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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 Jan 2016

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 ...


Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall Jan 1990

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 ...


The Exchange Potential In Path Integral Studies: Analytical Justification, Randall W. Hall Jan 1989

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 Treatment Of Exchange In Path Integral Simulations Via An Approximate Pseudopotential, Randall W. Hall Jan 1988

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 Jan 1987

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.