37 research outputs found
Structure factor and dynamics of the helix-coil transition
Thermodynamical properties of the helix-coil transition were successfully
described in the past by the model of Lifson, Poland and Sheraga. Here we
compute the corresponding structure factor and show that it possesses a
universal scaling behavior near the transition point, even when the transition
is of first order. Moreover, we introduce a dynamical version of this model,
that we solve numerically. A Langevin equation is also proposed to describe the
dynamics of the density of hydrogen bonds. Analytical solution of this equation
shows dynamical scaling near the critical temperature and predicts a gelation
phenomenon above the critical temperature. In the case when comparison of the
two dynamical approaches is possible, the predictions of our phenomenological
theory agree with the results of the Monte Carlo simulations.Comment: 11 pages, 7 figure
Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain
The multifractal properties of the electronic spectrum of a general
quasiperiodic chain are studied in first order in the quasiperiodic potential
strength. Analytical expressions for the generalized dimensions are found and
are in good agreement with numerical simulations. These first order results do
not depend on the irrational incommensurability.Comment: 10 Pages in RevTeX, 2 Postscript figure
Correlation inequalities for noninteracting Bose gases
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0
independent of the number of particles we derive the inequalities _N <
_{N+1}, _N _N _N for i\neq j, \partial
_N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation
number of the ith eigenstate of H^0, \beta is the inverse temperature and the
superscript + refers to adding an extra level to those of H^0. The results
follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde
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.
Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation
We present an algebraic framework for identifying the order parameter and the
possible phases of quantum systems that is based on identifying the local
dimension of the quantum operators and using the SU(N) group representing
the generators of generalized spin-particle mappings. We illustrate this for
=3 by presenting for any spatial dimension the exact solution of the
bilinear-biquadratic =1 quantum Heisenberg model at a high symmetry point.
Through this solution we rigorously show that itinerant ferromagnetism and
Bose-Einstein condensation may coexist.Comment: 5 pages, 1 psfigur
Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences
We comment on some recent investigations on the electronic properties of
models associated to the Thue-Morse chain and point out that their conclusions
are in contradiction with rigorously proven theorems and indicate some of the
sources of these misinterpretations. We briefly review and explain the current
status of mathematical results in this field and discuss some conjectures and
open problems.Comment: 15,CPT-94/P.3003,tex,
Self-consistent equation for an interacting Bose gas
We consider interacting Bose gas in thermal equilibrium assuming a positive
and bounded pair potential such that 0<\int d\br V(r) = a<\infty.
Expressing the partition function by the Feynman-Kac functional integral yields
a classical-like polymer representation of the quantum gas. With Mayer graph
summation techniques, we demonstrate the existence of a self-consistent
relation between the density and the
chemical potential , valid in the range of convergence of Mayer series.
The function is equal to the sum of all rooted multiply connected graphs.
Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in
the mean-field limit only tree diagrams contribute and function
reduces to the free gas density.
We also investigate how to extend the validity of the self-consistent
relation beyond the convergence radius of Mayer series (vicinity of
Bose-Einstein condensation) and study dominant corrections to mean field. At
lowest order, the form of function is shown to depend on single polymer
partition function for which we derive lower and upper bounds and on the
resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.
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
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
We prove a general rigorous lower bound for
, the exponent of the ground state
entropy of the -state Potts antiferromagnet, on an arbitrary Archimedean
lattice . We calculate large- series expansions for the exact
and compare these with our lower bounds on
this function on the various Archimedean lattices. It is shown that the lower
bounds coincide with a number of terms in the large- expansions and hence
serve not just as bounds but also as very good approximations to the respective
exact functions for large on the various lattices
. Plots of are given, and the general dependence on
lattice coordination number is noted. Lower bounds and series are also
presented for the duals of Archimedean lattices. As part of the study, the
chromatic number is determined for all Archimedean lattices and their duals.
Finally, we report calculations of chromatic zeros for several lattices; these
provide further support for our earlier conjecture that a sufficient condition
for to be analytic at is that is a regular
lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in
Phys. Rev.