Quantitative test of thermal field theory for Bose-Einstein condensates II

We have recently derived a gapless theory of the linear response of a Bose-condensed gas to external perturbations at finite temperature and used it to explain quantitatively the measurements of condensate excitations and decay rates made at JILA [D. S. Jin et.al., Phys. Rev. Lett. 78, 764 (1997)]. The theory describes the dynamic coupling between the condensate and non-condensate via a full quasiparticle description of the time-dependent normal and anomalous averages and includes all Beliaev and Landau processes. In this paper we provide a full discussion of the numerical calculations and a detailed analysis of the theoretical results in the context of the JILA experiment. We provide unambiguous proof that the dipole modes are obtained accurately within our calculations and present quantitative results for the relative phase of the oscillations of the condensed and uncondensed atom clouds. One of the main difficulties in the implementation of the theory is obtaining results which are not sensitive to basis cutoff effects and we have therefore developed a novel asymmetric summation method which solves this problem and dramatically improves the numerical convergence. This new technique should make the implementation of the theory and its possible future extensions feasible for a wide range of condensate populations and trap geometries.Comment: 23 pages, 11 figures, revtex 4. Submitted to PRA. Sequel to: S. A. Morgan et al, PRL, 91, 250403 (2003

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Precise Formulation of Neutrino Oscillation in the Earth

We give a perturbation theory of neutrino oscillation in the Earth. The perturbation theory is valid for neutrinos with energy E \gsim 0.5 GeV. It is formulated using trajectory dependent average potential. Non-adiabatic contributions are included as the first order effects in the perturbation theory. We analyze neutrino oscillation with standard matter effect and with non-standard matter effect. In a three flavor analysis we show that the perturbation theory gives a precise description of neutrino conversion in the Earth. Effect of the Earth matter is substantially simplified in this formulation.Comment: References added, 21 pages, 10 figures, version to appear in PR

Qualitative Criterion for Interception in a Pursuit/Evasion Game

A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from an initial position. A sufficient and necessary conditon that an opportunity to intercept always exist is that, after some initial time, the future cone of the target be contained within the future cone of the interceptor. The sufficient condition may be regarded as a kind of Nash equillibrium.Comment: 8 pages; revsions and corrigend

Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice

By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasi-periodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. {Finally, we consider the localization of a BEC in a random 1D potential in the form of several identical repulsive spikes arbitrarily distributed in space

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation we study different aspects of the localization of a non-interacting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a non-interacting BEC. We also simulate the non-linear dynamics when a harmonically trapped BEC is suddenly released into a quasi-periodic potential, {as done experimentally in a laser speckle potential [Billy et al., Nature 453, 891 (2008)]$ We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.Comment: 8 page

Components of the gravitational force in the field of a gravitational wave

Gravitational waves bring about the relative motion of free test masses. The detailed knowledge of this motion is important conceptually and practically, because the mirrors of laser interferometric detectors of gravitational waves are essentially free test masses. There exists an analogy between the motion of free masses in the field of a gravitational wave and the motion of free charges in the field of an electromagnetic wave. In particular, a gravitational wave drives the masses in the plane of the wave-front and also, to a smaller extent, back and forth in the direction of the wave's propagation. To describe this motion, we introduce the notion of `electric' and `magnetic' components of the gravitational force. This analogy is not perfect, but it reflects some important features of the phenomenon. Using different methods, we demonstrate the presence and importance of what we call the `magnetic' component of motion of free masses. It contributes to the variation of distance between a pair of particles. We explicitely derive the full response function of a 2-arm laser interferometer to a gravitational wave of arbitrary polarization. We give a convenient description of the response function in terms of the spin-weighted spherical harmonics. We show that the previously ignored `magnetic' component may provide a correction of up to 10 %, or so, to the usual `electric' component of the response function. The `magnetic' contribution must be taken into account in the data analysis, if the parameters of the radiating system are not to be mis-estimated.Comment: prints to 29 pages including 9 figures, new title, additional explanations and references in response to referee's comments, to be published in Class. Quant. Gra

Potential vorticity, angular momentum and inertial instabilities in the Martian atmospheric circulation from assimilated analyses of MGS/TES

Data based on re-analyses of the MGS/TES observations have been used to map distributions of potential vorticity and axial absolute angular momentum per unit mass. The data, discussed in more details in [1] and [2] stretches over nearly three Martian years and cover a wide range of atmospheric conditions. The spatial distribution and variation in time of angular momentum and potential vorticity are closely related to the zonal-mean circulation. Maps of potential vorticity distributions have been used to establish regions and times favourable for inertial instabilities. A narrow region near the equator which extends throughout the atmosphere is shown to be able to sustain inertial instabilities at different times of the year. The presence of inertial instabilities is predicted from the necessary (but not sufficient) condition for the occurrence of regions of atmosphere with PV of opposite sign to that of the planetary vorticity (PVanomalies). These regions are characterized as being favorable to mixing on small scales, while at larger scales there may be potential links to Rossby wave breaking (Knox et. al. 2005][3]. Analyses of the data indicates a hemispheric asymmetry where the northern hemisphere is more favorable to inertial instabilities particularly during NH winter. Barnes et. al. (1996)[4] used a global Martian circulation model to find that, during dusty solstice conditions, the Martian tropical and mid-latitude atmospheric circulation approximates to an angular-momentum conserving Hadley circulation, and is responsible for creating regions near the equator of low potential vorticity. Using the assimilated data we re-examine these results for a wider range of atmospheric states, including the period of the 2001 planet-encircling dust storm