Matteo Polettini - INFN Bologna #
State-Dependent Diffusion from General Covariance #
The form of the correct equations describing brownian motion 
with state-dependent diffusion is subject to long-standing debates. In 
this poster I discuss one proposal which is founded on the principle of 
general covariance, by which I mean: Covariance under coordinate 
transformations; Invariance under internal "gauge" transformations. I 
derive a generally covariant Langevin equation from first principles; the 
overdamping limit yields a first-oder SDE which is neither Ito, 
Straonovich, Klimontovich nor else. The corresponding Fokker-Planck 
equation affords an equilibrium (detailed-balanced) steady state, 
differing from other proposals. Among the experimentally testable 
consequences of the theory, the spatial density of the steady state is not 
uniform, dispensing with the equal-a-priori postulate.