Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published September 2003 | Published
Journal Article Open

Energy Growth in Schrödinger's Equation with Markovian Forcing

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/4A).

Additional Information

© 2003 Springer-Verlag. Received 07 October 2002; Accepted 28 February 2003; Published 25 July 2003. The authors are grateful to the Institute for Advanced Study (Princeton), where this work was commenced, and in particular, to Thomas Spencer for his interest in this problem. B.E. and R.K. were supported, in part, by NSF Grant DMS-9729992, W.S. was supported by NSF Grant DMS 0070538 and a Sloan fellowship.

Attached Files

Published - ErdogAn2003_Article_EnergyGrowthInSchrödingerSEqua.pdf

Files

ErdogAn2003_Article_EnergyGrowthInSchrödingerSEqua.pdf
Files (299.5 kB)

Additional details

Created:
August 22, 2023
Modified:
October 19, 2023