Symmetries of the stochastic Burgers equation

Details Symmetries of the stochastic Burgers equation Symmetries of the stochastic Burgers equation

1996-10-28

arxiv.org/abs/hep-th/9610221v2

J.Phys. A30 (1997) L525-L533

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, REVTeX, replaced with published version

Scientific paper

10.1088/0305-4470/30/15/008

All Lie symmetries of the Burgers equation driven by an external random force are found. Besides the generalized Galilean transformations, this equation is also invariant under the time reparametrizations. It is shown that the Gaussian distribution of a pumping force is not invariant under the symmetries and breaks them down leading to the nontrivial vacuum (instanton). Integration over the volume of the symmetry groups provides the description of fluctuations around the instanton and leads to an exactly solvable quantum mechanical problem.

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