Solitonic fixed point attractors in the complex Ginzburg-Landau equation for associative memories
arXiv:1909.05082 · doi:10.3390/sym12010024
Abstract
It was recently shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, \textit{Adv. Quantum Technol.} \textbf{2019} \textit{2}, 1800087] that the nonlinear Schrodinger equation with a simplified dissipative perturbation of special kind features a zero-velocity solitonic solution of non-zero amplitude which can be used in analogy to attractors of Hopfield's associative memory. In this work, we consider a more complex dissipative perturbation adding the effect of two-photon absorption and the quintic gain/loss effects that yields formally the complex Ginzburg-Landau equation (CGLE). We construct a perturbation theory for the CGLE with a small dissipative perturbation and define the behavior of the solitonic solutions with parameters of the system and compare the solution with numerical simulations of the CGLE. We show that similarly to the nonlinear Schrodinger equation with a simplified dissipation term, a zero-velocity solitonic solution of non-zero amplitude appears as an attractor for the CGLE. In this case the amplitude and velocity of the solitonic fixed point attractor does not depend on the quintic gain/loss effects. Furthermore, the effect of two-photon absorption leads to an increase in the strength of the solitonic fixed point attractor.
arXiv comment6 pages, 2 figures
References in corpus (34)
- Quantum Computing in the NISQ era and beyond
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Theory of Bose-Einstein condensation in trapped gases
- Feshbach Resonances in Ultracold Gases
- Making Sense of Non-Hermitian Hamiltonians
- The World of the Complex Ginzburg-Landau Equation
- Formation and Propagation of Matter Wave Soliton Trains
- Formation of a Matter-Wave Bright Soliton
- Dark Solitons in Bose-Einstein Condensates
- Microresonator Soliton Dual-Comb Spectroscopy
- Exciton-polariton condensates
- Excitations in a non-equilibrium Bose-Einstein condensate of exciton-polaritons
- Spatiotemporal mode-locking in multimode fiber lasers
- Observation of Quantum Shock Waves Created with Ultra Compressed Slow Light Pulses in a Bose-Einstein Condensate
- Polariton superfluids reveal quantum hydrodynamic solitons
- Bose--Einstein solitons in highly asymmetric traps
- Observation of bright polariton solitons in a semiconductor microcavity
- Temporal correlation detection using computational phase-change memory
- Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr Microresonator Frequency Combs
- Bright cavity polariton solitons
- Macroscopic quantum computation using Bose-Einstein condensates
- Multidimensional solitons: Well-established results and novel findings
- Mott transitions of exciton-polaritons and indirect excitons in a periodic potential
- Macroscopic quantum information processing using spin coherent states
- Entanglement generation in quantum networks of Bose-Einstein condensates
- Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
- Optimization using Bose-Einstein condensation and measurement-feedback circuits
- Quantum Brain: A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets
- Effective interaction and condensation of dipolaritons in coupled quantum wells
- Bose-Einstein condensation: Twenty years after
- Full Bloch sphere teleportation of spinor Bose-Einstein condensates and spin ensembles
- Observation of mode-locked spatial laser solitons
- Quantum metrology beyond Heisenberg limit with entangled matter wave solitons
- Stationary and traveling solitons via local dissipations in Bose-Einstein condensates in ring optical lattices