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Phil Attard

Publications and source records attributed to Phil Attard.

At least 37 records · Page 2Linked to original sources
arXiv2022

On the Fountain Effect in Superfluid Helium

The origin of the fountain pressure that arises from a small temperature difference in superfluid helium is analyzed. The osmotic pressure explanation due to Tisza (1938), based on the different fractions of ground state bosons, is formulated as an ideal solution and shown to overestimate the fountain pressure by an order of magnitude or more. The experimentally confirmed thermodynamic expression of H. London (1939), in which the temperature derivative of the pressure equals the entropy per unit volume, is shown to be equivalent to equality of chemical potential, not chemical potential divided by temperature. The former results from minimizing the energy at constant entropy, whereas the latter results from maximizing the entropy. It is concluded that superfluid flow in the fountain effect is driven by mechanical, not statistical, forces. This new principle appears to be a general law for flow in superfluids and superconductors.

physics.chem-ph↗
arXiv2022

New Theory for Cooper Pair Formation and Superconductivity

A new theory for Cooper pair formation and superconductivity is derived from quantum statistical mechanics. It is shown that zero momentum Cooper pairs have non-local permutations and behave as effective bosons with an internal weight close to unity when bound by a primary minimum in the potential of mean force. For a short-ranged, shallow, and highly curved minimum there is no thermodynamic barrier to condensation. The size of the condensing Cooper pairs found here is orders of magnitude smaller than those found in BCS theory. The new statistical theory is applicable to high temperature superconductors.

cond-mat.supr-con↗
arXiv2022

Bose-Einstein Condensation, the Lambda Transition, and Superfluidity for Interacting Bosons

Bose-Einstein condensation and the $λ$-transition are described in molecular detail for bosons interacting with a pair potential. New phenomena are identified that are absent in the usual ideal gas treatment. Monte Carlo simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons give a diverging heat capacity approaching the transition. Pure permutation loops give continuous growth in the occupancy of the ground momentum state. Mixed ground and excited momentum state permutation loops give a discontinuous transition to the condensed phase. The consequent latent heat for the $λ$-transition is 3\% of the total energy. The predicted critical velocity for superfluid flow is within a factor of three of the measured values over three orders of magnitude in pore diameter.

cond-mat.stat-mech↗
arXiv2020

Quantum Ornstein-Zernike Equation

The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial differential equation in temperature and space is given for this. The linear solution is obtained explicitly, which is valid at high and intermediate temperatures, or at low densities. An algorithm for solving the full non-linear problem is given. Symmetrization effects accounting for particle statistics are also written as a series of effective many-body potentials, of which the pair term is dominant at terrestrial densities. Casting these quantum functions as pair-wise additive, temperature-dependent, effective potentials enables the established techniques of classical statistical mechanics to be applied to quantum systems. The quantum Ornstein-Zernike equation is given as an example.

quant-ph↗
arXiv2020

Quantum Statistical Mechanics in Classical Phase Space. V. Quantum Local, Average Global

One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the non-commutativity of the position and momentum operators. Used in Monte Carlo simulations for a one-dimensional Lennard-Jones fluid, the results prove more reliable than a high temperature expansion and a harmonic local field approach, and at intermediate temperatures agree with benchmark numerical results. Results are presented for distinguishable particles, fermions, and bosons.

quant-ph↗
arXiv2019

Quantum Monte Carlo in Classical Phase Space. Mean Field and Exact Results for a One Dimensional Harmonic Crystal

Monte Carlo simulations are performed in classical phase space for a one-dimensional quantum harmonic crystal. Symmetrization effects for spinless bosons and fermions are quantified. The algorithm is tested for a range of parameters against exact results that use 20,000 energy levels. It is shown that the singlet mean field approximation is very accurate at high temperatures, and that the pair mean field approximation gives a systematic improvement in the intermediate and low temperature regime. The latter is derived from a cluster mean field approximation that accounts for the non-commutativity of position and momentum, and that can be applied in three dimensions.

quant-ph↗
arXiv2018

Quantum Statistical Mechanics in Classical Phase Space. III. Mean Field Approximation Benchmarked for Interacting Lennard-Jones Particles

A Monte Carlo computer simulation algorithm in classical phase space is given for the treatment of quantum systems. The non-commutativity of position and momentum is accounted for by a mean field approach and instantaneous effective harmonic oscillators. Wave function symmetrization is included at the dimer and double dimer level. Quantitative tests are performed against benchmarks given by Hernando and Vaníček (2013) for spinless neon--parahydrogen, modeled as interacting Lennard-Jones particles in a one dimensional harmonic trap. The mean field approach is shown to be quantitatively accurate for high to moderate temperatures $β\hbar ω_\mathrm{LJ} < 7$, and moderate densities, $ρσ\approx 1$. Results for helium show that at the lowest temperature studied, the average energy is about 4\% lower for bosons than for fermions. It is argued that the mean field algorithm will perform better in three dimensions than in one, and that it will scale sub-linearly with system size.

quant-ph↗
arXiv2018

Quantum Statistical Mechanics in Classical Phase Space. Test Results for Quantum Harmonic Oscillators

The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave function symmetrization is also given. The method is tested for quantum harmonic oscillators. For both the boson and fermion cases, the grand potential and the average energy obtained by numerical quadrature over classical phase space are shown to agree with the known analytic results. A mean field approximation is given which is suitable for condensed matter, and which allows the quantum statistical mechanics of interacting particles to be obtained in classical phase space.

quant-ph↗
arXiv2018

Quantum Statistical Mechanics in Classical Phase Space. Expressions for the Multi-Particle Density, the Average Energy, and the Virial Pressure

Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential and for the multi-particle density. Three binary choices (eight routes) for the average energy are shown to be mutually consistent. An expression for the phase space function that gives the average virial pressure is derived.

quant-ph↗
arXiv2018

Shear Thinning in Lennard-Jones Fluids by Stochastic Dissipative Molecular Dynamics Simulation

The shear viscosity of a Lennard-Jones fluid is obtained by stochastic dissipative molecular dynamics (SDMD) simulations. A generic constraint to the equations of motion is given that reduces the sensitivity of the shear viscosity to the value of the the fluctuation-dissipation or thermostat parameter. At high shear rates the shear viscosity becomes dependent on the size of the system, and corrections to the equipartition kinetic temperature arise. At constant kinetic temperature the shear viscosity is shown to decrease with increasing shear rate.

cond-mat.stat-mech↗
arXiv2017

Quantum Statistical Mechanics Results for Argon, Neon, and Helium Using Classical Monte Carlo

Quantum corrections to the classical pressure are obtained for Lennard-Jones models of argon, neon, and helium using classical Metropolis algorithm computer simulations. The corrections for non-commutativity are obtained to fourth order in Planck's constant. Compared to the classical virial pressure on all isotherms at liquid-like densities, the quantum correction is found to be ${\cal O}(10^{-2})$ for argon, ${\cal O}(10^{0})$ for neon, and ${\cal O}(10^{3})$ for helium. The first order correction due to wave function symmetrization is also obtained, but this is relatively negligible.

quant-ph↗
arXiv2016

Quantum Statistical Mechanics as an Exact Classical Expansion with Results for Lennard-Jones Helium

The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum contributions arises from the non-commutativity of the position and momentum operators. Although the formulation of the quantum states differs, the present results for separate averages of position operators and of momentum operators agree with Wigner (1932) and Kirkwood (1933). The second series arises from wave function symmetrization, and is given in terms of $l$-particle permutation loops in an infinite order re-summation. The series gives analytically the known exact result for the quantum ideal gas to all orders. The leading correction corrects a correction given by Kirkwood. The first four quantum corrections to the grand potential are calculated for a Lennard-Jones fluid using the hypernetted chain closure. For helium on liquid branch isotherms, the corrections range from several times to 1\% of the total classical pressure, with the effects of non-commutativity being significantly larger in magnitude than those of wave function symmetrization. All corrections are found to be negligible for argon at the densities and temperatures studied. The calculations are computationally trivial as the method avoids having to compute eigenfunctions, eigenvalues, and numerical symmetrization.

quant-ph↗
arXiv2016

Expansion for Quantum Statistical Mechanics Based on Wave Function Symmetrization

An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the symmetrization of the wave function with respect to localized particle interchange. Explicit application of the theory yields the full fugacity expansion for the quantum ideal gas, and the second fugacity coefficient for interacting quantum particles, which agree with known results. Compared to the Lee-Yang virial cluster expansion, the present expansion is expected to be more rapidly converging and the individual terms appear to be simpler to evaluate. The results obtained in this paper are intended for practical computer simulation algorithms for terrestrial condensed matter quantum systems.

cond-mat.stat-mech↗
arXiv2015

Direct Measurement of the Surface Tension of Nanobubbles

It is shown that when the nanobubble contact line is pinned to a penetrating tip the interface behaves like a Hookean spring with spring constant proportional to the nanobubble surface tension. Atomic force microscope (AFM) data for several nanobubbles and solutions are analysed and yield surface tensions in the range 0.04--0.05 N/m (compared to 0.072 N/m for saturated water), and supersaturation ratios in the range 2--5. These are the first direct measurements of the surface tension of a supersaturated air-water interface. The results are consistent with recent theories of nanobubble size and stability, and with computer simulations of the surface tension of a supersaturated solution.

cond-mat.soft↗
arXiv2015

Thermodynamic Stability of Nanobubbles

The observed stability of nanobubbles contradicts the well-known result in classical nucleation theory, that the critical radius is both microscopic and thermodynamically unstable. Here nanoscopic stability is shown to be the combined result of two non-classical mechanisms. It is shown that the surface tension decreases with increasing supersaturation, and that this gives a nanoscopic critical radius. Whilst neither a free spherical bubble nor a hemispherical bubble mobile on an hydrophobic surface are stable, it is shown that an immobilized hemispherical bubble with a pinned contact rim is stable and that the total entropy is a maximum at the critical radius.

physics.chem-ph↗
arXiv2014

Quantum Statistical Mechanics. IV. Non-Equilibrium Probability Operator and Stochastic, Dissipative Schrodinger Equation

The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schrödinger equation is also given. The dissipative and stochastic propagators are linked by the fluctuation-dissipation theorem that is derived from the unitary condition on the time propagator. The dissipative propagator is derived from thermodynamic force and entropy fluctuation operators that are in general non-linear.

physics.chem-ph↗