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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 (CC BY 3.0).

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

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