arXiv subjects
Publications and source records attributed to Oscar Bolina.
We present an elementary discussion of two basic properties of angular displacements, namely, the anticommutation of finite rotations and the commutation of infinitesimal rotations, and show how commutation is achieved as the angular displacements get smaller and smaller.
We give a new proof of the well-known upper bound on the correlation function of a gas of non-overlapping dipoles of fixed length and discrete orientation working directly in the charge representation, instead of the more usual sine-Gordon representation.
We develop a new method to determine the acceleration of a block sliding down along the face of a moving wedge. We have been able to link the solution of this problem to that of the inclined plane problem of elementary physics, thus providing a simpler solution to it.
The ground state nature of the Falicov-Kimball model with unconstrained hopping of electrons is investigated. We solve the eigenvalue problem in a pedagogical manner and give a complete account of the ground state energy both as a function of the number of electrons and nuclei and as a function of the total number of particles for any value of interaction U. We also study the energy gap and show the existence of a phase transition characterized by the absence of gap at the half--filled band for U<0. The model in consideration was proposed and solved by Farkasovsky for finite lattices and repulsive on-site interaction U>0. Contrary to his proposal we conveniently scale the hopping matrix to guarantee the existence of the thermodynamic limit. We also solve this model with bipartite unconstrained hopping matrices in order to compare with the Kennedy--Lieb variational analysis.