relevant system Hs(t), describing the wire, the field-matter interaction Hp(t) and reservoirs Hr modeling the leads... 

Figure 8. Model for interactions of an atom with individual and independent bosonic reservoirs decribing spin-flips (Aj, Bj, Cj) and dephasing (l)j, Ej, Fj).

We consider individual bosonic reservoirs / ,.. .., Fj with finite thermal energy ksT characterized by mode operators Ajk, Ajk, etc. Environmentally induced spin flips can be described by the interaction Hamiltonian... 

The system-reservoir interaction operators are products of the type Vak = AR, where A represents a molecule operator (aj, a, B, B) and R a reservoir operator b, b ). Because of the BO approximation the electronic operators commute with the phonon operators. Moreover, the pseudolocalized phonon operators commute with those of the baind phonons because of the boson commutation rules. This amounts to the statement that all molecule variables commute with the reservoir variables, [A,R] = 0. 

A major focus of the theory of quantum dissipation in a spin-bath is the conspicuous thermal behavior of the reservoir. Our analysis clearly shows that, at temperatures close to zero, a spin-bath behaves almost in the same way as a bosonic bath, implying a universality in the nature of bath as TWO. At higher temperatures (below saturation temperature), the system-bath coupling tends to diminish, which is reflected in the emergence of coherence in the dynamics, and the behavior of a spin-bath differs significantly from that of a bosonic bath. In what follows, we consider two specific examples to illustrate these aspects. 

---