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Energy Transfer Using Unitary Transformations
Institute for Theoretical Physics, KU Leuven, Leuven B-3001, Belgium
Physics Department, University of Antwerp, Universiteitsplein 1, Antwerpen B-2610, Belgium
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Received: 16 July 2013; in revised form: 22 October 2013 / Accepted: 18 November 2013 / Published: 26 November 2013
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
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MDPI and ACS Style
de Galway, W.O.; Naudts, J. Energy Transfer Using Unitary Transformations. Entropy 2013, 15, 5121-5143.
de Galway WO, Naudts J. Energy Transfer Using Unitary Transformations. Entropy. 2013; 15(12):5121-5143.
de Galway, Winny O.; Naudts, Jan. 2013. "Energy Transfer Using Unitary Transformations." Entropy 15, no. 12: 5121-5143.