A New Godunov Scheme for MHD, with Application to the MRI in disks

We describe a new numerical scheme for MHD which combines a higher order Godunov method (PPM) with Constrained Transport. The results from a selection of multidimensional test problems are presented. The complete test suite used to validate the method, as well as implementations of the algorithm in both F90 and C, are available from the web. A fully three-dimensional version of the algorithm has been developed, and is being applied to a variety of astrophysical problems including the decay of supersonic MHD turbulence, the nonlinear evolution of the MHD Rayleigh-Taylor instability, and the saturation of the magnetorotational instability in the shearing box. Our new simulations of the MRI represent the first time that a higher-order Godunov scheme has been applied to this problem, providing a quantitative check on the accuracy of previous results computed with ZEUS; the latter are found to be reliable.Comment: 11 pages, style files included, Conference Proceedings: "Magnetic Fields in the Universe: from Laboratory and Stars to Primordial Structures", More information on Athena can be found at http://www.astro.princeton.edu/~jstone/athena.htm

Correcting low-frequency noise with continuous measurement

Low-frequency noise presents a serious source of decoherence in solid-state qubits. When combined with a continuous weak measurement of the eigenstates, the low-frequency noise induces a second-order relaxation between the qubit states. Here we show that the relaxation provides a unique approach to calibrate the low-frequency noise in the time-domain. By encoding one qubit with two physical qubits that are alternatively calibrated, quantum logic gates with high fidelity can be performed.Comment: 10 pages, 3 figures, submitte

Impending carotid blowout stabilization using an LT-D tube

Adequate stabilization of a patient presenting with a carotid blowout is one of the most challenging issues an on-call ENT surgeon can be confronted with. Reducing the bleeding and securing the airway are essential before more definitive management. We present the case of a 72-year-old patient with head and neck cancer who arrived at the emergency room with a carotid blowout and who was successfully stabilized using a King LT-D ventilation tube

Bogoliubov dynamics of condensate collisions using the positive-P representation

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description as the number of realisations grows. The numerical effort grows linearly with the size of the computational lattice. We benchmark the efficiency and accuracy of our description against Wigner distribution and exact positive-P methods. We consider its regime of applicability, and show that it is the most efficient method in the common situation - when the total particle number in the system is insufficient for a truncated Wigner treatment.Comment: 9 pages. 5 figure

Number-Phase Wigner Representation for Efficient Stochastic Simulations

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many problems using these techniques remain intractable over long integrations times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase space representations. This process requires an effective sampling of a non-classical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.Comment: 7 pages, 1 figur

The stochastic Gross-Pitaevskii equation II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum conservation, and is based on a quasi-classical Wigner function representation of a "high temperature" master equation for a Bose gas, which includes only modes below an energy cutoff E_R that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provide noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation, and by the feasibility of its numerical implementation.Comment: 24 pages of LaTeX, one figur

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.

Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure

Number-Phase Wigner Representation for Scalable Stochastic Simulations of Controlled Quantum Systems

Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as BEC and atom lasers, full quantum field simulations must rely on scalable stochastic methods whose convergence time is restricted by the use of representations based on coherent states. Here we show that typical measurements on atom-optical systems have a common form that allows for an efficient simulation using the number-phase Wigner (NPW) phase-space representation. We demonstrate that a stochastic method based on the NPW can converge over an order of magnitude longer and more precisely than its coherent equivalent. This opens the possibility of realistic simulations of controlled multi-mode quantum systems.Comment: 5 pages, 1 figur