Effective action for dissipative and nonholonomic systems
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Afshin Besharat1, Jury Radkovski1, Sergey Sibiryakov1
1Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1 and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5.
Abstract:
We show that the action of a dynamical system can be supplemented by an effective action for its environment to reproduce arbitrary coordinate dependent ohmic dissipation and gyroscopic forces. The action is a generalization of the harmonic bath model and describes a set of massless interacting scalar fields in an auxiliary space coupled to the original system at the boundary. A certain limit of the model implements nonholonomic constraints. In the case of dynamics with nonlinearly realized symmetries the effective action takes the form of a two-dimensional nonlinear σ model. It provides a basis for application of path integral methods to general dissipative and nonholonomic systems.
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