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    Rights statement: Copyright 2018 American Institute of Physics. The following article appeared in Journal of Mathematical Physics, 59, (3) 2018 and may be found at http://dx.doi.org/10.1063/1.5016495 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

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Dynamical decoupling of unbounded Hamiltonians

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Article number032203
<mark>Journal publication date</mark>20/03/2018
<mark>Journal</mark>Journal of Mathematical Physics
Issue number3
Volume59
Number of pages16
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Bibliographic note

Copyright 2018 American Institute of Physics. The following article appeared in Journal of Mathematical Physics, 59, (3) 2018 and may be found at http://dx.doi.org/10.1063/1.5016495 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.