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Energy Growth in Schrödinger's Equation with Markovian Forcing

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Abstract

Schrödinger's equation is considered on a one-dimensional torus with time dependent potential v(θ,t)=λV(θ)X(t), where V(θ) is an even trigonometric polynomial and X(t) is a stationary Markov process. It is shown that when the coupling constant λ is sufficiently small, the average kinetic energy grows as the square-root of time. More generally, the H s norm of the wave function is shown to behave as t s/4.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA

    M. Burak Erdog˜an

  2. Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA

    Rowan Killip

  3. Department of Mathematics, 253-37, Caltech, Pasadena, CA 91125, USA

    Wilhelm Schlag

Authors
  1. M. Burak Erdog˜an
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  2. Rowan Killip
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  3. Wilhelm Schlag
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Erdog˜an, M., Killip, R. & Schlag, W. Energy Growth in Schrödinger's Equation with Markovian Forcing. Commun. Math. Phys. 240, 1–29 (2003). https://doi.org/10.1007/s00220-003-0892-7

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  • DOI: https://doi.org/10.1007/s00220-003-0892-7

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