Fourier transform fluctuation-dissipation theorem

By referring to Eqs.(3) and (41, the imaginary part of the Fourier transform of the OHD-OKE response divided by the Fourier transform of the lAF of the laser pulse is directly comparable to the LS spectrum divided by the Bose factor in addition to Because the dynamical behavior and the fluctuation ought to be correlated with each other through the fluctuation-dissipation theorem, this comparison can verify that the information provided by the two experiments are identical. To our knowledge, however, the direct comparison has not been made yet. In this report, we will describe the details of our experiments and thier results on this problem. 

Let us first consider spectroscopy. Linear-response theory, in particular the fluctuation dissipation theorem - which relates the absorption of an incident monochromatic field to the correlation function of (e.g. dipole) fluctuations in equilibrium - has changed our perspective on spectroscopy of dense media. It has moved away from a static Schrodinger picture -phrased in terms of transitions between immutable (but usually incomputable) quantum levels - to a dynamic Heisenberg picture, in which the spectral line shape is related by Fourier transform to a correlation function that describes the decay of fluctuations. Of course, any property that cannot be computed in the Schrodinger picture, cannot be computed in the Heisenberg picture either however, correlation functions, unlike wave-functions, have a clear meaning in the classical limit. This makes it much easier to come up with simple (semi) classical interpretations and approximations. 

Aepd is a kinetic Onsager coefficient, and rj denotes noise that satisfies the fluctuation-dissipation theorem. The Fourier transform of this new diffusion equation is simply ... 

The fluctuation-dissipation theorem (FDT) of Callen and Welton states a general relationship between the response of a given system to an external disturbance and the internal fluctuation of the system in the absence of the dismrbance. Such a response is characterized by a response function or equivalently by an admittance or an impedance. For dielectric relaxation, the complex dielectric function, e ( u), is related to the dipole moment correlation function < >( ) via Fourier transformation ... 

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