Objects: A Partial Reconstruction of Frege’s Grundgesetze in Object Theory∗ Edward N. Zalta† Center for the Study of Language and Information and Philosophy Department Stanford University In this paper, I derive a theory of numbers from a more general theory of abstract objects. The distinguishing feature of this derivation is that it involves no appeal to mathematical primitives or mathematica...

The incorporation of nuclear quantum effects and non-Born–Oppenheimer behavior into chemistry calculations molecular dynamics simulations is a longstanding challenge. nuclear–electronic orbital (NEO) approach treats specified nuclei, typically protons, mechanically on the same level as electrons with wave function density functional theory methods. This inherently includes delocalization zero-p...

We study periodic well-to-well flopping of rubidium atoms in one-dimensional grey optical lattices using a nondestructive, real-time measurement technique and quantum Monte Carlo wavefunction simulations. The observed flopping rates as well as flopping rates extracted from exact band structure calculations can largely be reproduced using adiabatic models that employ the Born–Oppenheimer approxi...

We consider heavy meson-antimeson pairs and their coupling to quarkonium in the context of nonrelativistic effective field theories (EFTs) incorporating adiabatic expansion. work out all leading order couplings obtain contributions masses widths quarkonia. match new potentials terms QCD. Using available lattice data for coupled system lowest lying pair, we extract mixing potential use it comput...

The time–dependent Born–Oppenheimer approximation describes the quantum mechanical motion of molecular systems. This approximation fails if a wavepacket propagates through an electron energy level crossing or “avoided crossing.” We discuss the various types of crossings and avoided crossings and describe what happens when molecular systems propagate through them. It is not practical to solve th...