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Phase space flows for non-Hamiltonian systems with constraints.

Alessandro Sergi1

  • 1Dipartimento di Fisica, Sezione Fisica Teorica, Universitá degli Studi di Messina, Contrada Papardo C.P., 50-98166 Messina, Italy. asergi@unime.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

This study generalizes Dirac's formalism for non-Hamiltonian systems with constraints. It introduces new brackets and operators to accurately describe phase space flows and linear response, avoiding spurious terms.

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics

Background:

  • Dirac's formalism is a standard tool for Hamiltonian systems.
  • Non-Hamiltonian systems with holonomic constraints present unique theoretical challenges.
  • Describing phase space flows in these systems requires advanced mathematical frameworks.

Purpose of the Study:

  • To generalize Dirac's formalism for non-Hamiltonian systems with holonomic constraints.
  • To develop methods for describing non-Hamiltonian phase space flows.
  • To apply the generalized formalism to non-Hamiltonian linear response calculations.

Main Methods:

  • Generalization of Dirac's formalism.
  • Introduction of generalized antisymmetric brackets (e.g., Nosé-Dirac bracket).
  • Development of general Liouville operators.

Related Experiment Videos

  • Application of Dirac's recipe for projecting constrained variables to time translation operators.

    • Main Results:

    • The generalized Dirac's formalism successfully describes non-Hamiltonian phase space flows.
    • The Nosé-Dirac bracket serves as an example of generalized antisymmetric brackets.
    • The generalized Dirac's recipe accurately handles non-Hamiltonian linear response.
    • Spurious terms in the response function of constrained systems are avoided.

    Conclusions:

    • The generalized Dirac's formalism provides a robust framework for studying non-Hamiltonian systems with constraints.
    • The developed methods offer accurate descriptions of phase space dynamics and linear response.
    • Careful consideration of phase space measure corrections is necessary for general perturbations.