Effective Action for Dissipative and Nonholonomic Systems

TL;DR

This paper introduces an effective action framework that models dissipative and nonholonomic systems using boundary-coupled scalar fields, enabling path integral methods for complex dynamics.

Contribution

It generalizes the harmonic bath model to include coordinate-dependent dissipation and gyroscopic forces, and connects nonholonomic constraints with a boundary limit of the model.

Findings

Effective action reproduces arbitrary ohmic dissipation.

Models nonholonomic constraints via a boundary limit.

Provides a path integral approach for complex systems.

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 sigma-model. It provides a basis for application of path integral methods to general dissipative and nonholonomic systems.