A new unitary quantum lattice gas (QLG) algorithm is proposed as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii equation for Bose-Einstein Condensates (BECs). This consists of an interleaved sequence of unitary collide-stream operators and is tested on the 1D nonlinear Schrodinger (NLS) equation since exact soliton solutions are well known. An earlier QLG algorithm, based on the[GRAPHICS]collision operator has been found to have limited application to spinor-BECs. Here, a new unitary collision operator, based on the recent QLG of Yepez for the Dirac particle, is used to model the 1D NLS soliton-soliton problem. It is found that this new unitary algorithm can handle parameters (soliton amplitudes and speeds) a factor of over 20 greater than those under the previous[GRAPHICS]algorithm.[Re: (v.07) To be submitted to special issue 'Plasma and Fluid Dynamics: Computational, Experimental and Theoretical Advancement']

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfven Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here. (C) 2014 AIP Publishing LLC.

Turbulence is of vital interest and importance to the study of fluid dynamics Pope (1990). In classical physics, turbulence was first studied carefully for incompressible flows whose evolution was given by the Navier-Stokes equations. One of the most celebrated results of incompressible classical turbulence (CT) is the existence of an inertial range with the cascade of kinetic energy from large to small spatial scales until one reaches scale lengths on the order of the dissipationwave length and the eddies/vortices are destroyed. The Kolmogorov kinetic energy spectrum in this inertial range follows the power law in wave number space.

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 algorithm, is employed to simulate the Bose-Einstein condensate governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincaré recurrence time. It is demonstrated that such short recurrence times are destroyed by stronger nonlinear interaction. The similar loss of Poincaré recurrence is also seen in the 3D GP equation. Various initial conditions are considered in an attempt to discern if 2D QT exhibits inverse cascades as is seen in 2D classical turbulence (CT). In our simulation parameter regimes, no dual cascade spectra were observed for 2D QT-unlike that seen in 2D CT.

A unitary qubit lattice algorithm, which scales almost perfectly to the full number of cores available (e.g., 216000 cores on a CRAY XT5), is used to examine quantum turbulence and its interrelationship to classical turbulence with production runs on grids up to 57603. The maximal grids achievable by conventional CFD for quantum turbulence is just 20483, and artificial dissipation had to be introduced. Our unitary algorithms preserve the Hamiltonian structure of the Gross-Pitaevskii equation which describes quantum turbulence in a zero-temperature Bose-Einstein condensate (BEC). As a result, parameter regimes have been uncovered which exhibit very short Poincare recurrence time, as well as a strong triple cascade structure in the kinetic energy spectrum. Moreover, a detailed examination of the incompressible kinetic energy spectrum has revealed for the first time within a turbulence simulation the k-17/5 quantum Kelvin wave cascade. By generalizing the unitary entanglement operators on the 2 qubits, a finite temperature BEC system is examined. These unitary qubit lattice algorithms are directly applicable to quantum computers as they become available.

Quantum vortex structures and energy cascades are examined for two dimensional quantum turbulence (2D QT) using a special unitary evolution algorithm. The qubit lattice gas (QLG) algorithm, is employed to simulate the weakly-coupled 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 very short Poincare recurrence time. This short recurrence time is destroyed as the nonlinear interaction energy is increased. Energy cascades for 2D QT are considered to examine whether 2D QT exhibits the inverse cascades of 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.

The time evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) gas is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-stream operators, a qubit lattice gas algorithm is devised, which on taking moments, recovers the Gross-Pitaevskii (GP) equation under diffusion ordering (time scales as length(2)). Unexpectedly, there is a class of initial states whose Poincaré recurrence time is extremely short and which, as the grid resolution is increased, scales with diffusion ordering (and not as length(3)). The spectral results of J. Yepez et al. [Phys. Rev. Lett. 103, 084501 (2009).] for quantum turbulence are revised and it is found that it is the compressible kinetic energy spectrum that exhibits three distinct spectral regions: a small-k classical-like Kolmogorov k(-5/3), a steep semiclassical cascade region, and a large-k quantum vortex spectrum k(-3). For most evolution times the incompressible kinetic energy spectrum exhibits a somewhat robust quantum vortex spectrum of k(-3) for an extended range in k with a k(-3.4) spectrum for intermediate k. For linear vortices of winding number 1 there is an intermittent loss of the quantum vortex cascade with its signature seen in the time evolution of the kinetic energy E(kin)(t), the loss of the quantum vortex k(-3) spectrum in the incompressible kinetic energy spectrum as well as the minimalization of the vortex core isosurfaces that would totally inhibit any Kelvin wave vortex cascade. In the time intervals around these intermittencies the incompressible kinetic energy also exhibits a multicascade spectrum.