de Broglie-Bohm formulation of quantum mechanics, quantum chaos and breaking of time-reversal invariance |
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Authors: | F H M Faisal U Schwengelbeck |
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Institution: | 1. Fakult?t für Physik, Universit?t Bielefeld, Postfach 100131, D33501, Bielefeld, Germany
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Abstract: | A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation
of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic
if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This
definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in
terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the
dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically,
proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under
chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism
towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’ |
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Keywords: | de Broglie-Bohm quantum mechanics quantum chaos Lyapunov numbers time-reversal invariance |
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