Dislocation-Mediated Melting in Superfluid Vortex Lattices

We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature -- rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.Comment: 9 pages, 2 figure

Rapidly rotating Bose-Einstein condensates in anharmonic potentials

Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.Comment: 5 pages, 5 figure

Theory of vortex-lattice melting in a one-dimensional optical lattice

We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.Comment: 17 pages, 17 figures, submitted to Phys. Rev. A, references update

Isostaticity in two dimensional pile of rigid disks

We study the static structure of piles made of polydisperse disks in the rigid limit with and without friction using molecular dynamic simulations for various elasticities of the disks and pile preparation procedures. The coordination numbers are calculated to examine the isostaticity of the pile structure. For the frictionless pile, it is demonstrated that the coordination number converges to 4 in the rigid limit, which implies that the structure of rigid disk pile is isostatic. On the other hand, for the frictional case with the infinite friction constant, the coordination number depends on the preparation procedure of the pile, but we find that the structure becomes very close to isostatic with the coordination number close to 3 in the rigid limit when the pile is formed through the process that tends to make a pile of random configuration.Comment: 3 pages, 3 figures, Submitted to J. Phys. Soc. Jp

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel

Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion (SFD) to the two-dimensional diffusion regime is investigated. This transition (regarding the calculation of the scaling exponent ($\alpha$) of the MSD $$ $\propto t^{\alpha}$) as a function of the width of the channel, is shown to change depending on the channel's confinement profile. In particular the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp/stepwise (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.Comment: 13 pages, 11 figure

Coherence simplices

Coherence simplices are generic topological correlation-function defects supported by a hierarchy of coherence functions. We classify coherence simplices based on their topology and discuss their structure and dynamics, together with their relevance to several physical systems.Comment: 15 pages, 4 figures, to appear in New Journal of Physic

Реалізація деяких принципів побудови візерунків засобами операторів мови MAPLE

The principles of the construction and ornamentation among the algorithmic language Maple.Рассмотрены принципы составления и построения орнаментов в среде алгоритмического языка Maple.Розглянуто принципи складання та побудови орнаментів у середовищі алгоритмічної мови Maple

Spectroscopic time-series analysis of R Canis Majoris

R Canis Majoris is the prototype of a small group of Algol-type stars showing short orbital periods and low mass ratios. A previous detection of short-term oscillations in its light curve has not yet been confirmed. We investigate a new time series of high-resolution spectra with the aim to derive improved stellar and system parameters, to search for the possible impact of a third component in the observed spectra, to look for indications of activity in the Algol system, and to search for short-term variations in radial velocities. We disentangled the composite spectra into the spectra of the binary components. Then we analysed the resulting high signal-to-noise spectra of both stars. Using a newly developed program code based on an improved method of least-squares deconvolution, we were able to determine the radial velocities of both components also during primary eclipse. This allowed us to develop a better model of the system including the Rossiter-McLaughlin effect and to derive improved orbital parameters. Combining the results with those from spectrum analysis, we obtain accurate stellar and system parameters. We further deduce at least one oscillation frequency of 21.38 c/d. It could be detected during primary eclipses only and confirms a previous photometric finding. Results point to an amplitude amplification of non-radial pulsation modes due to the eclipse mapping effect. The presence of a He\,I line in the spectra indicates mass transfer in the R CMa system. Calculations of its Roche geometry give evidence that the cool secondary component may fill its Roche lobe. No evidence of a third body in the system could be found in the observed spectra.Comment: 12 pages, 14 figures, 5 table