Energy Growth in Schrödinger's Equation with Markovian Forcing

M. Burak Erdog̃an, Rowan Killip, Wilhelm Schlag

Research output: Contribution to journalArticlepeer-review


Schrödinger's equation is considered on a one-dimensional torus with time dependent potential v(θ, t) = λ V(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 Hs norm of the wave function is shown to behave as ts/4.

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalCommunications in Mathematical Physics
Issue number1-2
StatePublished - Sep 2003
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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