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APS » Journals » Phys. Rev. Lett. » Volume 99 » Issue 6
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Phys. Rev. Lett. 99, 060201 (2007) [4 pages]

Quantizing Ulam’s Control Conjecture

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M. Gruebele1 and P. G. Wolynes2
1Department of Chemistry, Department of Physics, and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
2Department of Chemistry and Biochemistry, Department of Physics, and Center for Theoretical Biological Physics, University of California, 9500 Gilman Drive, La Jolla, California 92093, USA

Received 18 January 2007; published 6 August 2007

Like classically chaotic systems, can quantum systems be nudged from a given initial state to any other by arbitrarily weak control fields? We explore a scaling theory that sets fundamental limits on the time required for population transfer with weak control fields. Our results depend on the size of the quantum state space and on the rate and extent of energy flow within the system. When the unperturbed dynamics is quantum localized, the total distance in state space over which control can be achieved grows linearly with the number of photons that are expended.

© 2007 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.99.060201
DOI:
10.1103/PhysRevLett.99.060201
PACS:
02.30.Yy, 03.65.−w, 42.50.Ct
 
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