April 15-17

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Author: George Vahala
Requested Type: Pre-Selected Invited
Submitted: 2019-02-21 20:35:50

Co-authors: C. SImpson, L. Vahala, A. Ram and M. Soe

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

Abstract Text:
Parity-time (PT) symmetric systems were first considered by Bender [1] to generalize the canonical Hermitian operators with their subsequent real discrete eigenvalues to a larger class of operators with unbroken PT-symmetry. Such PT-systems are becoming very important in many fields of physics. For example, Qin [2]have considered the Kelvin-Helmholtz instability as the result of PT-symmetry breaking. Qin view that instabilities in PT-symmetric conservative systems arise from spontaneously broken PT-symmetry. Here we consider a PT-system that arises in nonlinear optics - a loss/gain system described by a coupled set of generalized non-integrable nonlinear Schrodinger equations (NLS). The total energy of the system is now oscillatory due to the loss/gain terms. Following Barashenkov [3] we perform a multi-scale perturbation expansion of these non-Hermitian generalized NLS equations. To remove secular terms, the constraints yielded a Hermitian set of coupled generalized NLS with energy conservation on this long time scale. A qubit unitary lattice algorithm (QLA) is developed to solve this Hamiltonian system. Soliton collisions, breather as well as rogue waves are examined. We are also investigating a direct embedding of the Barashenkov non-unitary PT system into a higher dimensional Hermitian system [4], and then developing a QLA for this higher dimensional system. Results from our simulations will be discussed. QLA are ideally parallelized on classical supercomputers (like their distance cousins lattice Boltzmann, and cellular automata) but the collide-stream operators must be unitary. Thus these codes can be readily run on quantum computers.

[1] C. M. Bender & S. Boettcher, Phys Rev. Lett. 80, 5243 (1998); C. M Bender, Rep. Prog. Phys. 70, 947 (2007).
[2] H. Qin, R. Zhang, A. S. Glasser and J. Xiao, arXiv:1810.11460 (2018)
[3] I. V. Barashenkov et. al. arXiv:1211.1835v1
[4]. R. Gutohrlein et. al. J Phys. A: Math Theor. 48,335302 (2015)

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