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Quantum Knots and Their Applications
by
Samuel Lomonaco
University of Maryland Baltimore County (UMBC)
Coauthors: Louis Kauffman
We begin by showing how to define a quantum system whose states, called quantum knots, represent a closed knotted piece of rope, i.e., represent the particular spatial configuration of a knot tied in a rope in 3-space. Such quantum systems, called quantum knot systems, are physically implementable in the same sense as Shor's quantum factoring algorithm is implementable.
Associated with a quantum knot system is a group of unitary transformations, called the ambient group, which represents all possible ways of moving a rope in 3-space without cutting the rope, and without letting the rope pass through itself.
We then investigate those quantum observables of a quantum knot system which are knot invariants. We also investigate ways of associating Hamiltonians with the generators of the ambient group, and the resulting dynamic behavior of quantum knots as determined by SchroedingerÂ’s equation.
Paper reference: arXiv:0805.0339 & arXiv:0910.5891
Date received: November 28, 2010
Copyright © 2010 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 # cbbr-23.