Abstract
The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process withT-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.
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Okabe, Y. On the theory of Brownian motion with the Alder-Wainwright effect. J Stat Phys 45, 953–981 (1986). https://doi.org/10.1007/BF01020584
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DOI: https://doi.org/10.1007/BF01020584