Topology Atlas | Conferences

Knots in Washington XXXV
December 7-9, 2012
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Quantum Dots, Squids, Cavity QED - A unified approach vie Lie theory
by
Viswanath Ramakrishna
Dept of Mathematical Sciences, University of Texas at Dallas
Coauthors: Zhigang Zhang, Goong Chen

We present a unified approach to three distinct types of two qubit systems - namely quantum dots, cavity QED and SQUIDS. We show that the Hamiltonians underpinning these three systems are very nearly conjugate, and that these conjugations can be found explicitly. We were lead to these conjugations by invoking the theory of KAK (or Cartan) decompositions (specifically of Type I) of the Lie group SU(4). In fact, this can be viewed as a very nice didcatic illustration of the various aspects (especially the non-uniqueness) of KAK decompositions.

Date received: November 18, 2012

Copyright © 2012 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbfw-29.