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Absence of ballistic motion

Abstract

For large classes of Schrödinger operators and Jacobi matrices we prove that ifh has only one point spectrum then for φ0 of compact support

$$\mathop {\lim }\limits_{t \to \infty } t^{ - 2} \left\| {xe^{ - ith} \phi _0 } \right\|^2 = 0.$$

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References

  1. Cycon, H., Froese, R., Kirsch, W., Simon, B.: Schrödinger Operators. Berlin, Heidelberg, New York: Springer 1987

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  2. Radin, C., Simon, B.: Invariant domains for the time-dependent Schrödinger equation. J. Diff. Eq.29, 289–296 (1978)

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Research partially supported by NSF grant number DMS-8801918

Communicated by T. Spencer

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Simon, B. Absence of ballistic motion. Commun.Math. Phys. 134, 209–212 (1990). https://doi.org/10.1007/BF02102095

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  • DOI: https://doi.org/10.1007/BF02102095

Keywords

  • Neural Network
  • Statistical Physic
  • Complex System
  • Nonlinear Dynamics
  • Large Classis