122800842
ANYONS AND SUPERCONDUCTIVITY: RANDOM PHASE APPROXIMATION
The two-dimensional ideal gas of particles obeying ν fractional statistics is recast as an interacting Fermi gas with long-range gauge potentials. A self-consistent dielectric description of the random phase approximation (RPA) provides a concise expression for the linear response of the fractional statistics gas to an external electromagnetic field. The RPA, believed to be correct for the present case of long-range interactions, yields two central results that are classic features of superconductivity: (1) a sharp undamped collective mode with a linear dispersion relation at long wavelengths: (2) a gauge-invariant Meissner effect in the transverse response to an external magnetic field.
12521588
Quantum mechanics of the fractional-statistics gas: Particle-hole interaction.
We compute the collective-mode spectrum of the fractional-statistics gas using the set of single particle-hole pairs of the Hartree-Fock ground state as a variational basis. We find that the particle-hole interaction reduces the energy of this mode to a finite value but does not cause it to disperse linearly to zero at long wavelengths, as would be expected of a superfluid. We attribute this to a flaw in the variational ground state, implicitly rectified by computing the response functions in the random-phase approximation. The formalism introduced in this paper provides the machinery for performing precise versions of such calculations.
39526102
Random-phase approximation in the fractional-statistics gas.
The random-phase approximation for a gas of particles obeying (1/2) fractional statistics, in the context of Feynman perturbation theory performed in the fermion representation, is shown to yield a gauge-invariant Meissner effect with full screening in the ground state, a coherence length comparable with the interparticle spacing, and a linearly dispersing undamped collective mode.
31625783
Quantum mechanics of the fractional-statistics gas: Hartree-Fock approximation.
The two-dimensional ideal gas of particles obeying {nu} fractional statistics is transformed to the Fermi representation and studied in the Hartree-Fock approximation. The extremal ground state is shown to be composed of Landau orbitals. When the filling factor (1{minus}{nu}){sup {minus}1} of the ground state is an integer, a logarithmically large energy gap appears in the single-particle excitation spectrum, and the particle and hole states are charged vortices with circulation {plus minus}(1{minus}{nu}){ital h}/{ital m}. The linear dependence of the total energy on the density, together with the presence of this gap, suggests that the true ground state at these fractions is a superfluid.
37135860
Efficiently enclosing the compact binary parameter space by singular-value decomposition
Gravitational-wave searches for the merger of compact binaries use matched filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high density. Previously it has been shown that singular-value decomposition can reduce the effective number of filters required to search the data. Here we study how the basis provided by the singular-value decomposition changes dimension as a function of template-bank density. We will demonstrate that it is sufficient to use the basis provided by the singular-value decomposition of a low-density bank to accurately reconstruct arbitrary points within the boundaries of the template bank. Since this technique is purely numerical, it may have applications to interpolating the space of numerical relativity waveforms.