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Phil Attard

Publications and source records attributed to Phil Attard.

At least 19 recordsLinked to original sources
arXiv2026

Power Series for the Quantum Statistical Mechanics Probability with Results for the Second Virial Coefficient of Helium

A power series for the Wigner-Kirkwood pair commutation function for quantum statistical mechanics in classical phase space is given with terms automatically generated by recursion. The calculated second virial coefficient agrees with the measured values of helium for temperatures greater than 65 K. Prospects for a general quantum Monte Carlo algorithm are discussed.

cond-mat.stat-mech↗
arXiv2026

Gaussian Reformulation of the Feynman Path Integral for Quantum Statistical Mechanics with Results for the Second Virial Coefficient of $^4$He

The Feynman path integral for quantum statistical mechanics is reformulated as Gaussian sampling of the neighborhood of each position configuration. The variance and mean are obtained from ring polymer statistics on a lattice, and from the high temperature expansion of the Wigner-Kirkwood commutation function, respectively. The algorithm avoids multiple temperature nodes for each configuration and the need for numerical cancelation in the statistical averages, which are problematic for conventional path integral quantum Monte Carlo. Analytic and simulation results for the second virial coefficient of helium are compared to laboratory measurements.

cond-mat.stat-mech↗
arXiv2026

Quantum Monte Carlo in Classical Phase Space with the Wigner-Kirkwood Commutation Function. II. Diagonal Approximation in Position Space

A third order expansion for Wigner-Kirkwood commutation function, a complex function in classical phase space that accounts for the Heisenberg uncertainty relation, is approximated and integrated over momentum to give a real function in position configuration space. Metropolis Monte Carlo computer simulation results are given for liquid Lennard-Jones $^4$He below 10\,K.

cond-mat.stat-mech↗
arXiv2025

Quantum Monte Carlo in Classical Phase Space with the Wigner-Kirkwood Commutation Function. Results for the Saturation Liquid Density of $^4$He

A Metropolis Monte Carlo algorithm is given for the case of a complex phase space weight, which applies generally in quantum statistical mechanics. Computer simulations using Lennard-Jones $^4$He near the $\lambda$-transition, including an expansion to third order of the Wigner-Kirkwood commutation function, give a saturation liquid density in agreement with measured values.

cond-mat.stat-mech↗
arXiv2025

Introduction to the Modern Theory of Bose-Einstein Condensation, Superfluidity, and Superconductivity

The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of Lennard-Jones $^4$He give the $\lambda$-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.

cond-mat.stat-mech↗
arXiv2025

Thermodynamic Explanation of the Meissner-Ochsenfeld Effect in Superconductors

The thermodynamic principle of superfluid flow -- that the energy is minimized at constant entropy -- is applied to superconducting currents to derive the Meissner-Ochsenfeld effect in which magnetic fields are expelled from superconductors. The principle gives a modified form for the first London equation that does not trap magnetic fields within a superconductor. The physical mechanism by which a critical magnetic field destroys superconductivity is identified.

physics.gen-ph↗
arXiv2025

The Two-Fluid Theory for Superfluid Hydrodynamics and Rotational Motion

The two-fluid theory for superfluid hydrodynamics is derived from the fountain pressure result that condensed bosons move at constant entropy and are driven by the chemical potential gradient. Explicit results for $^4$He show that the superfluid has vorticity, which is consistent with measured data but inconsistent with Landau's principle that superfluid flow is irrotational. The macroscopic wavefunction is criticised.

cond-mat.stat-mech↗
arXiv2025

Bose-Einstein Condensation and the Lambda Transition for Interacting Lennard-Jones Helium-4

An introduction to Bose-Einstein condensation and the $\lambda$-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.

cond-mat.stat-mech↗
arXiv2024

The molecular nature of superfluidity: Viscosity of helium from quantum stochastic molecular dynamics simulations over real trajectories

Using quantum equations of motion for interacting bosons, stochastic molecular dynamics simulations with quantized momenta are performed for Lennard-Jones helium-4. The viscosity of the quantum liquid is significantly less than that of the classical liquid, being almost 5 times smaller at the lowest temperature studied. The classical and quantum liquids are identical except for Bose-Einstein condensation, which pinpoints the molecular mechanism for superfluidity. The results rely on the existence of stochastic but real particle trajectories, which has implications for the interpretation of quantum mechanics.

cond-mat.quant-gas↗
arXiv2024

Information vs Thermodynamic Entropy

The Shannon information is shown to be different to the thermodynamic entropy, and indifferent to the Second Law of Thermodynamics.

cond-mat.stat-mech↗
arXiv2023

Comment on pressure driven flow of superfluid $^4$He through a nanopipe (Botimer and Taborek 2016)

Botimer and Taborek (2016) measured the mass flux of superfluid $^4$He through a capillary into an evacuated chamber for various temperatures and pressures of the reservoir chamber. They found a sharp transition from low flux at low pressures to high flux at large pressures. Here it is shown that the superfluid condition of chemical potential equality predicts the induced temperature and also the transition pressure, which is attributed to the transition from a semispherical cap to a pool of $^4$He at the exit of the capillary. The results show that the two-fluid equations of superfluid flow, Landau's phonon-roton theory, and Feynman's critical vortex theory are unnecessary for a quantitative account of the measured transition pressure.

cond-mat.other↗
arXiv2023

Double Fountain Effect in Superfluid Helium

A double fountain pressure model is used to analyze the recent measurements of Yu and Luo (arXiv2211.02236v4) of superfluid $^4$He flow between two chambers held at different temperatures via two superleaks and an intervening third chamber that spontaneously achieves a temperature higher than both fixed temperatures. The physical origin of the increased temperature in the intervening chamber is attributed to the balance between the rate of mechanical energy deposited by superfluid transport and the rate of convection back to the lower temperature chambers. An equation is given for the pressure of the third chamber, the measurement of which would confirm or refute the theory.

cond-mat.other↗
arXiv2023

The Paradox of Bose-Einstein Condensation

The paradox of Bose-Einstein condensation is that phenomena such as the $λ$-transition heat capacity and superfluid flow are macroscopic, whereas the occupancy of the ground state is microscopic. This contradiction is resolved with a simple derivation for ideal bosons that shows Bose-Einstein condensation is into multiple low-lying states, not just the ground state.

cond-mat.stat-mech↗
arXiv2023

Quantum Stochastic Molecular Dynamics Simulations of the Viscosity of Superfluid Helium

Decoherent quantum equations of motion are derived that yield the trajectory of an open quantum system. The viscosity of superfluid Lennard-Jones helium-4 is obtained with a quantum stochastic molecular dynamics algorithm. The momentum state occupancy entropy is counted with a continuous representation of boson number and averages are obtained with umbrella sampling. Instantaneous snapshots of the Bose-Einstein condensed system show multiple highly occupied momentum states. The viscosity is obtained from the Onsager-Green-Kubo relation with the time correlation function modified in the quantum case. On the saturation curve, at higher temperatures the viscosities of the classical and quantum liquids are equal. With decreasing temperature the viscosity of the classical liquid increases whereas that of the quantum liquid decreases. Below the $λ$-transition the viscosity lies significantly below the classical value, being small but positive due to the mixture of condensed and uncondensed bosons. The computed trajectories give a physical explanation of the molecular mechanism for superfluidity.

cond-mat.stat-mech↗
arXiv2022

Further On the Fountain Effect in Superfluid Helium

In the previous paper (Attard 2022d)on the fountain pressure in superfluid helium, it was shown that the experimentally confirmed expression of H. London (1939) was thermodynamically equivalent to equality of chemical potential. However this theoretical equivalence was not reflected in the experimental data. The problem has now been traced to errors in the enthalpy and entropy derived from the measured heat capacity by Donnelly and Barenghi (1998). In this paper the corrected thermodynamic data yields almost exact agreement between the two expressions and the measured fountain pressure. A physical explanation is given for energy minimization as the principle that drives the fountain effect and superfluid flow more generally.

cond-mat.stat-mech↗
arXiv2022

Attraction Between Electron Pairs in High Temperature Superconductors

It is proposed that in high temperature superconductors Cooper pairs form and condense due to the monotonic-oscillatory transition in the pair potential of mean force, which occurs quite generally at high coupling in charge systems. It is shown that the predicted transition temperatures are broadly in line with measured superconducting transition temperatures for reasonable values of the total electron density and the residual dielectric permittivity arising from the immobile electrons. The predicted transition is independent of the isotopic masses of the solid. Consequent design principles for high temperature superconductors are discussed.

cond-mat.supr-con↗