33 research outputs found
Classical and quantum scattering by a Coulomb potential
For relativistic energies the small angle classical cross section for
scattering on a Coulomb potential agrees with the first Born approximation for
quantum cross section for scalar particle only in the leading term. The
disagreement in other terms can be avoided if the sum of all corrections to the
first Born approximation for large enough Coulomb charge contain the classical
terms which are independent of that charge. A small part of the difference in
classical and quantum cross sections may be attributed to the fact that the
relativistic quantum particle can rush through the field without interaction.
We expect that smaller impact parameters and spin facilitate this affect.Comment: 5pages, no figure
Superconductors with Magnetic Impurities: Instantons and Sub-gap States
When subject to a weak magnetic impurity potential, the order parameter and
quasi-particle energy gap of a bulk singlet superconductor are suppressed.
According to the conventional mean-field theory of Abrikosov and Gor'kov, the
integrity of the energy gap is maintained up to a critical concentration of
magnetic impurities. In this paper, a field theoretic approach is developed to
critically analyze the validity of the mean field theory. Using the
supersymmetry technique we find a spatially homogeneous saddle-point that
reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions
to the density of states that render the quasi-particle energy gap soft at any
non-zero magnetic impurity concentration. The sub-gap states are associated
with supersymmetry broken field configurations of the action. An analysis of
fluctuations around these configurations shows how the underlying supersymmetry
of the action is restored by zero modes. An estimate of the density of states
is given for all dimensionalities. To illustrate the universality of the
present scheme we apply the same method to study `gap fluctuations' in a normal
quantum dot coupled to a superconducting terminal. Using the same instanton
approach, we recover the universal result recently proposed by Vavilov et al.
Finally, we emphasize the universality of the present scheme for the
description of gap fluctuations in d-dimensional superconducting/normal
structures.Comment: 18 pages, 9 eps figure