Quantum turbulence and correlations in Bose-Einstein condensate collisions

We investigate numerically simulated collisions between experimentally realistic Bose-Einstein condensate wavepackets, within a regime where highly populated scattering haloes are formed. The theoretical basis for this work is the truncated Wigner method, for which we present a detailed derivation, paying particular attention to its validity regime for colliding condensates. This paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)] and we investigate both single-trajectory solutions, which reveal the presence of quantum turbulence in the scattering halo, and ensembles of trajectories, which we use to calculate quantum-mechanical correlation functions of the field

Non-Markovian master equation for a damped oscillator with time-varying parameters

We derive an exact non-Markovian master equation that generalizes the previous work [Hu, Paz and Zhang, Phys. Rev. D {\bf 45}, 2843 (1992)] to damped harmonic oscillators with time-varying parameters. This is achieved by exploiting the linearity of the system and operator solution in Heisenberg picture. Our equation governs the non-Markovian quantum dynamics when the system is modulated by external devices. As an application, we apply our equation to parity kick decoupling problems. The time-dependent dissipative coefficients in the master equation are shown to be modified drastically when the system is driven by $\pi$ pulses. For coherence protection to be effective, our numerical results indicate that kicking period should be shorter than memory time of the bath. The effects of using soft pulses in an ohmic bath are also discussed

Solitary-wave description of condensate micro-motion in a time-averaged orbiting potential trap

We present a detailed theoretical analysis of micro-motion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time dependent behaviour of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular centre of mass motion in the lab frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.Comment: 12 pages, 2 figure

The dynamics of loop formation in a semiflexible polymer

The dynamics of loop formation by linear polymer chains has been a topic of several theoretical/experimental studies. Formation of loops and their opening are key processes in many important biological processes. Loop formation in flexible chains has been extensively studied by many groups. However, in the more realistic case of semiflexible polymers, not much results are available. In a recent study (K. P. Santo and K. L. Sebastian, Phys. Rev. E, \textbf{73}, 031293 (2006)), we investigated opening dynamics of semiflexible loops in the short chain limit and presented results for opening rates as a function of the length of the chain. We presented an approximate model for a semiflexible polymer in the rod limit, based on a semiclassical expansion of the bending energy of the chain. The model provided an easy way to describe the dynamics. In this paper, using this model, we investigate the reverse process, i.e., the loop formation dynamics of a semiflexible polymer chain by describing the process as a diffusion-controlled reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain which leads to results that are physically expected. Such a multidimensional analysis leading to these results does not seem to exist in the literature so far.Comment: 37 pages 4 figure

Field-Induced Magnetic and Structural Domain Alignment in PrO2

We present a neutron diffraction study of the magnetic structure of single crystal PrO2 under applied fields of 0-6 T. As the field is increased, changes are observed in the magnetic Bragg intensities. These changes are found to be irreversible when the field is reduced, but the original intensities can be recovered by heating to T > 122 K, then re-cooling in zero field. The antiferromagnetic ordering temperature TN = 13.5 K and the magnetic periodicity are unaffected by the applied field. We also report measurements of the magnetic susceptibility of single crystal PrO2 under applied fields of 0-7 T. These show strong anisotropy, as well as an anomaly at T = 122 +/- 2 K which coincides with the temperature TD = 120 +/- 2 K at which a structural distortion occurs. For fields applied along the [100] direction the susceptibility increases irreversibly with field in the temperature range TN < T < TD. However, for fields along [110] the susceptibility is independent of field in this range. We propose structural domain alignment, which strongly influences the formation of magnetic domains below TN, as the mechanism behind these changes.Comment: 11 pages, 13 figures, 5 tables. Minor typographical changes in v

Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift velocity in the limits of low and high particle inertia, is derived. It is also shown that some previously proposed stochastic models are not compatible with this transport equation in the limit of high particle inertia. The drift and diffusion parameters of these stochastic differential equations are then estimated using direct numerical simulation (DNS) data. It is observed that, contrary to the conventional modeling, they are highly space dependent and anisotropic. To investigate the performance of the present stochastic model, a comparison is made with DNS data as well as with two different stochastic models. A good prediction of the first and second order statistical moments of the particle and fluid seen velocities is obtained with the three models considered. Even for some components of the triple particle velocity correlations, an acceptable accordance is noticed. The performance of the three different models mainly diverges for the particle concentration and the drift velocity. The proposed model is seen to be the only one which succeeds in predicting the good evolution of these latter statistical quantities for the range of particle inertia studied

Winding up by a quench: vortices in the wake of rapid Bose-Einstein condensation

A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. We use quantum kinetic theory to show that this mechanism, originally postulated in the cosmological context, and analysed so far only on the mean field classical level, should allow spontaneous generation of vortex lines in trapped Bose-Einstein condensates of simple topology, or of winding number in toroidal condensates.Comment: 4 pages, 2 figures; misprint correcte

The Morphologies of the Small Magellanic Cloud

We compare the distribution of stars of different spectral types, and hence mean age, within the central SMC and find that the asymmetric structures are almost exclusively composed of young main sequence stars. Because of the relative lack of older stars in these features, and the extremely regular distribution of red giant and clump stars in the SMC central body, we conclude that tides alone are not responsible for the irregular appearance of the central SMC. The dominant physical mechanism in determining the current-day appearance of the SMC must be star formation triggered by a hydrodynamic interaction between gaseous components. These results extend the results of population studies (cf. Gardiner and Hatzidimitriou) inward in radius and also confirm the suggestion of the spheroidal nature of the central SMC based on kinematic arguments (Dopita et al; Hardy, Suntzeff & Azzopardi). Finally, we find no evidence in the underlying older stellar population for a ``bar'' or ``outer arm'', again supporting our classification of the central SMC as a spheroidal body with highly irregular recent star formation.Comment: 8 pages, accepted for publication in ApJ Letters (higher quality figures available at http://ngala.as.arizona.edu/dennis/mcsurvey.html

Unraveling quantum dissipation in the frequency domain

We present a quantum Monte Carlo method for solving the evolution of an open quantum system. In our approach, the density operator evolution is unraveled in the frequency domain. Significant advantages of this approach arise when the frequency of each dissipative event conveys information about the state of the system.Comment: 4 pages, 4 Postscript figures, uses RevTe

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