Two-Dimensional Wigner Crystal in Anisotropic Semiconductor

We investigate the effect of mass anisotropy on the Wigner crystallization transition in a two-dimensional (2D) electron gas. The static and dynamical properties of a 2D Wigner crystal have been calculated for arbitrary 2D Bravais lattices in the presence of anisotropic mass, as may be obtainable in Si MOSFETs with (110) surface. By studying the stability of all possible lattices, we find significant change in the crystal structure and melting density of the electron lattice with the lowest ground state energy.Comment: 4 pages, revtex, 4 figure

London equation studies of thin-film superconductors with a triangular antidot lattice

We report on a study of vortex pinning in nanoscale antidot defect arrays in the context of the London Theory. Using a wire network model, we discretize the array with a fine mesh, thereby providing a detailed treatment of pinning phenomena. The use of a fine grid has enabled us to examine both circular and elongated defects, patterned in the form of a rhombus. The latter display pinning characteristics superior to circular defects constructed with the similar area. We calculate pinning potentials for defects containing zero and single quanta, and we obtain a pinning phase diagram for the second matching field, $H = 2 \Phi_{o}$.Comment: 10 pages and 14 figure

An experimental study to discriminate between the validity of diffraction theories for off-Bragg replay

We show that experiments clearly verify the assumptions made by the first-order two-wave coupling theory for one dimensional lossless unslanted planar volume holographic gratings using the beta-value method rather than Kogelnik's K-vector closure method. Apart from the fact that the diffraction process is elastic, a much more striking difference between the theories becomes apparent particularly in the direction of the diffracted beam in off-Bragg replay. We therefore monitored the direction of the diffracted beam as a function of the off-Bragg replay angle in two distinct cases: [a] the diffracted beam lies in the plane of incidence and [b] the sample surface normal, the grating vector and the incoming beam do not form a plane which calls for the vectorial theory and results in conical scattering.Comment: Corrected Eqs. (3) & (6); 14 pages, 8 figure

Universality in the Screening Cloud of Dislocations Surrounding a Disclination

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective fractional charge which can be computed from the properties of the grain boundaries forming the dislocation cloud. Expressions are also given when the crystal is subjected to an external two-dimensional pressure. The analytical results are generalized to a scaling form for the energy which up to core energies is given by the Young modulus of the crystal times a universal function. The accuracy of the universality hypothesis is numerically checked to high accuracy. The numerical approach, based on a generalization from previous work by S. Seung and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own and allows to compute the energy for an {\em arbitrary} distribution of defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy} with very minor additional computational effort. Some implications for recent experimental, computational and theoretical work are also discussed.Comment: 35 pages, 21 eps file

Stability of the lattice formed in first-order phase transitions to matter containing strangeness in protoneutron stars

Well into the deleptonization phase of a core collapse supernova, a first-order phase transition to matter with macroscopic strangeness content is assumed to occur and lead to a structured lattice defined by negatively charged strange droplets. The lattice is shown to crystallize for expected droplet charges and separations at temperatures typically obtained during the protoneutronstar evolution. The melting curve of the lattice for small spherical droplets is presented. The one-component plasma model proves to be an adequate description for the lattice in its solid phase with deformation modes freezing out around the melting temperature. The mechanical stability against shear stresses is such that velocities predicted for convective phenomena and differential rotation during the Kelvin-Helmholtz cooling phase might prevent the crystallization of the phase transition lattice. A solid lattice might be fractured by transient convection, which could result in anisotropic neutrino transport. The melting curve of the lattice is relevant for the mechanical evolution of the protoneutronstar and therefore should be included in future hydrodynamics simulations.Comment: accepted for publication in Physical Review

Skymrion lattice melting in the quantum Hall system

The melting and magnetic disordering of the skyrmion lattice in the quantum Hall system at filling factor $\nu\approx 1$ are studied. A Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to describe the coupled magnetic and translational degrees of freedom. The non-trivial magnetic properties of the skyrmion system stem from the in-plane components of the non-collinear magnetization in the vicinity of skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the `particles' are the topological defects of the XY model (vortices) and of the lattice (dislocations and disclinations). The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the skyrmion system. It results in a rich T=0 phase diagram. We propose that the triangular and square skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.Comment: 15 pages with 5 figures. Minor revisions. Important reference to M. Rao, S. Sengupta, and R. Shankar, Phys. Rev. Lett. 79, 3998 (1997) adde

Critical Dynamics of Magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole--dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon--spin--resonance, electron--spin--resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three--dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin--wave spectrum in two--dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.Comment: Review article (154 pages, figures included

Atom-optics hologram in the time domain

The temporal evolution of an atomic wave packet interacting with object and reference electromagnetic waves is investigated beyond the weak perturbation of the initial state. It is shown that the diffraction of an ultracold atomic beam by the inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram, whose thickness is proportional to the interaction time. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis a method for reconstruction of the object image with matter waves is offered.Comment: RevTeX, 13 pages, 8 figures; minor grammatical change

Role of dipolar and exchange interactions in the positions and widths of EPR transitions for the single-molecule magnets Fe8 and Mn12

We examine quantitatively the temperature dependence of the linewidths and line shifts in electron paramagnetic resonance experiments on single crystals of the single-molecule magnets Fe$_8$ and Mn$_{12}$, at fixed frequency, with an applied magnetic field along the easy axis. We include inter-molecular spin-spin interactions (dipolar and exchange) and distributions in both the uniaxial anisotropy parameter $D$ and the Land\'{e} $g$-factor. The temperature dependence of the linewidths and the line shifts are mainly caused by the spin-spin interactions. For Fe$_8$ and Mn$_{12}$, the temperature dependence of the calculated line shifts and linewidths agrees well with the trends of the experimental data. The linewidths for Fe$_8$ reveal a stronger temperature dependence than those for Mn$_{12}$, because for Mn$_{12}$ a much wider distribution in $D$ overshadows the temperature dependence of the spin-spin interactions. For Fe$_8$, the line-shift analysis suggests two competing interactions: a weak ferromagnetic exchange coupling between neighboring molecules and a longer-ranged dipolar interaction. This result could have implications for ordering in Fe$_8$ at low temperatures.Comment: published versio

N-body simulations of gravitational dynamics

We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N-body simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu