GEOMETRIC PHASES IN DISSIPATIVE SYSTEMS WITH SYMMETRY

Abstract: Classical dissipative systems with symmetry can exhibit a geometric phase effect wherein an adiabatic variation of a parameter drives a shift in the symmetry direction. Viewing the parameter as a control variable, the effect may be useful in the parametric control of dissipative systems, many of which exhibit pattern-forming solutions. Earlier work by A.S. Landsberg developed a theory for this effect in systems admitting an abelian symmetry. In this paper we present a generalization allowing for arbitrary continuous symmetries. This generalization is achieved by defining a new principal connection, here called the Landsberg connection, on an appropriate principal fiber bundle. A simple example is presented to illustrate the theory