Stochastic theory single molecule spectroscopy

Y. Jung, E. Barkai, and R. J. Silbey, A Stochastic theory of single molecule spectroscopy. Adv. Chem. Phys. 123 199-266 (2002). 

Some interesting behavior in single-molecule spectroscopy involves the stochastic migration of lines. Usual statistical quantum theory describes only mean values or dispersions of observables, but not the actual fluctuations in the dynamics of single quantum systems. In an individual formalism of quantum mechanics, such fluctuations are of great importance. 

Unfortunately, a rigorous derivation of stochastic pure-state dynamics is still lacking. Nevertheless it is gratifying that such stochastic dynamics are important and in fact form the basis of a quantum theory of individual (quantum) objects. One hint in this direction comes from single-molecule spectroscopy (SMS), where single molecule always is to be understood as a single molecule embedded into a polymorphic matrix or a crystal.The example used in Fig. 9 is a single... 

A STOCHASTIC THEORY OF SINGLE MOLECULE SPECTROSCOPY 251 This equations yields the solution... 

In this chapter, we developed a stochastic theory of single molecule fluorescence spectroscopy. Fluctuations described by Q are evaluated in terms of a three-time correlation function C iXi, X2, T3) related to the response function in nonlinear spectroscopy. This function depends on the characteristics of the spectral diffusion process. Important time-ordering properties of the three-time correlation function were investigated here in detail. Since the fluctuations (i.e., Q) depend on the three-time correlation function, necessarily they contain more information than the line shape that depends on the one-time correlation function Ci(ti) via the Wiener-Khintchine theorem. 

Averaging over all different possible stochastic behaviors in SMS yields the master equation used in ensemble spectroscopy, but the averaged master equation does not determine the dynamics of the (pure) states of individual molecules. Certain attempts have been made to derive a proper theory of individual behavior of single quantum systems, but a rigorous interpretation is still lacking. 

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