On the Spectrum of the Local $${\mathbb {P}}^2$$ Mirror Curve

We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local $${\mathbb {P}}^2$$ P 2 in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.

NOISE AND CORRELATED TRANSPORT IN ION CHANNELS

The motion of an ion through a channel is described as a classical/quantum mechanical hopping process between the individual sites of a channel. The transition rates are due to the coupling of an ion to suitable reservoirs. If fluctuating forces are added to the rate equations for the occupation numbers, the equations become quantum mechanical operator equations. Using previous results, the fluctuating forces are uniquely determined by the requirement of quantum mechanical consistency. The resulting equations are solved for several cases and the occupation number fluctuations discussed. Particular emphasis is laid on a model of correlated transport.

Chemical interpretation: basis set use and the Periodic Table

Examination of contemporary quantum chemistry literature and texts strongly indicates the need for new interpretative measures and indices that have heuristic chemical appeal, but are rigorously defined by physics. A closer look at the Periodic Table in search of such measures leads to configurationenergy (CE), the average energy of a valence electron, which adds a third intrinsic dimension to the Table itself, and is also strongly correlated with atomic energy level spacings. CE can be translated into a quantum mechanical operator whose expectation value in molecules and solids is the Energy Index, EIA. Many chemical effects: rotation and inversion barriers, the anomeric and α-effects, hyperconjugation, etc., appear capable of being quantified, unified, and simplified by EIA, but because it is a one-electron entity, it does not correlate with binding energies or heats of formation. EIA is insitu electronegativity, and systematic release of basis set contraction constraints permits a controlled analysis of bond polarity in terms of radial and angular hybridization changes.