We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized two-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributio...

Bose-Einstein condensation is the occupation of a single quantum state by a large number of identical particles. This implies that particles are assumed to be bosons, satisfying the Bose-Einstein statistics allowing for many particles to pile up in the same quantum state. This is contrary to fermions, satisfying the Fermi-Dirac statistics, for which the Pauli exclusion principle does not allow ...

We generalize the Einstein photoelectric equation for the case that the matter is irradiated by the polychromatic light of blackbody, or, by the synchrotron radiation. The work function of the collective motion of photoelectrons is discussed.

A method for finding solutions of the Riccati differential equation y′ = P (x) + Q(x)y + R(x)y2 is introduced. Provided that certain relations exist between the coefficient P (x), Q(x) and R(x), the above equation can be solved in closed form. We determine the required relations and find the general solutions to the aforementioned equation. The method is then applied to the Riccati equation ari...

This paper contains a classification of all 3-dimensional manifolds with constant scalar curvature S 6= 0 that carry a non-trivial solution of the Einstein-Dirac equation. Subj. Class.: Differential Geometry. 1991 MSC: 53C25, 58G30