George K. Horton

Bio: George K. Horton is an academic researcher from Rutgers University. The author has contributed to research in topics: Monte Carlo method & Anharmonicity. The author has an hindex of 14, co-authored 54 publications receiving 1186 citations. Previous affiliations of George K. Horton include University of Birmingham & National Research Council.

Thermodynamic Properties of Solid Ar, Kr, and Xe Based Upon a Short-Range Central Force and the Conventional Perturbation Expansion of the Partition Function

Abstract: Thermodynamic properties of the rare-gas solids Ar, Kr, and Xe are calculated using phenomenological two-body central potentials. The cubic and quartic anharmonic terms in the crystal Hamiltonian have been included, using conventional perturbation theory. Although some definite discrepancies with experiment exist for $Tl\frac{1}{3}{T}_{\mathrm{melting}}$ these simple models give a fair over-all account of both the volume and temperature dependence of the Helmholtz energy. However, for $Tg\frac{1}{3}{T}_{\mathrm{melting}}$ (rms deviations greater than \ensuremath{\sim}6% of the nearest-neighbor distance), anharmonic contributions to the thermodynamic properties become unrealistically large, indicating, we believe, the breakdown of perturbation theory to the order considered in this work.

Vibration Spectra and Specific Heats of Cubic Metals. II. Application to Silver

Abstract: The frequency spectrum of silver, and hence its specific heat ${C}_{v}$ at constant volume as a function of temperature, are calculated by solving the secular equation derived in Part I of this work for the determination of the frequencies of the normal modes of vibration of a monovalent face-centered cubic metal The calculations are made with two sets of elastic constants, namely with their values at absolute zero of temperature and at room temperature The calculated ${C}_{v}$ are compared with the experimental data and with the earlier calculations based on a two force-constant model (in contrast to the three appearing in our secular equation) by plotting the corresponding effective Debye temperatures $\ensuremath{\Theta}$ against temperature It is found that, except for temperatures below about 7\ifmmode^\circ\else\textdegree\fi{}K, the agreement between theory and experiment is satisfactory It is shown that the discrepancy between the two sets of values below 7\ifmmode^\circ\else\textdegree\fi{}K can be partly removed by making a choice for the elastic constants slightly different from that actually used in the calculation However, it appears that the explanation of the entire discrepancy at low temperatures for silver and of a similar one found by Bhatia for sodium lies elsewhere

Phonon Energies and Lifetimes in Solid Ne and He in the First-Order Self-Consistent Approximation

Abstract: We discuss the response of a crystal in the presence of a neutron distortion in the first-order self-consistent approximation and we stress the importance of the self-consistency condition. The resultant integral equation for the phonon energies is solved by direct matrix inversion instead of truncating a series expansion. Numerical results are presented for solid Ne and fcc ${\mathrm{He}}^{4}$ at 10.0 and 11.5 ${\mathrm{cm}}^{3}$/mole.

A New Mixing of Hartree-Fock and Local Density-Functional Theories

Abstract: Previous attempts to combine Hartree–Fock theory with local density‐functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.

Density-Functional Theory for Time-Dependent Systems

Abstract: The response of an interacting many-particle system to a time-dependent external field can usually be treated within linear response theory. Due to rapid experimental progress in the field of laser physics, however, ultra-short laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach the strength of the electric field caused by atomic nuclei. If an atomic system is placed in the focus of such a laser pulse one observes a wealth of new phenomena [1] which cannot be explained by traditional perturbation theory. The non-perturbative quantum mechanical description of interacting particles moving in a very strong time-dependent external field therefore has become a prominent problem of theoretical physics. In principle, it requires a full solution of the time-dependent Schrodinger equation for the interacting many-body system, which is an exceedingly difficult task. In view of the success of density functional methods in the treatment of stationary many-body systems and in view of their numerical simplicity, a time-dependent version of density functional theory appears highly desirable, both within and beyond the regime of linear response.

Electronic Structure: Basic Theory and Practical Methods

Abstract: Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Path integrals in the theory of condensed helium

Abstract: One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.