Counting the exponents of single transfer matrices

Details Counting the exponents of single transfer matrices Counting the exponents of single transfer matrices

2011-02-08

arxiv.org/abs/1102.1641v1

J. Math. Phys. 52 (2011) 063501

Physics

Mathematical Physics

9 pages, 2 figures

Scientific paper

10.1063/1.3594654

The eigenvalue equation of a band or a block tridiagonal matrix, the tight binding model for a crystal, a molecule, or a particle in a lattice with random potential or hopping amplitudes: these and other problems lead to three-term recursive relations for (multicomponent) amplitudes. Amplitudes n steps apart are linearly related by a transfer matrix, which is the product of n matrices. Its exponents describe the decay lengths of the amplitudes. A formula is obtained for the counting function of the exponents, based on a duality relation and the Argument Principle for the zeros of analytic functions. It involves the corner blocks of the inverse of the associated Hamiltonian matrix. As an illustration, numerical evaluations of the counting function of quasi 1D Anderson model are shown.

Affiliated with

Also associated with

No associations

Rating

Counting the exponents of single transfer matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting the exponents of single transfer matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting the exponents of single transfer matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-502758