Phase space flows for non-Hamiltonian systems with constraints

Details Phase space flows for non-Hamiltonian systems with constraints Phase space flows for non-Hamiltonian systems with constraints

2005-08-08

arxiv.org/abs/cond-mat/0508192v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.72.031104

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nos\'e-Dirac bracket is introduced as an example. In the second one, Dirac's recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac's formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.

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