Article

# Quantum lattice gas representation of some classical solitons

Department of Physics, William & Mary, Williamsburg, VA 23187, USA; Air Force Research Laboratory, 29 Randolph Road, Hanscom AFB, MA 01731, USA; Department of Electrical & Computer Engineering, Old Dominion University, Norfolk, VA 23529, USA

Physics Letters A (Impact Factor: 1.63). 01/2003; DOI: 10.1016/S0375-9601(03)00334-7 - [Show abstract] [Hide abstract]

**ABSTRACT:**This dissertation focuses on two connected areas: quantum computation and quantum control. Two proposals to construct a quantum computer, using nuclear magnetic resonance (NMR) and superconductivity, are introduced. We give details about the modeling, qubit realization, one and two qubit gates and measurement in the language that mathematicians can understand and fill gaps in the original literatures. Two experimental examples using liquid NMR are also presented. Then we proceed to investigate an example of quantum control, that of a magnetometer using quantum feedback. Previous research has shown that feedback makes the measurement robust to an unknown parameter, the number of atoms involved, with the assumption that the feedback is noise free. To evaluate the effect of the feedback noise, we extend the original model by an input noise term. We then compute the steady state performance of the Kalman filter for both the closed-loop and open-loop cases and retrieve the estimation error variances. The results are compared and criteria for evaluating the effects of input noise are obtained. Computations and simulations show that the level of input noise affects the measurement by changing the region where closed loop feedback is beneficial. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, the lattice Boltzmann method for convection-diffusion equation with source term is applied directly to solve some important nonlinear complex equations, including nonlinear Schrödinger (NLS) equation, coupled NLS equations, Klein-Gordon equation and coupled Klein-Gordon-Schrödinger equations, by using complex-valued distribution function and relaxation time. Detailed simulations of these equations are carried out. Numerical results agree well with the analytical solutions, which show that the lattice Boltzmann method is an effective numerical solver for complex nonlinear systems.01/1970: pages 818-825; - [Show abstract] [Hide abstract]

**ABSTRACT:**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.Physical Review E 10/2011; 84(4 Pt 2):046713. · 2.31 Impact Factor

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