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Entropy 2013, 15(12), 5121-5143; doi:10.3390/e15125121
Article

Energy Transfer Using Unitary Transformations

1
 and 2,*
1 Institute for Theoretical Physics, KU Leuven, Leuven B-3001, Belgium 2 Physics Department, University of Antwerp, Universiteitsplein 1, Antwerpen B-2610, Belgium
* Author to whom correspondence should be addressed.
Received: 16 July 2013 / Revised: 22 October 2013 / Accepted: 18 November 2013 / Published: 26 November 2013
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Abstract

We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by time-dependent external fields. The S-matrix (scattering matrix) of the cycle is obtained in analytic form. The total number of quanta contained in the system is a conserved quantity. As a consequence, the spectrum of the S-matrix is purely discrete, and the evolution of the system is quasi-periodic. The explicit knowledge of the S-matrix makes it possible to do accurate numerical evaluations of the time-dependent wave function. They confirm the quasi-periodic behavior. In particular, the energy flows back and forth between the two oscillators in a quasi-periodic manner.
Keywords: quantum stirring; S-matrix; driven quantum system; three-level system quantum stirring; S-matrix; driven quantum system; three-level system
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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de Galway, W.O.; Naudts, J. Energy Transfer Using Unitary Transformations. Entropy 2013, 15, 5121-5143.

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