Kink-Based Path Integral Calculations of Atoms He-Ne

An adaptive, kink-based path integral formalism is used to calculate the ground state energies of the atoms He-Ne. The method uses an adaptive scheme to virtually eliminate the sign difficulties. This is done by using a Monte Carlo scheme to identify states that contribute significantly to the canonical partition function and then include them in the wavefunctions to calculate the canonical averages. The calculations use the 6-31G basis set and obtain both precision and accuracy.Comment: To appear in Chem. Phys. Let

Simulation of geometric and electronic degrees of freedom using a kink-based path integral formulation: application to molecular systems

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH$_4$, NH$_3$, and H$_2$O demonstrate this method to be accurate for both geometries and energies. Comparison with DFT and MP2 level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.Comment: 23 pages, 2 figure

Intermolecular Forces and the Glass Transition

Random first order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first order transition theory, is used to treat individual glassy configurations, while the liquid phase is treated using common liquid state approximations. The transition temperature $T^{*}_{A}$, the temperature where the onset of activated behavior is predicted by mean field theory, the lower crossover temperature $T_{c}^{*}$ where barrierless motions actually occur through fractal or stringy motions, and $T^{*}_{K}$, the Kauzmann temperature, are calculated in addition to $T^{*}_{g}$, the glass transition temperature that corresponds to laboratory cooling rates. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for $\Delta C_{V}$ and $\Delta C_{p}$ that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the $\alpha$-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.Comment: Submitted to J. Phys. Chem. A, June 2007 Replaced with accepted version Sept. 200

The Treatment of Exchange in Path Integral Simulations via an Approximate Pseudopotential

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

An Index of Choral Music Performed During the National Conventions of the American Choral Directors Association (1991-2019)

The purpose of this study was to index and examine the repertoire of choirs selected to perform at the American Choral Directors Association (ACDA) National Conventions/Conferences between the years of 1991-2019. This is a replicated study of William Jones’s dissertation, An Index of Choral Music Performed during National Conventions of the American Choral Directors Association (1960-1987). The researcher accumulated and examined National Convention/Conference programs with the following objectives in mind: to investigate literature trends reflected in National Conventions/Conferences, and to provide choral conductors a guide through which they may gain an overview of literature performed on National Convention/Conference programs. The researcher provided tables listing the frequency of performance data. Additionally, the researcher provided an index of compositions performed sorted by title and composer/arranger

The Exchange Potential in Path Integral Studies: Analytical Justification

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 (allowed) correlated Boltzmannwave functions have negligible amplitude for like‐spin fermion–fermion distances less than the diameter of the individual particle wave packets. For example, in the case of two spin‐up (or spin‐down) fermions, if one fermion is located at r, then ‖Ψ(r,q)‖2 is negligible if q≂r. This should be the case for systems where a tight binding model is appropriate or for systems with strong interparticle repulsions

Path Integral Studies of the 2D Hubbard Model Using a New Projection Operator

Feynman’s path integral formulation of quantum mechanics, supplemented by an approximate projection operator (exact in the case of noninteracting particles), is used to study the 2D Hubbard model. The projection operator is designed to study Hamiltonians defined on a finite basis set, but extensions to continuous basis sets are suggested. The projection operator is shown to reduce the variance by a significant amount relative to straightforward Monte Carlo integration. Approximate calculations are usually within one standard deviation of exact results and virtually always within two to three standard deviations. In addition, the algorithm scales with the number of discretization points P as either P or P 2 (depending on the method of implementation), rather than the P 3 of the Hubbard–Stratonovich transformation. Accuracy to about 5%–10% in energies and spin–spin correlation functions are found using moderate amounts of computer time

Local Discrete Symmetry in the Brane Neighborhood

With the ansatz that there exist local or global discrete symmetries in the special branes' neighborhoods, we can construct the extra dimension models with only zero modes, or the models which have large extra dimensions and arbitrarily heavy KK modes because there is no simple relation between the mass scales of extra dimensions and the masses of KK states. In addition, the bulk gauge symmetry and supersymmetry can be broken on the special branes for all the modes, and in the bulk for the zero modes by local and global discrete symmetries. To be explicit, we discuss the supersymmetric SU(5) model on $M^4\times S^1/Z_2$ in which there is a local $Z_2'$ symmetry in the special 3-brane neighborhood along the fifth dimension.Comment: Latex, 10 pages, add references, version to appear in PL

Meat

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