ar X iv : m at h - ph / 0 40 80 14 v 2 1 3 Ja n 20 06 The Flux - Across - Surfaces Theorem under conditions on the scattering state

ar X iv : m at h - ph / 9 90 80 08 v 1 6 A ug 1 99 9 The Flux - Across - Surfaces Theorem for a Point Interaction Hamiltonian

The flux-across-surfaces theorem establishes a fundamental relation in quantum scattering theory between the asymptotic outgoing state and a quantity which is directly measured in experiments. We prove it for a hamil-tonian with a point interaction, using the explicit expression for the propaga-tor. The proof requires only assuptions on the initial state and it covers also the case of zero-ener...

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : m at h - ph / 0 20 70 10 v 2 2 3 Se p 20 02 Flux - Across - Surfaces Theorem for a Dirac Particle

We consider the asymptotic evolution of a relativistic spin-1 2 particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability , that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as th...

ar X iv : m at h - ph / 0 50 90 44 v 2 1 1 Ja n 20 06 RANDOM POLYNOMIALS , RANDOM MATRICES AND L - FUNCTIONS

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.

ar X iv : m at h - ph / 0 60 10 40 v 1 2 0 Ja n 20 06 REMARKS ON THE COMPLEX GEOMETRY OF THE 3 - MONOPOLE

We develop the Ercolani-Sinha construction of SU (2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number theoretic problem and a recently proven identity of Ramanujan provides a ...