7,255 research outputs found
Scattering from isospectral quantum graphs
Quantum graphs can be extended to scattering systems when they are connected
by leads to infinity. It is shown that for certain extensions, the scattering
matrices of isospectral graphs are conjugate to each other and their poles
distributions are therefore identical. The scattering matrices are studied
using a recently developed isospectral theory. At the same time, the scattering
approach offers a new insight on the mentioned isospectral construction
Effective Field Theories
Three lectures on effective field theory given at the Seventh Summer School
in Nuclear Physics, Seattle June 19-30 1995.Comment: 40 pages uuencoded with figures; requires macros harvmac, epsf.te
Direct computation of scattering matrices for general quantum graphs
We present a direct and simple method for the computation of the total
scattering matrix of an arbitrary finite noncompact connected quantum graph
given its metric structure and local scattering data at each vertex. The method
is inspired by the formalism of Reflection-Transmission algebras and quantum
field theory on graphs though the results hold independently of this formalism.
It yields a simple and direct algebraic derivation of the formula for the total
scattering and has a number of advantages compared to existing recursive
methods. The case of loops (or tadpoles) is easily incorporated in our method.
This provides an extension of recent similar results obtained in a completely
different way in the context of abstract graph theory. It also allows us to
discuss briefly the inverse scattering problem in the presence of loops using
an explicit example to show that the solution is not unique in general. On top
of being conceptually very easy, the computational advantage of the method is
illustrated on two examples of "three-dimensional" graphs (tetrahedron and
cube) for which other methods are rather heavy or even impractical.Comment: 20 pages, 4 figure
Weak localization of disordered quasiparticles in the mixed superconducting state
Starting from a random matrix model, we construct the low-energy effective
field theory for the noninteracting gas of quasiparticles of a disordered
superconductor in the mixed state. The theory is a nonlinear sigma model, with
the order parameter field being a supermatrix whose form is determined solely
on symmetry grounds. The weak localization correction to the field-axis thermal
conductivity is computed for a dilute array of s-wave vortices near the lower
critical field H_c1. We propose that weak localization effects, cut off at low
temperatures by the Zeeman splitting, are responsible for the field dependence
of the thermal conductivity seen in recent high-T_c experiments by Aubin et al.Comment: RevTex, 8 pages, 1 eps figure, typos correcte
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