4 research outputs found
The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness
We determine the average number , of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for , there exists a connectivity critical value such that () for and
for . We find that is not a
constant, but scales very slowly with , as . The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.Comment: 4 figures 18 page
Asymptotics of Rydberg States for the Hydrogen Atom
The asymptotics of Rydberg states, i.e., highly excited bound states of the hydrogen atom Hamiltonian, and various expectations involving these states are investigated. We show that suitable linear combinations of these states, appropriately rescaled and regarded as functions either in momentum space or configuration space, are highly concentrated on classical momentum space or configuration space Kepler orbits respectively, for large quantum numbers. Expectations of momentum space or configuration space functions with respect to these states are related to time-averages of these functions over Kepler orbits. 1 Section I. Introduction Let H be the hydrogen atom Hamiltonian H = \Gamma 1 2 \Delta \Gamma jxj \Gamma1 acting in L 2 (R 3 ), with \Delta the 3-dimensional Laplacian. The purpose of this article is to investigate the asymptotics of Rydberg states of the Hamiltonian H, i.e., states with large principal quantum number k, and to investigate the asymptotics of various ex..