Decoherence and correspondence in conservative chaotic dynamics

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 2, 1999, Pages 1643-1647

  Gong, Jiangbin ^a   Brumer, Paul ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001570302     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.1643     Document Type: Article

References (31)

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27. Note that we begin with a dimensionless scaled Hamiltonian [Eq. (3)]. As a result, all relevant variables are understood to be dimensionless and scaled. The relation between the scaled variables and unscaled variables is, however, crucial for retrieving specific units when necessary. For a general Hamiltonian (Formula presented) with all variables with tildes denoting ordinary unscaled variables, we can define the dimensionless scaled variables (Formula presented) (Formula presented) (Formula presented), and (Formula presented) Here (Formula presented) has units of action, and (Formula presented) and (Formula presented) are ordinary constants with units of mass and frequency. Typically, (Formula presented) is taken as the average frequency of this system and (Formula presented) is taken to scale the true Planck constant; that is, (Formula presented), where (Formula presented) is the ordinary Planck constant and (Formula presented) is the dimensionless scaled Planck constant. The scaled variables satisfy the canonical equations of motion for the scaled time (Formula presented) and the scaled Hamiltonian (Formula presented). For quantum descriptions one can verify that (Formula presented) (Formula presented).
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