Published September 2003
| Version Published
Journal Article
Open
Energy Growth in Schrödinger's Equation with Markovian Forcing
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1.
University of California, Berkeley
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2.
University of Pennsylvania
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3.
California Institute of Technology
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
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ErdogAn2003_Article_EnergyGrowthInSchrödingerSEqua.pdf
Additional details
Identifiers
- Eprint ID
- 101965
- Resolver ID
- CaltechAUTHORS:20200318-095352622
Funding
- NSF
- DMS-9729992
- NSF
- DMS-0070538
- Alfred P. Sloan Foundation
Dates
- Created
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2020-03-18Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field