Abstract
Classical ergodic invariants like the Lyapunov exponent and the entropy, defined in a space of densities acted upon by the Perron-Frobenius operator, provide an intuitive framework to construct the corresponding notions in quantum mechanics.
Rigorous existence conditions obtained for quantum characteristic exponents and a definition of quantum entropy based on the Brin-Katok construction are steps towards a quantum ergodic theory, where a rigorous definition of quantum chaos may be established.
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© 1995 Springer-Verlag
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Vilela Mendes, R. (1995). Entropy and quantum characteristic exponents. steps towards a quantum pesin theory. In: Garbaczewski, P., Wolf, M., Weron, A. (eds) Chaos — The Interplay Between Stochastic and Deterministic Behaviour. Lecture Notes in Physics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60188-0_60
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DOI: https://doi.org/10.1007/3-540-60188-0_60
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