Fluctuating Fields at a Sphaleron and a Generalized Levinson Theorem

Generalized Levinson theorem for singular potentials in two dimensions

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states Nm b in a given mth partial wave is related to the phase shift dm(k) and the singularity strength of the potential. When the effective potential has an inverse square singularity at the origin of the form n/r and inverse square tail at ...

Levinson-like theorem for scattering from a Bose-Einstein condensate.

A relation between the number of bound elementary excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalizes Levinson's theorem. Specific features of the Bogoliubov model such as complex energy and continuum bound states are discussed and a nu...

2 6 A pr 1 99 9 COSMOLOGICAL LEVINSON THEOREM

If at least some Wheeler-DeWitt solutions can be interpreted as zero-energy resonances then the total s-wave cross section of the corresponding quantum universes is infinite. The present, common 'quantum' cosmological framework is based on the Wheeler-DeWitt equation, which being a 'stationary', zero-energy differential equation appears to have no obvious time dependence and therefore forcing o...

A Fixed Point Theorem in Generalized D-metric Spaces

Generalized Levinson–durbin Sequences and Binomial Coefficients

Abstract The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson– Durbin sequence is also defined, and we note that binomial c...