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Effective action for dissipative and nonholonomic systems.

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.

Physical Review. E

|June 22, 2024

Summary

Researchers developed an effective action for dynamical systems to model dissipation and gyroscopic forces. This generalized harmonic bath model uses auxiliary scalar fields and can be applied to path integral methods for complex systems.

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Area of Science:

Theoretical Physics
Dynamical Systems Theory
Quantum Field Theory

Background:

Dynamical systems often exhibit dissipation and gyroscopic forces.
Modeling these effects accurately is crucial for understanding complex physical phenomena.
Existing models like the harmonic bath model have limitations.

Purpose of the Study:

To develop a generalized model for simulating ohmic dissipation and gyroscopic forces in dynamical systems.
To introduce an effective action that incorporates environmental interactions.
To provide a framework for applying path integral methods to dissipative and nonholonomic systems.

Main Methods:

Supplementing the system's action with an effective environmental action.
Utilizing a set of massless interacting scalar fields in an auxiliary space.
Coupling the auxiliary fields to the original system at the boundary.
Investigating a limit that implements nonholonomic constraints.
Analyzing the effective action for systems with nonlinearly realized symmetries, revealing a two-dimensional nonlinear sigma model.

Main Results:

The proposed effective action successfully reproduces arbitrary coordinate-dependent ohmic dissipation and gyroscopic forces.
The model generalizes the harmonic bath model.
A specific limit of the model leads to nonholonomic constraints.
For dynamics with nonlinearly realized symmetries, the effective action reduces to a two-dimensional nonlinear sigma model.

Conclusions:

The developed effective action provides a powerful tool for modeling complex dissipative and nonholonomic systems.
This approach offers a new basis for applying path integral methods to a broader range of physical problems.
The connection to nonlinear sigma models opens avenues for further theoretical exploration.