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Gary A. Williams

Publications and source records attributed to Gary A. Williams.

At least 19 recordsLinked to original sources
arXiv2022

Coulomb gas sum rules for vortex-pair fluctuations in 2D superfluids

Vortex fluctuations above and below the critical Kosterlitz-Thouless (KT) transition temperature are characterized using simulations of the 2D XY model. The net winding number of vortices at a given temperature in a circle of radius $R$ is computed as a function of $R$. The average squared winding number is found to vary linearly with the perimeter of the circle at all temperatures above and below $T_{KT}$, and the slope with $R$ displays a sharp peak near the specific heat peak, decreasing then to a value at infinite temperature that is in agreement with an early theory by Dhar. We have also computed the vortex-vortex distribution functions, finding an asymptotic power-law variation in the vortex separation distance at all temperatures. In conjunction with a Coulomb-gas sum rule on the perimeter fluctuations, these can be used to successfully model the start of the perimeter-slope peak in the region below $T_{KT}$.

cond-mat.stat-mech↗
arXiv2021

Fundamental connection between temperature-quenched 2D superfluids and 2D quantum turbulence

There is a fundamental connection between temperature-quenched 2D superfluids and 2D quantum turbulence: the mechanism responsible for the decay of the vorticity after the quench is the enstrophy cascade of 2D turbulence. The range of the cascade is shown to increase with time after the quench as $t^{1/2}$, being equal to the dynamic scaling length characterizing the quench. These results may apply to other phase-ordering transitions involving the decay of topological objects.

cond-mat.stat-mech↗
arXiv2020

Renormalized analytic solution for the enstrophy cascade in two-dimensional quantum turbulence

The forward enstrophy cascade in two-dimensional quantum turbulence in a superfluid film connected to a thermal bath is investigated using a Fokker-Planck equation based on Kosterlitz-Thouless renormalization. The steady-state cascade is formed by injecting vortex pairs of large initial separation at a constant rate. They diffuse with a constant flux to smaller scales, finally annihilating when reaching the core size. The energy spectrum varies as $k^{-3}$, similar to the spectrum known for 2D classical-fluid enstrophy cascades. The dynamics of the cascade can also be studied, and for the case of a sharply peaked initial vortex-pair distribution, it takes about four eddy turnover times for the system to evolve to the decaying $k^{-3}$ cascade, in agreement with recent computer simulations. These insights into the nature of the cascade also allow a better understanding of the phase-ordering process of temperature-quenched 2D superfluids, where the decay of the vorticity is found to proceed via the turbulent cascade. This connection with turbulence may be a fundamental characteristic of phase-ordering in general.

cond-mat.quant-gas↗
arXiv2019

Vortex-loop calculation of the specific heat of superfluid $^4$He under pressure

Vortex-loop renormalization is used to compute the specific heat of superfluid $^4$He near the lambda point at various pressures up to 26 bars. The input parameters are the the pressure dependence of T$_λ$ and the superfluid density, which determine the non-universal parameters of the vortex core energy and core size. The results for the specific heat are found to be in good agreement with experimental data, matching the expected universal pressure dependence to within about 5$\%$. The non-universal critical amplitude of the specific heat is found to be in reasonable agreement, a factor of four larger than the experiments. We point out problems with recent Gross-Pitaevskii simulations that claimed the vortex-loop percolation temperature did not match the critical temperature of the superfluid phase transition.

cond-mat.stat-mech↗
arXiv2019

Superfluid Onset and Compressibility of $^4$He Films Adsorbed on Carbon Nanotubes

Third sound measurements of superfluid $^4$He thin films adsorbed on 10 nm diameter multiwall carbon nanotubes are used to probe the superfluid onset temperature as a function of the film thickness, and to study the temperature dependence of the film compressibility. The nanotubes provide a highly ordered carbon surface, with layer-by-layer growth of the adsorbed film as shown by oscillation peaks in the third sound velocity at the completion of the third, fourth, and fifth atomic layers, arising from oscillations in the compressibility. In temperature sweeps the third sound velocity at very low temperatures is found to be linear with temperature, but oscillating between positive and negative slope depending on the film thickness. Analysis shows that this can be attributed to a linearly decreasing compressibility of the film with temperature that appears to hold even near zero temperature. The superfluid onset temperature is found to be linear in the film thickness, as predicted by the Kosterlitz-Thouless theory, but the slope is anomalous, a factor of three smaller than the predicted universal value.

cond-mat.other↗
arXiv2016

Theory of adiabatic fountain resonance

The theory of "Adiabatic Fountain Resonance" with superfluid $^4$He is clarified. In this geometry a film region between two silicon wafers bonded at their outer edge opens up to a central region with a free surface. We find that the resonance in this system is not a Helmholtz resonance as claimed by Gasparini and co-workers, but in fact is a fourth sound resonance. We postulate that it occurs at relatively low frequency because the thin silicon wafers flex appreciably from the pressure oscillations of the sound wave.

cond-mat.other↗
arXiv2014

Dynamics of the forward vortex cascade in two-dimensional quantum turbulence

The dynamics of the forward vortex cascade in 2D turbulence in a superfluid film is investigated using analytic techniques. The cascade is formed by injecting pairs with the same initial separation (the stirring scale) at a constant rate. They move to smaller scales with constant current under the action of frictional forces, finally reaching the core size separation, where they annihilate and the energy is removed by a thermal bath. On switching off the injection, the pair distribution first decays starting from the initial stirring scale, with the total vortex density decreasing linearly in time at a rate equal to the initial injection rate. As pairs at smaller scales decay, the vortex density then falls off as a power law, the same power law found in recent exact solutions of quenched 2D superfluids.

cond-mat.stat-mech↗
arXiv2014

Third sound measurements of superfluid $^4$He films on multiwall carbon nanotubes below 1K

Third sound is studied for superfluid films of 4He adsorbed on multiwall carbon nanotubes packed into an annular resonator. The third sound is generated with mechanical oscillation of the cell, and detected with carbon bolometers. A filling curve at temperatures near 250 mK shows oscillations in the third sound velocity, with maxima at the completion of the 4th and 5th atomic layers. Sharp changes in the Q factor of the third sound are found at partial layer fillings. Temperature sweeps at a number of fill points show strong broadening effects on the Kosterlitz-Thouless (KT) transition, and rapidly increasing dissipation, in qualitative agreement with the predictions of Machta and Guyer. At the 4th layer completion there is a sudden reduction of the transition temperature $T_{KT}$, and then a recovery back to linear variation with temperature, although the slope is considerably smaller than the KT prediction. Some of these effects may be related to changes in the gas-liquid coexistence regions.

cond-mat.other↗
arXiv2013

Non-universal Casimir Effect in Saturated Superfluid $^4$He Films at T$_λ$

Measurements of Casimir effects in $^4$He films in the vicinity of the bulk superfluid transition temperature $T_λ$ have been carried out, where changes in the film thickness and the superfluid density are both monitored as a function of temperature. The Kosterlitz-Thouless superfluid onset temperature in the film is found to occur just as the Casimir dip in the film thickness from critical fluctuations becomes evident. Additionally, a new film-thickening effect is observed precisely at $T_λ$ when the temperature is swept extremely slowly. We propose that this is a non-universal Casimir effect arising from the viscous suppression of second sound modes in the film.

cond-mat.stat-mech↗
arXiv2013

Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids

An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature $T_{KT}$. An approximate solution for quenches at and above above $T_{KT}$ provides insights into the origin of logarithmic transients in the vortex decay, and are in general agreement with recent simulations of the quenched XY model. These results confirm that there is no "creation" of vortices whose density increases with the quench rate as predicted by the Kibble-Zurek theory, but only monotonic decay of the thermal vortices already present at the initial temperature.

cond-mat.stat-mech↗
arXiv2008

Adsorption properties and third sound propagation in superfluid $^4$He films on carbon nanotubes

We consider the adsorption properties of superfluid $^4$He films on carbon nanotubes. One major factor in the adsorption is the surface tension force arising from the very small diameter of the nanotubes. Calculations show that surface tension keeps the film thickness on the tubes very thin even when the helium vapor is increased to the saturated pressure. The weakened Van der Waals force due to the cylindrical geometry also contributes to this. Both of these effects act to lower the predicted velocity of third sound propagation along the tubes. It does not appear that superfluidity will be possible on single-walled nanotubes of diameter about one nm, since the film thickness is less than 3 atomic layers even at saturation. Superfluidity is possible on larger-diameter nanotube bundles and multi-walled nanotubes, however. We have observed third sound signals on nanotube bundles of average diameter 5 nm which are sprayed onto a Plexiglass surface, forming a network of tubes.

cond-mat.mtrl-sci↗
arXiv2008

Finite-frequency dynamics of vortex loops at the $^4$He superfluid phase transition

The finite-frequency dynamics of the $^4$He superfluid phase transition can be formulated in terms of the response of thermally excited vortex loops to an oscillating flow field. The key parameter is the Hausdorff fractal dimension $d_H$ of the loops, which affects the dynamics because the frictional force on a loop is proportional to the total perimeter $P$ of the loop, which varies as $P \sim a^{d_H}$ where $a$ is the loop diameter. Solving the 3D Fokker-Planck equation for the loop response at frequency $ω$ yields a superfluid density which varies at $T_λ$ as $ω^{1/(d_H -1)}$. This power-law variation with $ω$ agrees with the scaling form found by Fisher, Fisher, and Huse, since the dynamic exponent $z$ is identified as $z = d_H-1$. Flory scaling for the self-avoiding loops gives a fractal dimension in terms of the space dimension $d$ as $d_H = (d+2)/2$, yielding $z = d/2 = 3/2$ for d = 3, in complete agreement with dynamic scaling.

cond-mat.stat-mech↗
arXiv2006

Anisotropic Kosterlitz-Thouless Transition Induced by Hard-Wall Boundaries

The spatial dependence of the superfluid density is calculated for the Kosterlitz-Thouless transition in the presence of hard-wall boundaries, for the case of a single wall bounding the half-infinite plane, and for a superfluid strip bounded by two walls. The boundaries induce additional vortices that cause the superfluid density to become anisotropic, with the tensor component perpendicular to the wall falling to zero at the wall, whereas the component parallel to the wall remains finite. The effects of the boundaries are found to extend over all measured length scales, since the correlation length is infinite in the superfluid phase.

cond-mat.stat-mech↗
arXiv2003

Vortex Fluctuations in the Critical Casimir Effect of Superfluid and Superconducting Films

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when size of the thermal vortex loops is comparable to the film thickness, and the results for T < Tc are found to match very well with perturbative renormalization theories that have only been carried out for T > Tc. When applied to a high-Tc superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and bulk, and estimates show that this may be readily measurable.

cond-mat.supr-con↗
arXiv2001

One-dimensional Excitations in Superfluid $^4$He and $^3$He-$^4$He Mixture Films Adsorbed in Porous Materials

A normal-fluid component varying as T$^{2}$ is observed at very low temperatures in superfluid $^4$He and $^3$He-$^4$He mixture films adsorbed in alumina powder. The normal fluid appears to arise from thermally excited third sound that has one-dimensional propagation characteristics. A Landau model of third sound excitations in an infinite cylindrical pore by Saam and Cole provides good agreement with the experimental measurements over a wide range of $^4$He and $^3$He coverages. However, it is unclear why the powder substrate can be modeled as having cylindrical pores.

cond-mat.stat-mech↗
arXiv2001

Rapidly Quenched Kosterlitz-Thouless Superfluid Transitions

Rapidly quenched Kosterlitz-Thouless (KT) superfluid transitions are studied by solving the Fokker-Planck equation for the vortex-pair dynamics in conjunction with the KT recursion relations. Power-law decays of the vortex density at long times are found, and the results are in agreement with a scaling proposal made by Minnhagen and co-workers for the dynamical critical exponent. The superfluid density is strongly depressed after a quench, with the subsequent recovery being logarithmically slow for starting temperatures near T$_{KT}$. No evidence is found of vortices being ''created'' in a rapid quench, there is only decay of the existing thermal vortex pairs.

cond-mat.stat-mech↗
arXiv1999

Quenched Kosterlitz-Thouless Superfluid Transitions

The properties of rapidly quenched superfluid phase transitions are computed for two-dimensional Kosterlitz-Thouless (KT) systems. The decay in the vortex-pair density and the recovery of the superfluid density after a quench are found by solving the Fokker-Planck equation describing the vortex dynamics, in conjunction with the KT recursion relations. The vortex density is found to decay approximately as the inverse of the time from the quench, in agreement with computer simulations and with scaling theories.

cond-mat.stat-mech↗