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Ensemble dynamics of chaos
Author(s) -
Driebe Dean J.,
Hasegawa Hiroshi H.
Publication year - 2004
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10836
Subject(s) - ilya , statistical physics , eigenvalues and eigenvectors , hamiltonian (control theory) , lyapunov exponent , hamiltonian system , operator (biology) , quantum chaos , physics , quantum , chaos (operating system) , chaotic , mathematics , classical mechanics , computer science , quantum dynamics , quantum mechanics , nonlinear system , artificial intelligence , philosophy , mathematical optimization , linguistics , biochemistry , chemistry , computer security , repressor , transcription factor , gene
Systems of deterministic chaos demonstrate that the ensemble and trajectory descriptions of dynamics are not equivalent. This is shown through explicit constructions of the generalized spectral decompositions of the time evolution operator for probability densities. This realizes part of the long‐standing goal of the Brussels–Austin groups directed by Ilya Prigogine to elucidate the dynamical foundations of irreversibility. A brief review of the main aspects of the work are given here along with a new derivation of the fractality of eigenstates in some systems and a discussion of a Lyapunov functional in an unstable Hamiltonian system. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004