By Gert-Ludwig Ingold (auth.), Andreas Buchleitner, Klaus Hornberger (eds.)
In the final 20 years striking growth within the experimental dealing with of unmarried quantum items has spurred theoretical examine into investigating the coupling among quantum structures and their setting. Decoherence, the sluggish deterioration of entanglement as a result of dissipation and noise fed into the approach by means of the surroundings, has emerged as a important inspiration. the current set of lectures is meant as a high-level, yet self-contained, creation into the fields of quantum noise and dissipation. specifically their impression on decoherence and functions relating quantum details and quantum verbal exchange are studied, top the nonspecialist researchers and the complex scholars steadily to the leading edge of research.
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Additional info for Coherent Evolution in Noisy Environments
For the following discussion, we will not consider this latter case. In analogy to Sect. 67) of the free particle. Even though it may seem that determining the prefactor is a formidable task since the ﬂuctuation determinant for a given potential has to be evaluated, this task can be greatly simpliﬁed. In addition, the following considerations oﬀer the beneﬁt of providing a physical interpretation of the prefactor. In our evaluation of the prefactor we follow Marinov . 81) dx C(xf , t, x , t )C(x , t , xi , 0) exp i Scl (xf , t, x , t ) + Scl (x , t , xi , 0) where the prefactor C depends on the ﬂuctuation contribution.
161) where the inﬂuence functional F[¯ q ] describes the inﬂuence of the environment on the system. Here, the partition function Z should not be confused with the partition function Zβ of system plus environment. The relation between the two quantities will be discussed shortly. 163) is the partition function of a single bath oscillator. 164) with the action β SnE [¯ q, x ¯n ] = dτ 0 mn 2 cn x ¯˙ n + ωn2 x ¯n − q¯ 2 mn ωn2 2 . 165) The partition function Z of the damped system is related to the full partition function Zβ by the partition function of the environmental oscillators ZB = N n=1 Zn according to Z = Zβ /ZB .
At this point, we want to brieﬂy elucidate the origin of the term “Ohmic damping”. Let us consider the electric circuit shown in Fig. 9 consisting of a 32 Gert-Ludwig Ingold R C L Fig. 9. LC oscillator with Ohmic damping due to a resistor R resistance R, a capacitance C and an inductance L. 140) LQ C which shows that an Ohmic resistor leads indeed to memoryless damping. 138) to account for its dissipative nature. 138) for Ohmic damping unfortunately diverges at high frequencies which, as already mentioned, cannot be the case in practice.