21 research outputs found
Green's function of a finite chain and the discrete Fourier transform
A new expression for the Green's function of a finite one-dimensional lattice
with nearest neighbor interaction is derived via discrete Fourier transform.
Solution of the Heisenberg spin chain with periodic and open boundary
conditions is considered as an example. Comparison to Bethe ansatz clarifies
the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20,
No. 5 (2006) 593-60
Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)
An infinite regular three-dimensional network is composed of identical
resistors each of resistance joining adjacent nodes. What is the equivalent
resistance between the lattice site and the lattice site, when two bonds are
removed from the perfect network? Three cases are considered here, and some
numerical values are calculated. Finally, the asymptotic behavior of the
equivalent resistance is studied for large distances between the two sites.Comment: 11 pages, 3 figures, published in EPJ-A
Infinite Networks of Identical Capacitors
The capacitance between the origin and any other lattice site in an infinite
square lattice of identical capacitors is studied. The method is generalized to
infinite Simple Cubic (SC) lattice. We make use of the superposition principle
and the symmetry of the infinite gridComment: 16 pages, 5 figures, 2 table