Time-Reversal Invariance and the Relation between Wave Chaos and Classical Chaos

  • Roel Snieder
Part of the Topics in Applied Physics book series (TAP, volume 84)


Many imaging techniques depend on the fact that the waves used for imaging are invariant for time reversal. The physical reason for this is that in imaging one propagates the recorded waves backward in time to the place and time when the waves interacted with the medium. In this chapter, the invariance for time reversal is shown for Newton’s law, Maxwell’s equations, the Schrödinger equation and the equations of fluid mechanics. The invariance for time reversal can be used as a diagnostic tool to study the stability of the temporal evolution of systems. This is used to study the relation between classical chaos and wave chaos, which also has implications for quantum chaos. The main conclusion is that in classical chaos perturbations in the system grow exponentially in time [exp(μt)], whereas for the corresponding wave system perturbations grow at a much smaller rate algebraically with time (√t).


Time Reversal Scattered Wave Particle Propagation Fresnel Zone Coda Wave 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Roel Snieder
    • 1
  1. 1.Department of Geophysics and Center for Wave PhenomenaColorado School of MinesUSA

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