Search results for " singularity"
showing 10 items of 203 documents
Symmetry breaking and singularity structure in Bose-Einstein condensates
2012
We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the tra…
Sound velocity and dimensional crossover in a superfluid Fermi gas in an optical lattice
2005
We study the sound velocity in cubic and non-cubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothened by interactions and eventually vanishes when interactions are strong enough. For non-cubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the 1D and 2D limits.
Band Tails in a Disordered System
1993
In crystalline solids electronic excitations have a band structure. Energy intervals, in which excitations occur, are separated by band gaps, where the density of electronic states vanishes. At the band edge the density-of-states (DOS) has power law singularities, so-called van Hove singularities.
Correlation Functions and Finite–Size Effects in Granular Media
2014
A model is considered, where the local order parameter is an n–component vector. This model allows us to calculate correlation functions, describing the correlations between local order parameter at different spatial coordinates. The longitudinal and transverse Fourier–transformed two–point correlation functions \(G_{\parallel }(\mathbf{k})\) and \(G_{\perp }(\mathbf{k})\) in presence of an external field h are considered in some detail. In the thermodynamic limit, these correlation functions exhibit the so-called Goldstone mode singularities below certain critical temperature at an infinitesimal external field \(h = +0\). The actual model can be applied to granular media, in which case it …
Singularities in L^p-quasidisks
2021
We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remove singularities. We give, in a connection of quasidisks, a sharp integrability condition for the distortion function to answer this question. peerReviewed
On numerical relativistic hydrodynamics and barotropic equations of state
2012
The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.
Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles
2017
Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $\textbf 2 \to \textbf 2$, $\textbf 2 \to \textbf 3$ and $\textbf 3 \to \textbf 3$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle $K$ matrix has no singularities below the three-particle threshold. The quan…
Regularized Euler-alpha motion of an infinite array of vortex sheets
2016
We consider the Euler- $$\alpha $$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.
The Palatini Approach Beyond Einstein’s Gravity
2014
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these theories, governed by second-order equations and having no new degrees of freedom, makes them specially suitable to address certain aspects of quantum gravity phenomenology, construct nonsingular bouncing cosmologies, and explore black hole interiors, which in the Reissner-Nordstrom case develop a compact core of finite density instead of a point-like singularity.
Geons in Palatini Theories of Gravity
2017
An explicit implementation of geons in the context of gravitational theories extending general relativity is discussed in detail. Such extensions are formulated in the Palatini approach, where metric and affine connection are regarded as independent entities. This formulation is inspired on the macroscopic description of the physics of crystalline structures with defects in the context of solid-state physics, whose study can provide valuable lessons for going beyond GR. We discuss several theories for the gravitational field including additional contributions of the Ricci tensor in four and higher dimensions. As opposed to the standard metric approach, the Palatini formulation generates gho…