Brownian Motion of Solitons in the $Φ^4$ Model

Details Brownian Motion of Solitons in the $Φ^4$ Model Brownian Motion of Solitons in the $Φ^4$ Model

1995-11-27

arxiv.org/abs/cond-mat/9511129v1

Int.J.Mod.Phys. B10 (1996) 1329-1338

Physics

Condensed Matter

latex, 1 eps figure at end of file

Scientific paper

We derive an expression for the correlation function of the random force on a soliton which is consistent with the constraints needed to integrate out the zero modes which appear due to the broken translational symmetry of the soliton solution. It is shown that when the constraint does not commute with the operator which defines the correlation function, i.e. when the operator is not physical, only low frequency phonons contributions may be considered. On the contrary, when the correlation function of the random force on the soliton is constructed with physical operators one may also include in a correct manner the contributions from the optical phonons.

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