A new Proposal for a Quasielectron Trial Wavefunction for the FQHE on a Disk

In this letter, we propose a new quasielectron trial wavefunction for $N$ interacting electrons in two dimensions moving in a strong magnetic field in a disk geometry. Requiring that the trial wavefunction exhibits the correct filling factor of a quasielectron wavefunction, we obtain $N+1$ angular momentum eigenfunctions. The expectation values of the energy are calculated and compared with the data of an exact numerical diagonalization.Comment: 8 page

Quantum Glassiness

Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. This paper presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses.Comment: 4 page

Testing the locality of transport in self-gravitating accretion discs - II. The massive disc case

In this paper, we extend our previous analysis (Lodato & Rice 2004) of the transport properties induced by gravitational instabilities in cooling, gaseous accretion discs to the case where the disc mass is comparable to the central object. In order to do so, we have performed global, three-dimensional smoothed particle hydrodynamics simulations of massive discs. These new simulations show a much more complex temporal evolution with respect to the less massive case. Whereas in the low disc mass case a self-regulated, marginally stable state (characterized by an approximately constant radial profile of the stability parameter $Q$) is easily established, in the high disc mass case we observe the development of an initial transient and subsequent settling down in a self-regulated state in some simulations, or a series or recurrent spiral episodes, with low azimuthal wave number $m$, in others. Accretion in this last case can therefore be a highly variable process. On the other hand, we find that the secular evolution of the disc is relatively slow. In fact, the time-average of the stress induced by self-gravity results in accretion time-scales much longer than the dynamical timescale, in contrast with previous isothermal simulations of massive accretion discs. We have also compared the resulting stress tensor with the expectations based on a local theory of transport, finding no significant evidence for global wave energy transport.Comment: MNRAS, accepted (higher quality, colour figures can be found at http://www.ast.cam.ac.uk/~giuseppe/Publications/Locality_II/

Mesoscale simulations of surfactant dissolution and mesophase formation

The evolution of the contact zone between pure surfactant and solvent has been studied by mesoscale simulation. It is found that mesophase formation becomes diffusion controlled and follows the equilibrium phase diagram adiabatically almost as soon as individual mesophases can be identified, corresponding to times in real systems of order 10 microseconds.Comment: 4 pages, 2 figures, ReVTeX

Non-Universal Fractional Quantum Hall States in a Quantum wire

The ground state as well as low-lying excitations in a 2D electron system in strong magnetic fields and a parabolic potential is investigated by the variational Monte Calro method. Trial wave functions analogous to the Laughlin state are used with the power-law exponent as the variational parameter. Finite size scaling of the excitation energy shows that the correlation function at long distance is characterized by anon-universal exponent in sharp contrast to the standard Laughlin state.The Laughlin-type state becomes unstable depending on strength of the confining potential.Comment: 10 pages, REVTE

Spin Susceptibility and Gap Structure of the Fractional-Statistics Gas

This paper establishes and tests procedures which can determine the electron energy gap of the high-temperature superconductors using the $t\!-\!J$ model with spinon and holon quasiparticles obeying fractional statistics. A simpler problem with similar physics, the spin susceptibility spectrum of the spin 1/2 fractional-statistics gas, is studied. Interactions with the density oscillations of the system substantially decrease the spin gap to a value of $(0.2 \pm 0.2)$ $\hbar \omega_c$, much less than the mean-field value of $\hbar\omega_c$. The lower few Landau levels remain visible, though broadened and shifted, in the spin susceptibility. As a check of the methods, the single-particle Green's function of the non-interacting Bose gas viewed in the fermionic representation, as computed by the same approximation scheme, agrees well with the exact results. The same mechanism would reduce the gap of the $t\!-\!J$ model without eliminating it.Comment: 35 pages, written in REVTeX, 16 figures available upon request from [email protected]

Cumulative and Differential Effects of Early Child Care and Middle Childhood Out-of-School Time on Adolescent Functioning.

Effects associated with early child care and out-of-school time (OST) during middle childhood were examined in a large sample of U.S. adolescents (N = 958). Both higher quality early child care AND more epochs of organized activities (afterschool programs and extracurricular activities) during middle childhood were linked to higher academic achievement at age 15. Differential associations were found in the behavioral domain. Higher quality early child care was associated with fewer externalizing problems, whereas more hours of early child care was linked to greater impulsivity. More epochs of organized activities was associated with greater social confidence. Relations between early child care and adolescent outcomes were not mediated or moderated by OST arrangements in middle childhood, consistent with independent, additive relations of these nonfamilial settings

Substellar companions and isolated planetary mass objects from protostellar disc fragmentation

Self-gravitating protostellar discs are unstable to fragmentation if the gas can cool on a time scale that is short compared to the orbital period. We use a combination of hydrodynamic simulations and N-body orbit integrations to study the long term evolution of a fragmenting disc with an initial mass ratio to the star of M_disc/M_star = 0.1. For a disc which is initially unstable across a range of radii, a combination of collapse and subsequent accretion yields substellar objects with a spectrum of masses extending (for a Solar mass star) up to ~0.01 M_sun. Subsequent gravitational evolution ejects most of the lower mass objects within a few million years, leaving a small number of very massive planets or brown dwarfs in eccentric orbits at moderately small radii. Based on these results, systems such as HD 168443 -- in which the companions are close to or beyond the deuterium burning limit -- appear to be the best candidates to have formed via gravitational instability. If massive substellar companions originate from disc fragmentation, while lower-mass planetary companions originate from core accretion, the metallicity distribution of stars which host massive substellar companions at radii of ~1 au should differ from that of stars with lower mass planetary companions.Comment: 5 pages, accepted for publication in MNRA

Statistical Interparticle Potential between Two Anyons

The density matrix of a two-anyon system is evaluated and used to investigate the "statistical interparticle potential" following the theory of Uhlenbeck. The main purpose is to see how the statistical potential will depend on the fractional statistical parameter $\alpha$. The result shows that the statistical potential for a two-anyon system with $\alpha\ge {1\over2}$ is always repulsive. For the system with $0<\alpha< {1\over2}$, the potential is repulsive at short distances and becomes attractive at long distances. It remains only in the boson system ($\alpha=0$) that the repulsive potential arising from the exclusion principle can disappear and lead to an attractive potential at all distances.Comment: Latex 5 pages, correct typos and figur

Possible Stellar Metallicity Enhancements from the Accretion of Planets

A number of recently discovered extrasolar planet candidates have surprisingly small orbits, which may indicate that considerable orbital migration takes place in protoplanetary systems. A natural consequence of orbital migration is for a series of planets to be accreted, destroyed, and then thoroughly mixed into the convective envelope of the central star. We study the ramifications of planet accretion for the final main sequence metallicity of the star. If maximum disk lifetimes are on the order of 10 Myr, stars with masses near 1 solar mass are predicted to have virtually no metallicity enhancement. On the other hand, early F and late A type stars with masses of 1.5--2.0 solar masses can experience significant metallicity enhancements due to their considerably smaller convection zones during the first 10 Myr of pre-main-sequence evolution. We show that the metallicities of an aggregate of unevolved F stars are consistent with an average star accreting about 2 Jupiter-mass planets from a protoplanetary disk having a 10 Myr dispersal time.Comment: 14 pages, AAS LaTeX, 3 figures, accepted to ApJ Letter