Transitions between electron-molecule states in electrostatic quantum dots

Intermediate spin states that occur in electrostatic dots in the magnetic field regime just beyond the maximum density droplet are investigated. The 5-electron system is studied with exact diagonalization and group theory. The results indicate that the intermediate spin states are mixed symmetry states with a superposition of 5- and 4-fold electron-molecule configurations. A superposition of 5- and 4-fold correlation functions is found to reproduce the exact mixed symmetry pair correlation function to around 2%.Comment: 4 pages, 3 figure

Symmetry of `molecular' configurations of interacting electrons in a quantum dot in strong magnetic fields

A molecular description for magic-number configurations of interacting electrons in a quantum dot in high magnetic fields developed by one of the authors has been elaborated for four, five and six electron dots. For four electrons, the magic spin-singlet states are found to alternate between two different resonating valence bond (RVB)-like states. For the five-electron spin-polarized case, the molecular description is shown to work for the known phenomenon of magic-number sequences that correspond to both the N-fold symmetric ring configuration and a $(N-1)$-fold symmetric one with a center electron. A six-electron dot is shown here to have an additional feature in which inclusion of quantum mechanical mixing between classical configurations, which are deformed and degenerate, restores the N-fold symmetry and reproduces the ground-state energy accurately.Comment: 4 pages, to be published in Physisca

A structure theorem in probabilistic number theory

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the distribution of an additive function on the integers, and its distribution on the primes.Comment: 10 page

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5–2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K