Erdoğan, M. Burak and Killip, Rowan and Schlag, Wilhelm (2003) Energy Growth in Schrödinger's Equation with Markovian Forcing. Communications in Mathematical Physics, 240 (1-2). pp. 1-29. ISSN 0010-3616. doi:10.1007/s00220-003-0892-7. https://resolver.caltech.edu/CaltechAUTHORS:20200318-095352622
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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/4A).
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| 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. | |||||||||
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| Subject Keywords: | Kinetic Energy; Wave Function; Markov Process; Trigonometric Polynomial; Dependent Potential | |||||||||
| Issue or Number: | 1-2 | |||||||||
| DOI: | 10.1007/s00220-003-0892-7 | |||||||||
| Record Number: | CaltechAUTHORS:20200318-095352622 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200318-095352622 | |||||||||
| Official Citation: | Erdoğan, 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 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 101965 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 18 Mar 2020 19:23 | |||||||||
| Last Modified: | 16 Nov 2021 18:07 |
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