scholarly journals Efficient and Deterministic Propagation of Mixed Quantum-Classical Liouville Dynamics

2018 ◽  
Vol 9 (14) ◽  
pp. 3928-3933 ◽  
Author(s):  
Junjie Liu ◽  
Gabriel Hanna
Keyword(s):  
Liouville Dynamics

Multidimensional classical Liouville dynamics with quantum initial conditions

2002 ◽  
Vol 117 (10) ◽  
pp. 4643-4650 ◽  
Author(s):  
Illia Horenko ◽  
Burkhard Schmidt ◽  
Christof Schütte
Keyword(s):  
Initial Conditions ◽  
Liouville Dynamics

scholarly journals GENERALIZED n-POISSON BRACKETS ON A SYMPLECTIC MANIFOLD

1998 ◽  
Vol 13 (39) ◽  
pp. 3185-3192 ◽  
Author(s):  
J. GRABOWSKI ◽  
G. MARMO
Keyword(s):  
Symplectic Manifold ◽  
Poisson Brackets ◽  
Generalized Poisson ◽  
Dirac Brackets ◽  
Liouville Dynamics

On a symplectic manifold (M,ω) we study a family of generalized Poisson brackets associated with 2k-forms ωk. The extreme cases are related to the Hamiltonian and Liouville dynamics. We show that the Dirac brackets can be obtained in a similar way.

SYMMETRY REDUCTION IN THE VARIATIONAL APPROACH TO LIOUVILLE DYNAMICS

2005 ◽  
Vol 02 (04) ◽  
pp. 657-674 ◽  
Author(s):  
GIUSEPPE GAETA ◽  
PAOLA MORANDO ◽  
OSMAN TEOMAN TURGUT
Keyword(s):  
Variational Principle ◽  
Conservation Laws ◽  
Variational Approach ◽  
Vector Fields ◽  
Symmetry Reduction ◽  
Conserved Quantities ◽  
Volume Form ◽  
Liouville Dynamics

In a recent paper, a variational principle for Liouville dynamics (vector fields preserving a volume form) was introduced. In the present paper, we discuss the relation between symmetries and conservation laws in Liouville dynamics. We recall a result by Crampin relating symmetries and conserved quantities in Liouville dynamics, and discuss how symmetry reduction is implemented in the frame of the variational principle for Liouville dynamics.

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