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Phil Attard

Publications and source records attributed to Phil Attard.

47 records · Page 3Linked to original sources
arXiv2014

Quantum Statistical Mechanics. II. Stochastic Schrodinger Equation

The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the density matrix, which is an explicit, stochastic form of the Lindblad master equation. A quantum fluctuation-dissipation theorem is also derived. The time correlation function is discussed.

cond-mat.stat-mech↗
arXiv2013

Quantum Statistical Mechanics. I. Decoherence, Wave Function Collapse, and the von Neumann Density Matrix

The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum average. The mechanism for the collapse is found to be quite general: it results from the conservation law for a conserved, exchangeable variable (such as energy) and the entanglement of the total system wave function that necessarily follows. The relevance of the present results to the einselection mechanism for decoherence, to the quantum measurement problem, and to the classical nature of the macroscopic world are discussed.

cond-mat.stat-mech↗
arXiv2013

More Reliable Measurements of the Slip Length with the Atomic Force Microscope

Further improvements are made to the non-linear data analysis algorithm for the atomic force microscope [P. Attard, arXiv:1212.3019v2 (2012)]. The algorithm is required when there is curvature in the compliance region due to photo-diode non-linearity. Results are obtained for the hydrodynamic drainage force, for three surfaces: hydrophilic silica (symmetric, Si-Si), hydrophobic dichlorodimethylsilane (symmetric, DCDMS-DCDMS), and hydrophobic octadecyltrichlorosilane (asymmetric, Si-OTS). The drainage force was measured in the viscous liquid di-n-octylphthalate. The slip-lengths are found to be 3nm for Si, 2nm for DCDMS, and 2nm for OTS, with an uncertainty on the order of a nanometer. These slip lengths are a factor of 4--15 times smaller than those obtained from previous analysis of the same raw data [L. Zhu et al., Langmuir, 27, 6712 (2011). Ibid, 28, 7768 (2012)].

cond-mat.soft↗
arXiv2013

How to Measure Forces when the Atomic Force Microscope shows Non-Linear Compliance

A spreadsheet algorithm is given for the atomic force microscope that accounts for non-linear behavior in the deflection of the cantilever and in the photo-diode response. In addition, the data analysis algorithm takes into account cantilever tilt, friction in contact, and base-line artifacts such as drift, virtual deflection, and non-zero force. These are important for accurate force measurement and also for calibration of the cantilever spring constant. The zero of separation is determined automatically, avoiding human intervention or bias. The method is illustrated by analyzing measured data for the silica-silica drainage force and slip length.

cond-mat.soft↗
arXiv2012

Is the Information Entropy the Same as the Statistical Mechanical Entropy?

It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the expression for the entropy as a function of the probability. A simple derivation of the general formula is given.

cond-mat.stat-mech↗
arXiv2012

Thermodynamics for Non-equilibrium Pattern Formation

The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is derived. The Navier-Stokes equations in Boussinesq approximation for straight roll convection are solved by a Fourier expansion technique. Results for the velocity amplitude are in good agreement with previous computations and experimental measurements. For the spontaneous transitions between straight roll states reported in the literature, it is shown that the measured change in convective pattern wave length corresponds to an increase in the entropy. This paper has been superseded by arXiv:1208.5105v1.

cond-mat.stat-mech↗
arXiv2012

Design of Chemotaxis Devices Using Nano-Motors

Several designs for micro-devices for chemotaxis based on nano-motors are proposed. The nano- or micro-motors are the conventional Janus rods or spheres that are powered by the catalytic reaction of fuels such as hydrogen peroxide. It is shown how these can be linked to make a device that can follow a concentration gradient of the fuel. The feasibility of assembling the devices using micromanipulation or metallic deposition is discussed. A possible design principle is suggested for a device that follows the concentration gradient of an analyte other than the fuel.

cond-mat.soft↗
arXiv2012

Optimising Principle for Non-Equilibrium Phase Transitions and Pattern Formation with Results for Heat Convection

Spontaneous transitions between non-equilibrium patterns are characterised by hydrodynamic calculations of ideal straight roll steady state heat convection. The calculations are tested quantitatively against existing experimental data. It is shown that at a given Rayleigh number the final wave number depends upon whether the initial state was the conducting state, or, in the case of the cross roll transition, the wave number of the initial straight roll state. The final wave number does not correspond to the maximum or to the minimum heat flux (entropy production or dissipation), nor to the maximum sub-system entropy. In all cases the entropy of the total system increases monotonically during the spontaneous transition. It is concluded that there does not exist any single time thermodynamic property or variational principle for non-equilibrium systems. It is further concluded that the second entropy is the two time variational principle that determines the optimum non-equilibrium state or pattern.

cond-mat.stat-mech↗
arXiv1997

Entropic Forces in Binary Hard Sphere Mixtures: Theory and Simulation

We perform extensive Monte Carlo simulations of binary hard-sphere mixtures (with diameter ratios of 5 and 10), to determine the entropic force between (1) a macrosphere and a hard wall, and (2) a pair of macrospheres. The microsphere background fluid (at volume fractions ranging from 0.1 to 0.34) induces an entropic force on the macrosphere(s); the latter component is at infinite dilution. We find good overall agreement, in both cases, with the predictions of an HNC-based theory for the entropic force. Our results also argue for the validity of the Derjaguin approximation relating the force between convex bodies to that between planar surfaces. The earlier Asakura-Oosawa theory, based on a simple geometric argument, is only accurate in the low-density limit.

cond-mat.stat-mech↗