90 research outputs found
Quantum algorithm for Bose-Einstein condensate quantum fluid dynamics
The dynamics of vortex solitons in a BEC superfluid is studied. A quantum
lattice-gas algorithm (localization-based quantum computation) is employed to
examine the dynamical behavior of vortex soliton solutions of the
Gross-Pitaevskii equation (phi^4 interaction nonlinear Schroedinger equation).
Quantum turbulence is studied in large grid numerical simulations: Kolmogorov
spectrum associated with a Richardson energy cascade occurs on large flow
scales. At intermediate scales a k^{-6} power law emerges, in a
classical-quantum transition from vortex filament reconnections to Kelvin
wave-acoustic wave coupling. The spontaneous exchange of intermediate vortex
rings is observed. Finally, at very small spatial scales a k^{-3} power law
emerges, characterizing fluid dynamics occurring within the scale size of the
vortex cores themselves, a characteristic Kelvin wave cascade region. Poincare
recurrence is studied: in the free non-interacting system, a fast Poincare
recurrence occurs for regular arrays of line vortices. The recurrence period is
used to demarcate dynamics driving the nonlinear quantum fluid towards
turbulence, since fast recurrence is an approximate symmetry of the nonlinear
quantum fluid at early times. This class of quantum algorithms is useful for
studying BEC superfluid dynamics over a broad range of wave numbers, from
quantum flow to a pseudo-classical inviscid flow regime to a Kolmogorov
inertial subrange.Comment: 10 pages, 6 figure
A unitary quantum lattice gas algorithm for two dimensional quantum turbulence
Quantum vortex structures and energy cascades are examined for two
dimensional quantum turbulence (2D QT) at zero temperature. A special unitary
evolution algorithm, the quantum lattice gas (QLG) algorithm, is employed to
simulate the Bose-Einstein condensate (BEC) governed by the Gross-Pitaevskii
(GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is
a short Poincar\'e recurrence time. It is demonstrated that such short
recurrence times are destroyed as the nonlinear interaction is strengthened.
The similar loss of Poincar\'e recurrence is also reported in 3D QT [1] Energy
cascades for 2D QT are considered to examine whether 2D QT exhibits inverse
cascades as in 2D classical turbulence. In the parameter regime considered, the
spectra analysis reveals no such dual cascades-dual cascades being a hallmark
of 2D classical turbulence
Lattice Quantum Algorithm for the Schrodinger Wave Equation in 2+1 Dimensions With a Demonstration by Modeling Soliton Instabilities
A lattice-based quantum algorithm is presented to model the non-linear Schrödinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit-qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. The model is tested on the transverse modulation instability of a one dimensional soliton wave train, both in its linear and non-linear stages. In the integrable cases where analytical solutions are available, the numerical predictions are in excellent agreement with the theory
Quantum Algorithm for Bose-Einstein Condensate Quantum Fluid Dynamics: Twisting of Filamentary Vortex Solitons Demarcated by Fast Poincare Recursion
The dynamics of vortex solitons is studied in a BEC superfluid. A quantum lattice-gas algorithm (measurementbased quantum computation) is employed to examine the dynamical behavior vortex soliton solutions of the Gross-Pitaevskii equation (ø4 interaction nonlinear Schroedinger equation). Quantum turbulence is studied in large grid numerical simulations: Kolmogorov spectrum associated with a Richardson energy cascade occurs on large flow scales. At intermediate scales, a new k-6 power law emerges, due to vortex filamentary reconnections associated with Kelvin wave instabilities (vortex twisting) coupling to sound modes and the exchange of intermediate vortex rings. Finally, at very small spatial scales a k-3power law emerges, characterizing fluid dynamics occurring within the scale size of the vortex cores themselves. Poincaré recurrence is studied: in the free non-interacting system, a fast Poincaré recurrence occurs for regular arrays of line vortices. The recurrence period is used to demarcate dynamics driving a nonlinear quantum fluid towards turbulence, since fast recurrence is an approximate symmetry of the nonlinear quantum fluid at early times. This class of quantum algorithms is useful for studying BEC superfluid dynamics and, without modification, should allow for higher resolution simulations (with many components) on future quantum computers
Close-Coupling Calculations for NaAr, NaNe, and NaHe
The non-adiabatic close-coupled theory, developed by Mies and by George, is employed in a time-independent molecular calculation for Na-rare gas collisions in a radiations field. The intensity of the Na D1/D2 lines is calculated for both blue- and red-wing excitation and is in good agreement with the experimental results of Havey, Copeland, and Wang for NaAr. The effects of different Born-Oppenheimer potentials on D1/D2 line intensity is considered by also treating NaNe and NaHe. The individual parity contributions to the line intensities are significantly different from each other
Turbulence Modeling of the Toroidal Wall Heat Load Due to Shear Flows over Cavities in the Neutral Gas Blanket Divertor Regime
Heat loads to the target plate in reactor tokamaks are estimated to be orders of magnitude higher than those that can be withstood by known materials. In regimes of plasma detachment, there is strong evidence that plasma recombination occurs near the divertor plate, leading to a cold neutral gas blanket. Because of the strong coupling between the plasma and the neutrals within the divertor region, there is significant neutral flows along field lines up to Mach 1.2 and Reynolds numbers over 1000. The effects of three dimensional (3D) neutral turbulence within the gas blanket on heat deposition to the toroidal wall are examined. Both two dimensional (2D) mean shear flows over toroidal cavities as well as a fully 3D initial value problem of heat pulse propagation are considered. The results for algebraic stress model, K-ϵ and laminar flows are compared. It is found that 3D velocity shear turbulence has profound effects on the heat loads, indicating that simple (linear) Reynolds stress closure schemes are inadequate
Effects of Quantum Noise on a Two-Level System in a Single-Mode Cavity
The effects of quantum noise on a two-level system in the bad-cavity regime are considered perturbatively in the form of closure at the pair-correlation level. It is found that pair-correlation effects can reduce the level of semiclassical chaos. However, under the rotating-wave approximation (RWA), quantum noise can lead to chaos if there is an initial population inversion, while the full RWA Hamiltonian system remains integrable
Higher Order Isotropic Velocity Grids in Lattice Methods
Kinetic lattice methods are a very attractive representation of nonlinear macroscopic systems because of their inherent parallelizability on multiple processors and their avoidance of the nonlinear convective terms. By uncoupling the velocity lattice from the spatial grid, one can employ higher order (non-space-filling) isotropic lattices-lattices which greatly enhance the stable parameter regions, particularly in thermal problems. In particular, the superiority of the octagonal lattice over previous models used in 2D (hexagonal or square) and 3D (projected face-centered hypercube) is shown
Quantum Lattice Representation of Dark Solitons
The nonlinear Schrodinger (NLS) equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate (BEC) is described by the Gross-Pitaevskii equation, which for a highly anisotropic (cigar-shaped) magnetic trap reduces to a one-dimensional (1D) cubic NLS in an external potential. A quantum lattice algorithm is developed for the dark solitons. Simulations are presented for both black (stationary) solitons as well as (moving) dark solitons. Collisions of dark solitons are compared with the exact analytic solutions and coupled dark-bright vector solitons are examined. The quantum algorithm requires 2 qubits per scalar field at each spatial node. The unitary collision operator quantum mechanically entangles the on-site qubits, and this transitory entanglement is spread throughout the lattice by the streaming operators. These algorithms are suitable for a Type-II quantum computers, with wave function collapse induced by quantum measurements required to determine the coupling potentials
Effects of Large Aspect Ratios and Fluctuations on Hard X-Ray-Detection in Lower Hybrid Driven Divertor Tokamaks
It is shown that lower hybrid wave scattering from fluctuations plays a critical role in large aspect ratio divertor plasmas even through the edge density fluctuation levels are only at 1%. This is seen in the theoretically calculated electron power-density profiles which can be directly correlated to the standard experimental chordal hard x-ray profiles. It thus seems that fluctuation effects must be included in determining rf current-density profiles
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