arXiv subjects

Eric D. Chisolm

Publications and source records attributed to Eric D. Chisolm.

At least 19 recordsLinked to original sources

arXiv2016

V-T theory for the Self-Intermediate Scattering Function in a Monatomic Liquid

In V-T theory the atomic motion is harmonic vibrations in a liquid-specific potential energy valley, plus transits, which move the system rapidly among the multitude of such valleys. In its first application to the self intermediate scattering function (SISF), V-T theory produced an accurate account of molecular dynamics (MD) data at all wave numbers q and time t. Recently, analysis of the mean square displacement (MSD) resolved a crossover behavior that was not observed in the SISF study. Our purpose here is to apply the more accurate MSD calibration to the SISF, and assess the results. We derive and discuss the theoretical equations for vibrational and transit contributions to the SISF. The time evolution is divided into three successive intervals: the vibrational interval when the vibrational contribution alone accurately accounts for the MD data; the crossover when the vibrational contribution saturates and the transit contribution becomes resolved; and the diffusive interval when the transit contribution alone accurately accounts for the MD data. The resulting theoretical error is extremely small at all q and t. Comparison of V-T and mode-coupling theories for the MSD and SISF reveals that, while their formulations differ substantially, their underlying atomic motions are in logical correspondence.

cond-mat.stat-mech↗

arXiv2015

Atomic Motion from the Mean Square Displacement in a Monatomic Liquid

V-T theory is constructed in the many-body Hamiltonian formulation, and differs at the foundation from current liquid dynamics theories. In V-T theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion , and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na, and find the motion evolves in three successive time intervals: On the first "vibrational" interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second "crossover" interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third "random walk" interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. This motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.

cond-mat.stat-mech↗

arXiv2014

Application of vibration-transit theory to distinct dynamic response for a monatomic liquid

We examine the distinct part of the density autocorrelation function Fd(q,t), also called the intermediate scattering function, from the point of view of the vibration-transit (V-T) theory of monatomic liquid dynamics. A similar study has been reported for the self part, and we study the self and distinct parts separately because their damping processes are not simply related. We begin with the perfect vibrational system, which provides precise definitions of the liquid correlations, and provides the vibrational approximation Fdvib(q,t) at all q and t. Two independent liquid correlations are defined, motional and structural, and these are decorrelated sequentially, with a crossover time tc(q). This is done by two independent decorrelation processes: the first, vibrational dephasing, is naturally present in Fdvib(q,t) and operates to damp the motional correlation; the second, transit-induced decorrelation, is invoked to enhance the damping of motional correlation, and then to damp the structural correlation. A microscopic model is made for the "transit drift", the averaged transit motion that damps motional correlation on 0 < t < tc(q). Following the previously developed self-decorrelation theory, a microscopic model is also made for the "transit random walk," which damps the structural correlation on t > tc(q). The complete model incorporates a property common to both self and distinct decorrelation: simple exponential decay following a delay period, where the delay is tc(q, the time required for the random walk to emerge from the drift. Our final result is an accurate expression for Fd(q,t) for all q through the first peak in Sd(q). The theory is calibrated and tested using molecular dynamics (MD) calculations for liquid Na at 395K; however, the theory itself does not depend on MD, and we consider other means for calibrating it.

cond-mat.stat-mech↗

arXiv2013

Thermal electronic excitations in liquid metals

Thermal electronic excitations in metal crystals are calculated by starting with a reference structure for the nuclei: the crystal structure of the appropriate phase. Here we explain the corresponding theory for metal liquids, starting with an appropriate reference structure for a liquid. We explain the significance of these structures, and we briefly review how to find them and calculate their properties. Then we examine the electronic densities of states for liquid structures of Na, Al, and Cu, comparing them to their crystal forms. Next we explain how to calculate the dominant electronic thermal excitation term, considering issues of accuracy that do not arise in the crystal theory. Finally we briefly discuss the contribution from the interaction between excited electrons and moving nuclei.

cond-mat.mtrl-sci↗

arXiv2010

Liquid state properties from first principles DFT calculations: Static properties

In order to test the Vibration-Transit (V-T) theory of liquid dynamics, ab initio density functional theory (DFT) calculations of thermodynamic properties of Na and Cu are performed and compared with experimental data. The calculations are done for the crystal at T = 0 and T_m, and for the liquid at T_m. The key theoretical quantities for crystal and liquid are the structural potential and the dynamical matrix, both as function of volume. The theoretical equations are presented, as well as details of the DFT computations. The properties compared with experiment are the equilibrium volume, the isothermal bulk modulus, the internal energy and the entropy. The agreement of theory with experiment is uniformly good. Our primary conclusion is that the application of DFT to V-T theory is feasible, and the resulting liquid calculations achieve the same level of accuracy as does ab initio lattice dynamics for crystals. Moreover, given the well established reliability of DFT, the present results provide a significant confirmation of V-T theory itself.

cond-mat.stat-mech↗

arXiv2010

Statistical mechanics model for the transit free energy of monatomic liquids

In applying Vibration-Transit (V-T) theory of liquid dynamics to the thermodynamic properties of monatomic liquids, the point has been reached where an improved model is needed for the small (approx. 10%) transit contribution. Toward this goal, an analysis of the available high-temperature experimental entropy data for elemental liquids was recently completed [D. C. Wallace, E. D. Chisolm, and N. Bock, Phys. Rev. B 79, 051201 (2009)]. This analysis yields a common curve of transit entropy vs. T/θ_{tr}, where T is temperature and θ_{tr} is a scaling temperature for each element. In the present paper, a statistical mechanics model is constructed for the transit partition function, and is calibrated to the experimental transit entropy curve. The model has two scalar parameters, and captures the temperature scaling of experiment. The calibrated model fits the experimental liquid entropy to high accuracy at all temperatures. With no additional parameters, the model also agrees with both experiment and molecular dynamics for the internal energy vs. T for Na. With the calibrated transit model, V-T theory provides equations subject to ab initio evaluation for thermodynamic properties of monatomic liquids. This will allow the range of applicability of the theory, and its overall accuracy, to be determined. More generally, the hypothesis of V-T theory, which divides the many-atom potential energy valleys into random and symmetric classes, can also be tested for its application beyond monatomic systems.

cond-mat.soft↗

arXiv2009

An \emph{ab initio} method for locating characteristic potential energy minima of liquids

It is possible in principle to probe the many--atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys. Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid Molecular Dynamics (MD) configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations.

cond-mat.stat-mech↗

arXiv2009

Probability sum rules and consistent quantum histories

An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the linearly positive probability formula from weak to minimal decoherence gives probabilities that are different from those calculated in the usual way using the Born and von Neumann rules and a projection operator at each time.

quant-ph↗

arXiv2009

An improved model for the transit entropy of monatomic liquids

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of 2% among elemental liquids, and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of 0.1% to the available experimental high temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/θ_0), where T is temperature and θ_0 is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/θ_{tr}), where θ_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived, in a single formula applying to normal and anomalous melting alike. An ab initio calculation of θ_0, based on density functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.

cond-mat.other↗

arXiv2008

V-T Theory of Self Dynamic Response in a Monatomic Liquid

A new theoretical model for self dynamic response is developed using Vibration-Transit (V-T) theory, and is applied to liquid sodium at all wavevectors q from the hydrodynamic regime to the free particle limit. In this theory the zeroth-order Hamiltonian describes the vibrational motion in a single random valley harmonically extended to infinity. This Hamiltonian is tractable, is evaluated a priori for monatomic liquids, and the same Hamiltonian (the same set of eigenvalues and eigenvectors) is used for equilibrium and nonequlibrium theory. Here, for the self intermediate scattering function Fself(q,t) we find the vibrational contribution is in near perfect agreement with molecular dynamics (MD) through short and intermediate times, at all q. This is direct confirmation that normal mode vibrational correlations are present in the motion of the liquid state. The primary transit effect is diffusive motion of the vibrational equilibrium positions, as the liquid transits rapidly among random valleys. This motion is modeled as a standard random walk, and the resulting theoretical Fself(q,t) is in excellent agreement with MD results at all q and t. In the limit for q to infinity, the theory automatically exhibits the correct approach to the free-particle limit. Also in the limit for q to zero, the hydrodynamic limit emerges as well. In contrast to the benchmark theories of generalized hydrodynamics and mode coupling, the present theory is near a priori, while achieving modestly better accuracy. Therefore, in our view, it constitutes an improvement over the traditional theories.

cond-mat.soft↗

arXiv2007

Vibrational Contribution to Density and Current Autocorrelations in a Monatomic Liquid

We consider for a monatomic liquid the density and current autocorrelation functions from the point of view of the Vibration-Transit (V-T) theory of liquid dynamics. We also consider their Fourier transforms, one of which is measured by X-ray and neutron scattering. In this description, the motion of atoms in the liquid is divided into vibrations in a single characteristic potential valley, called a random valley, and nearly-instantaneous transitions called transits between valleys. The theory proposes a Hamiltonian for the vibrational motion, to be corrected to take transits into account; this Hamiltonian is used to calculate the autocorrelation functions, giving what we call their vibrational contributions. We discuss the multimode expansions of the autocorrelation functions, which provide a physically helpful picture of the decay of fluctuations in terms of n-mode scattering processes; we also note that the calculation and Fourier transform of the multimode series are numerically problematic, as successive terms require larger sums and carry higher powers of the temperature, which is a concern for the liquid whose temperature is bounded from below by melt. We suggest that these problems are avoided by directly computing the autocorrelation functions, for which we provide straightforward formulas, and Fourier transforming them numerically.

cond-mat.stat-mech↗

arXiv2006

Decohering histories and open quantum systems

I briefly review the ''decohering histories'' or ''consistent histories'' formulation of quantum theory, due to Griffiths, Omnes, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.

quant-ph↗

arXiv2005

Time correlation functions in Vibration-Transit theory of liquid dynamics

Within the framework of V-T theory of monatomic liquid dynamics, an exact equation is derived for a general equilibrium time correlation function. The purely vibrational contribution to such a function expresses the system's motion in one extended harmonic random valley. This contribution is analytically tractable and has no adjustable parameters. While this contribution alone dominates the thermodynamic properties, both vibrations and transits will make important contributions to time correlation functions. By way of example, the V-T formulation of time correlation functions is applied to the dynamic structure factor S(q,w). The vibrational contribution alone is shown to be in near perfect agreement with low-temperature molecular dynamics simulations, and a model simulating the transit contribution with three adjustable parameters achieves equally good agreement with molecular dynamics results in the liquid regime. The theory indicates that transits will broaden without shifting the Rayleigh and Brillouin peaks in S(q,w), and this behavior is confirmed by the MD calculations. We find the vibrational contribution alone gives the location and much of the width of the liquid-state Brillouin peak. We also discuss this approach to liquid dynamics compared with potential energy landscape formalisms and mode coupling theory, drawing attention to the distinctive features of our approach and to some potential energy landscape results which support our picture of the liquid state.

cond-mat.soft↗

arXiv2005

Application of Vibration-Transit Theory of Liquid Dynamics to the Brillouin Peak Dispersion Curve

The Brillouin peak appears in the dynamic structure factor S(q,w), and the dispersion curve is the Brillouin peak frequency as function of q. The theoretical function underlying S(q,w) is the density autocorrelation function F(q,t). A broadly successful description of time correlation functions is provided by mode coupling theory, which expresses F(q,t) in terms of processes through which the density fluctuations decay. In contrast, vibration-transit (V-T) theory is a Hamiltonian formulation of monatomic liquid dynamics in which the motion consists of vibrations within a many-particle random valley, interspersed with nearly instantaneous transits between such valleys. Here, V-T theory is applied to S(q,w). The theoretical vibrational contribution to S(q,w) is the sum of independent scattering cross sections from the normal vibrational modes, and contains no explicit reference to decay processes. For a theoretical model of liquid Na, we show that the vibrational contribution with no adjustable parameters gives an excellent account of the Brillouin peak dispersion curve, as compared to MD calculations and to experimental data.

cond-mat.mtrl-sci↗

arXiv2004

Dynamics of monatomic liquids

We present a theory of the dynamics of monatomic liquids built on two basic ideas: (1) The potential surface of the liquid contains three classes of intersecting nearly-harmonic valleys, one of which (the ``random'' class) vastly outnumbers the others and all whose members have the same depth and normal mode spectrum; and (2) the motion of particles in the liquid can be decomposed into oscillations in a single many-body valley, and nearly instantaneous inter-valley transitions called transits. We review the thermodynamic data which led to the theory, and we discuss the results of molecular dynamics (MD) simulations of sodium and Lennard-Jones argon which support the theory in more detail. Then we apply the theory to problems in equilibrium and nonequilibrium statistical mechanics, and we compare the results to experimental data and MD simulations. We also discuss our work in comparison with the QNM and INM research programs and suggest directions for future research.

cond-mat.stat-mech↗

arXiv2004

Generalizing the Heisenberg uncertainty relation

The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions on the state to which the relation is applied, increasing its generality. The restrictions necessary for the standard inequality to apply are not widely known, and they are discussed in detail. The classical analog of the Heisenberg relation is also derived, and the two are compared. Finally, the modified relation is used to address the apparent paradox that eigenfunctions of the z component of angular momentum L_z do not satisfy the ϕ-L_z Heisenberg relation; the resolution is that the restrictions mentioned above make the usual inequality inapplicable to these states. The modified relation does apply, however, and it is shown to be consistent with explicit calculations.

quant-ph↗

arXiv2004

Observation of Single Transits in Supercooled Monatomic Liquids

A transit is the motion of a system from one many-particle potential energy valley to another. We report the observation of transits in molecular dynamics (MD) calculations of supercooled liquid argon and sodium. Each transit is a correlated simultaneous shift in the equilibrium positions of a small local group of particles, as revealed in the fluctuating graphs of the particle coordinates versus time. This is the first reported direct observation of transit motion in a monatomic liquid in thermal equilibrium. We found transits involving 2 to 11 particles, having mean shift in equilibrium position on the order of 0.4 R_1 in argon and 0.25 R_1 in sodium, where R_1 is the nearest neighbor distance. The time it takes for a transit to occur is approximately one mean vibrational period, confirming that transits are fast.

cond-mat.mtrl-sci↗

arXiv2004

Theoretical estimates of the logarithmic phonon spectral moment for monatomic liquids

We calculate the logarithmic moment of the phonon frequency spectrum at a single density for 29 monatomic liquids using two methods, both suggested by Wallace's theory of liquid dynamics: The first method relies on liquid entropy data, the second on neutron scattering data in the crystal phase. This theory predicts that for a class of elements called ``normal melters,'' including all 29 of these materials, the two estimates should closely match, and we find that they agree to within a few percent. We also perform the same calculations for four ``anomalous melters,'' for which we expect the two estimates to differ markedly; we find that they disagree by factors almost up to three. From our results we conclude that the liquid entropy estimates of the logarithmic moment, applicable both to normal and anomalous melters, are trustworthy to a few percent, which makes them reliable for use in estimates of various liquid transport coefficients.

cond-mat.mtrl-sci↗