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

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

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

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

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

Effect of Fluctuations on Lower Hybrid Power Deposition and Hard X-Ray Detection

The hard X-ray intensity radial profiles from lower hybrid current drive experiments are interpreted as being correlated with fluctuations in the bulk plasma. This view seems to be dictated by comparing the hard X-ray data for various n║ with the Monte Carlo solutions of the lower hybrid wave energy deposition on plasma electrons. Information on internal magnetic fluctuations may, under certain conditions, be unfolded from a n║ scan of the hard X-ray profiles

Effect of Magnetic and Density Fluctuations on the Propagation of Lower Hybrid Waves in Tokamaks

Lower hybrid waves have been used extensively for plasma heating, current drive, and ramp-up as well as sawteeth stabilization, The wave kinetic equation for lower hybrid wave propagation is extended to include the effects of both magnetic and density fluctuations. This integral equation is then solved by Monte Carlo procedures for a toroidal plasma. It is shown that even for magnetic/density fluctuation levels on the order of 10-4, there are significant magnetic fluctuation effects on the wave power deposition into the plasma. This effect is quite pronounced if the magnetic fluctuation spectrum is peaked within the plasma. For Alcator-C-Mod [I. H. Hutchinson and the Alcator Group, Proceedings of the IEEE 13th Symposium on Fusion Engineering (IEEE, New York, 1990), Cat. No. 89CH 2820-9, p. 13] parameters, it seems possible to be able to infer information on internal magnetic fluctuations from hard x-ray data-especially since the effects of fluctuations on electron power density can explain the hard x-ray data from the JT-60 tokamak [H. Kishimoto and JT-60 Team, in Plasma Physics and Controlled Fusion (International Atomic Energy Agency, Vienna, 1989), Vol. I, p. 67]