Phase space flows for non-Hamiltonian systems with constraints.
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 Nosé-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.
Sergi
Alessandro
A
Dipartimento di Fisica, Sezione Fisica Teorica, Universitá degli Studi di Messina, Contrada Papardo C.P., 50-98166 Messina, Italy. asergi@unime.it