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Articles 1 - 7 of 7
Full-Text Articles in Physics
Sign Learning Kink-Based (Silk) Quantum Monte Carlo For Molecular Systems, Xiaoyao Ma, Randall W. Hall, Frank Loffler, Karol Kowalski, Kiran Bhaskaran-Nair, Mark Jarrell, Juana Moreno
Sign Learning Kink-Based (Silk) Quantum Monte Carlo For Molecular Systems, Xiaoyao Ma, Randall W. Hall, Frank Loffler, Karol Kowalski, Kiran Bhaskaran-Nair, Mark Jarrell, Juana Moreno
Collected Faculty and Staff Scholarship
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initioground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of …
Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes
Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes
Collected Faculty and Staff Scholarship
By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the …
Microscopic Theory Of Network Glasses, Randall W. Hall, Peter G. Wolynes
Microscopic Theory Of Network Glasses, Randall W. Hall, Peter G. Wolynes
Collected Faculty and Staff Scholarship
A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are “strong” while van der Waals liquids without coordination are “fragile.”
Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall
Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall
Collected Faculty and Staff Scholarship
Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4–Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results …
The Exchange Potential In Path Integral Studies: Analytical Justification, Randall W. Hall
The Exchange Potential In Path Integral Studies: Analytical Justification, Randall W. Hall
Collected Faculty and Staff Scholarship
We present analytical justification for our previously described exchange pseudopotential. We show how the fermi quantum partition function can be constructed from the Boltzmann (distinguishable particle) wave functions if the states that correspond to like‐spin electrons occupying the same quantum state are excluded. A class of weighting functions that satisfy this constraint approximately is discussed. Our previous pseudopotential falls under this class. Essentially, our pseudopotential forces the unwanted states to have high energy and, hence, to make negligible contribution to the partition function. Exchange potentials of the form discussed in this article should be useful for studying systems where the …
The Treatment Of Exchange In Path Integral Simulations Via An Approximate Pseudopotential, Randall W. Hall
The Treatment Of Exchange In Path Integral Simulations Via An Approximate Pseudopotential, Randall W. Hall
Collected Faculty and Staff Scholarship
An approximate form that includes the effects of exchange is suggested for the short time propagator used in path integral simulations. The form is inspired physically by the approximation made in Hartree–Fock treatments of atoms and molecules. The approximate propagator is used with q u a n t i t a t i v e accuracy in two systems: an ideal gas of fermions localized in a three‐dimensional harmonic well and the triplet state of the sodium dimer.
The Aperiodic Crystal Picture And Free Energy Barriers In Glasses, Randall W. Hall, Peter G. Wolynes
The Aperiodic Crystal Picture And Free Energy Barriers In Glasses, Randall W. Hall, Peter G. Wolynes
Collected Faculty and Staff Scholarship
The aperiodic crystal picture associates the glass transition with freezing into a nonperiodic structure. Dynamics in the glassy state involves activated jumps between different aperiodic free energy minima. Activation barriers may be estimated through the use of freezing theory and the theory of dense solids. The results resemble, but are distinct from, free volume theory. Reasonable fits to experimental data are obtained.