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Classical and quantum transport in deterministic Hamiltonian ratchets
Author(s) -
Dittrich T.,
Ketzmerick R.,
Otto M.F.,
Schanz H.
Publication year - 2000
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/1521-3889(200010)9:9/10<755::aid-andp755>3.0.co;2-v
Subject(s) - phase space , physics , chaotic , quantum , hamiltonian (control theory) , quantum chaos , classical mechanics , position and momentum space , space (punctuation) , sign (mathematics) , quantum mechanics , statistical physics , quantum dynamics , mathematics , computer science , mathematical analysis , mathematical optimization , artificial intelligence , operating system
We study directed transport in classical and quantum area‐preserving maps, periodic in space and momentum. On the classical level, we show that a sum rule excludes directed transport of the entire phase space, leaving only the possibility of transport in (dynamically defined) subsets, such as regular islands or chaotic areas. As a working example, we construct a mapping with a mixed phase space where both the regular and the chaotic components support directed currents, but with opposite sign. The corresponding quantum system shows transport of similar strength, associated to the same subsets of phase space as in the classical map.