Fokker − Planck Equations: Quantum Fluctuations

Tür:

Kitap Bölümü

Yazar:

E R Pike frs; Sarben Sarkar

Yayın yılı:

1995

Yayıncı:

Oxford University PressOxford

Dil:

en

Abstract In the last chapter we examined the small-fluctuation limit of the master equation. However, we were not able to be very precise about what we meant by ‘small’. Although it is clear that approximations such as (8.9) would be unacceptable if fluctuations were large, their domain of validity still needs to be understood. Intuitively reasonable approximations are easy to state. A rather different approximation, for example, from the semi-classical approach is to replace the discrete structure of ℱm (cf. Exercise 7.3) by a smooth envelope. This smoothing is equivalent to a finite truncation of the operator is an extensive variable this truncation may seem a very acceptable thing to do. However, the derivative acting on P may bring down a quantity which too has some extensive properties and so we would need to examine P before we could be sure that a certain truncation was reasonable. These concerns have been expressed clearly in some classic work by van Kampen (1981) which suggests a framework for a quantitative study of such questions. One of the major successes of the theory of quantum fluctuations is the understanding of photon statistics. Moreover, we can determine how quantum fluctuations modify the chaos and instabilities found in the last chapter.

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