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Author: Armen Oganesov
Requested Type: Poster
Submitted: 2017-03-16 19:05:12

Co-authors: G. Vahala, L. Vahala, J. Yepez, Z. Butler and M. Soe

Contact Info:
William & Mary
300 Ukrop Way
Williamsburg, VA   23185
USA

Abstract Text:
A fundamental difference between classical and quantum physics is in their vortices. A classical vortex has a continuous range of circulation making its birth fuzzy with vortex-vortex reconnection occurring only in dissipative systems. With the advent of atomic gas BECs, the simplest mean field theory of this many body problem is the (scalar) nonlinear Schrodinger (NLS) equation. NLS is a ubiquitous equation of nonlinear optics, fluids and plasma physics. The NLS can be transformed into an compressible inviscid Euler equation with an additional tensorial stress term that permits vortex-vortex reconnection without dissipation. A quantum vortex is now a topological singularity, existing with only discrete quantized circulation. Moreover these are vortices have zero density at the core. From the symmetries of the full Hamiltonian to the ground state solution symmetries one can investigate the corresponding factor group of the order parameter. This yields the possible topological structures that can be seen experimentally. In particular, if a BEC is trapped in an optical well, the s spin degrees of freedom now require a mean-field theory that results in a coupled set of (2s+1) NLS equations. Of much interest are the spin-2 systems with tetrahedral symmetry leading to non-Abelian quantum vortices. All scalar and spin-1 ground states leading to Abelian vortices. The dynamics of these vortices are significantly different: e.g., Abelian vortices permit reconnection of Trefoil knot vortices into simple loop vortices, while non-Abelian vortices topological forbid this form of reconnection. We are investigating these NLS equations using a unitary qubit lattice gas approach. Closure is achieved by a 2nd order truncation in the non-commuting kinetic energy and interaction operators. These qubit algorithms are ideally parallelized, tested to over 850,000 cores on MIRA. We consider the role of these different reconnection topologies on the energy spectrum.

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