Representations of the wavefunction of the multiparticle Schrödinger equation using an unconstrained sum of Slater determinants have the potential to be very efficient, except that they cannot capture the interelectron cusp. To remedy this shortcoming, we extend these representations to include interelectron geminals and analyze the algorithmic implications of doing so.

Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin determinant suitable for explicit computations.

The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum-or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations...

We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are by Guoce Xin and Christian Krattenthaler. Our proofs employ computer algebra methods, namely the holonomic ansatz proposed by Doron Zeilberger and variations thereof. These variati...

Because QCD in four dimensions is renormalizable, not super-renormalizable, the fluctuations of the fermion determinant are significant at all physical scales. Fortunately the short distance behaviour of QCD is very well understood. In particular, we know that for sufficiently high momentum scales this physics should be accurately described by an improved gauge action. In the truncated determin...

Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of three-dimensional homogeneous electron gas at very low density. Fermi fluid body-centered cubic Wigner crystal ground-state energies determined using Slater-Jastrow-backflow Slater-Jastrow many-body wave functions different densities spin polarizations in finite simulation cel...

Given a tournament T = (X, A), we consider two tournament solutions applied to T: Slater’s solution and Copeland’s solution. Slater’s solution consists in determining the linear orders obtained by reversing a minimum number of directed edges of T in order to make T transitive. Copeland’s solution applied to T ranks the vertices of T according to their decreasing out-degrees. The aim of this pap...

Klahr Slater and Quinn Piaget chapter FINAL.docx 2 The Swiss psychologist Jean Piaget (1896-1980) remains unchallenged as the most influential developmental psychologist in history. Indeed, as one prominent researcher put it over 25 years ago, " Before Piaget began his work, no recognizable field of cognitive development existed " (Siegler, 1986 ,pp 21-22). The vast sweep of Piaget's theories, ...

Using a hybrid density-functional theory (DFT) calculation including spin-orbit coupling (SOC), we predict that the zigzag antiferromagnetic (AFM) ground state of the honeycomb layered compound Na₂IrO₃ opens the observed insulating gap through a long-range magnetic order. We show that the effect of SOC and the correction of self-interaction error inherent in previous local or semilocal DFT calc...