Gravitational Radiation from Preheating with Many Fields

Parametric resonances provide a mechanism by which particles can be created just after inflation. Thus far, attention has focused on a single or many inflaton fields coupled to a single scalar field. However, generically we expect the inflaton to couple to many other relativistic degrees of freedom present in the early universe. Using simulations in an expanding Friedmann-Lema\^itre-Robertson-Walker spacetime, in this paper we show how preheating is affected by the addition of multiple fields coupled to the inflaton. We focus our attention on gravitational wave production--an important potential observational signature of the preheating stage. We find that preheating and its gravitational wave signature is robust to the coupling of the inflaton to more matter fields.Comment: 7 pages, 8 figures, v2 submission version, thank you for comments

Phase diagram of the extended Hubbard chain with charge-dipole interactions

We consider a modified extended Hubbard model (EHM) which, in addition to the on-site repulsion U and nearest-neighbor repulsion V, includes polarization effects in second-order perturbation theory. The model is equivalent to an EHM with renormalized U plus a next-nearest-neighbor repulsion term. Using a method based on topological quantum numbers (charge and spin Berry phases), we generalize to finite hopping t the quantum phase diagram in one dimension constructed by van den Brink et al. (Phys. Rev. Lett. 75, 4658 (1995)). At hopping t=0 there are two charge density-wave phases, one spin density-wave phase and one intermediate phase with charge and spin ordering, depending on the parameter values. At t \neq 0 the nature of each phase is confirmed by studying correlation functions. However, in addition to the strong-coupling phases, a small region with bond ordering appears. The region occupied by the intermediate phase first increases and then decreases with increasing t, until it finally disappears for t of the order but larger than U. For small t, the topological transitions agree with the results of second order perturbation theory.Comment: 6 pages, 5 figures, two columns latex version. Accepted for publication in Physical Review B. Mistaken reference 16 has been correcte

Gravitational waves from self-ordering scalar fields

Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as $\Omega_{\rm GW}(f) \propto f^3$ with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer time, until a given mode which is initially superhorizon ($k\eta_* \ll 1$), enters the horizon, for $k\eta \gtrsim 1$, we find that the gravitational wave energy density is frequency independent, i.e. scale invariant. Moreover, its amplitude for a GUT scale scenario turns out to be within the range and sensitivity of BBO and marginally detectable by LIGO and LISA. This new gravitational wave background can compete with the one generated during inflation, and distinguishing both may require extra information.Comment: 21 pages, 2 figures, added discussion about numerical integration and a new figure to illustrate the scale-invariance of the GW power spectrum, conclusions unchange

On the shape of vortices for a rotating Bose Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived in Aftalion-Riviere Phys. Rev. A 64, 043611 (2001) in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex which needs to be minimized taking into account the anisotropy of the trap and the rotation term which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis while in the case of a cigar, the vortex is bent

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations

All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity

Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which remains in general arbitrary. Spacetimes for fluids fulfilling linear and polytropic state equations are explicitly derived; they describe, among others, stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate fermions, incoherent and pure radiation. As a by--product, we demonstrate the uniqueness of the constant energy density perfect fluid within the studied class of metrics. A full similarity of the perfect fluid solutions with constant energy density of the 2+1 and 3+1 gravities is established.Comment: revtex4, 8 page

Extended WKB method, resonances and supersymmetric radial barriers

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.Comment: 12 pages, 4 figures, 3 table

One- and many-body effects on mirages in quantum corrals

Recent interesting experiments used scanning tunneling microscopy to study systems involving Kondo impurities in quantum corrals assembled on Cu or noble metal surfaces. The solution of the two-dimensional one-particle Schrodinger equation in a hard wall corral without impurity is useful to predict the conditions under which the Kondo effect can be projected to a remote location (the quantum mirage). To model a soft circular corral, we solve this equation under the potential W*delta(r-r0), where r is the distance to the center of the corral and r0 its radius. We expand the Green's function of electron surface states Gs0 for r<r0 as a discrete sum of contributions from single poles at energies epsilon_i-I*delta_i. The imaginary part delta_i is the half-width of the resonance produced by the soft confining potential, and turns out to be a simple increasing function of epsilon_i. In presence of an impurity, we solve the Anderson model at arbitrary temperatures using the resulting expression for Gs0 and perturbation theory up to second order in the Coulomb repulsion U. We calculate the resulting change in the differential conductance Delta dI/dV as a function of voltage and space, in circular and elliptical corrals, for different conditions, including those corresponding to recent experiments. The main features are reproduced. The role of the direct hybridization between impurity and bulk, the confinement potential, the size of the corral and temperature on the intensity of the mirage are analyzed. We also calculate spin-spin correlation functions.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev. B. Calculations of spin correlations within an additional approximation adde

On the Transverse-Traceless Projection in Lattice Simulations of Gravitational Wave Production

It has recently been pointed out that the usual procedure employed in order to obtain the transverse-traceless (TT) part of metric perturbations in lattice simulations was inconsistent with the fact that those fields live in the lattice and not in the continuum. It was claimed that this could lead to a larger amplitude and a wrong shape for the gravitational wave (GW) spectra obtained in numerical simulations of (p)reheating. In order to address this issue, we have defined a consistent prescription in the lattice for extracting the TT part of the metric perturbations. We demonstrate explicitly that the GW spectra obtained with the old continuum-based TT projection only differ marginally in amplitude and shape with respect to the new lattice-based ones. We conclude that one can therefore trust the predictions appearing in the literature on the spectra of GW produced during (p)reheating and similar scenarios simulated on a lattice.Comment: 22 pages, 8 figures, Submitted to JCA