18 research outputs found
The Measure of the Orthogonal Polynomials Related to Fibonacci Chains: The Periodic Case
The spectral measure for the two families of orthogonal polynomial systems
related to periodic chains with N-particle elementary unit and nearest
neighbour harmonic interaction is computed using two different methods. The
interest is in the orthogonal polynomials related to Fibonacci chains in the
periodic approximation. The relation of the measure to appropriately defined
Green's functions is established.Comment: 19 pages, TeX, 3 scanned figures, uuencoded file, original figures on
request, some misprints corrected, tbp: J. Phys.
Physical nature of critical wave functions in Fibonacci systems
We report on a new class of critical states in the energy spectrum of general
Fibonacci systems. By introducing a transfer matrix renormalization technique,
we prove that the charge distribution of these states spreads over the whole
system, showing transport properties characteristic of electronic extended
states. Our analytical method is a first step to find out the link between the
spatial structure of these critical wave functions and the quasiperiodic order
of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in
Phys. Rev. Let
Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
We study the asymptotic limiting function , where is the chromatic polynomial for a graph
with vertices. We first discuss a subtlety in the definition of
resulting from the fact that at certain special points , the
following limits do not commute: . We then
present exact calculations of and determine the corresponding
analytic structure in the complex plane for a number of families of graphs
, including circuits, wheels, biwheels, bipyramids, and (cyclic and
twisted) ladders. We study the zeros of the corresponding chromatic polynomials
and prove a theorem that for certain families of graphs, all but a finite
number of the zeros lie exactly on a unit circle, whose position depends on the
family. Using the connection of with the zero-temperature Potts
antiferromagnet, we derive a theorem concerning the maximal finite real point
of non-analyticity in , denoted and apply this theorem to
deduce that and for the square and
honeycomb lattices. Finally, numerical calculations of and
are presented and compared with series expansions and bounds.Comment: 33 pages, Latex, 5 postscript figures, published version; includes
further comments on large-q serie
Basics of Bose-Einstein Condensation
The review is devoted to the elucidation of the basic problems arising in the
theoretical investigation of systems with Bose-Einstein condensate.
Understanding these challenging problems is necessary for the correct
description of Bose-condensed systems. The principal problems considered in the
review are as follows: (i) What is the relation between Bose-Einstein
condensation and global gauge symmetry breaking? (ii) How to resolve the
Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to
describe Bose-condensed systems in strong spatially random potentials? (iv)
Whether thermodynamically anomalous fluctuations in Bose systems are
admissible? (v) How to create nonground-state condensates? Detailed answers to
these questions are given in the review. As examples of nonequilibrium
condensates, three cases are described: coherent modes, turbulent superfluids,
and heterophase fluids.Comment: Review articl