468 research outputs found
Self-Similarity and Localization
The localized eigenstates of the Harper equation exhibit universal
self-similar fluctuations once the exponentially decaying part of a wave
function is factorized out. For a fixed quantum state, we show that the whole
localized phase is characterized by a single strong coupling fixed point of the
renormalization equations. This fixed point also describes the generalized
Harper model with next nearest neighbor interaction below a certain threshold.
Above the threshold, the fluctuations in the generalized Harper model are
described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include
Conductivity of 2D lattice electrons in an incommensurate magnetic field
We consider conductivities of two-dimensional lattice electrons in a magnetic
field. We focus on systems where the flux per plaquette is irrational
(incommensurate flux). To realize the system with the incommensurate flux, we
consider a series of systems with commensurate fluxes which converge to the
irrational value. We have calculated a real part of the longitudinal
conductivity . Using a scaling analysis, we have found
behaves as \,
when and the Fermi energy is near
zero. This behavior is closely related to the known scaling behavior of the
spectrum.Comment: 16 pages, postscript files are available on reques
Collision and symmetry-breaking in the transition to strange nonchaotic attractors
Strange nonchaotic attractors (SNAs) can be created due to the collision of
an invariant curve with itself. This novel ``homoclinic'' transition to SNAs
occurs in quasiperiodically driven maps which derive from the discrete
Schr\"odinger equation for a particle in a quasiperiodic potential. In the
classical dynamics, there is a transition from torus attractors to SNAs, which,
in the quantum system is manifest as the localization transition. This
equivalence provides new insights into a variety of properties of SNAs,
including its fractal measure. Further, there is a {\it symmetry breaking}
associated with the creation of SNAs which rigorously shows that the Lyapunov
exponent is nonpositive. By considering other related driven iterative
mappings, we show that these characteristics associated with the the appearance
of SNA are robust and occur in a large class of systems.Comment: To be appear in Physical Review Letter
Stripe Ansatzs from Exactly Solved Models
Using the Boltzmann weights of classical Statistical Mechanics vertex models
we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems,
characterized by a strong anisotropy, which gives rise to stripe like
structures. In the case of the six vertex model we compute exactly, in the
thermodynamic limit, the norm of the ansatz and other observables. Employing
this ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ
Hamiltonians along the legs coupled by an Ising term. Finally, we suggest a
connection between the six and eight-vertex Anisotropic Tensor Product Ansatzs,
and their associated Hamiltonians, with the smectic stripe phases recently
discussed in the literature.Comment: REVTEX4.b4 file, 10 pages, 2 ps Figures. Revised version to appear in
PR
Ground states of integrable quantum liquids
Based on a recently introduced operator algebra for the description of a
class of integrable quantum liquids we define the ground states for all
canonical ensembles of these systems. We consider the particular case of the
Hubbard chain in a magnetic field and chemical potential. The ground states of
all canonical ensembles of the model can be generated by acting onto the
electron vacuum (densities ), suitable
pseudoparticle creation operators. We also evaluate the energy gaps of the
non-lowest-weight states (non - LWS's) and non-highest-weight states (non -
HWS's) of the eta-spin and spin algebras relative to the corresponding ground
states. For all sectors of parameter space and symmetries the {\it exact ground
state} of the many-electron problem is in the pseudoparticle basis the
non-interacting pseudoparticle ground state. This plays a central role in the
pseudoparticle perturbation theory.Comment: RevteX 3.0, 43 pages, preprint Univ.Evora, Portuga
The Energy-Scaling Approach to Phase-Ordering Growth Laws
We present a simple, unified approach to determining the growth law for the
characteristic length scale, , in the phase ordering kinetics of a system
quenched from a disordered phase to within an ordered phase. This approach,
based on a scaling assumption for pair correlations, determines
self-consistently for purely dissipative dynamics by computing the
time-dependence of the energy in two ways. We derive growth laws for conserved
and non-conserved models, including two-dimensional XY models and
systems with textures. We demonstrate that the growth laws for other systems,
such as liquid-crystals and Potts models, are determined by the type of
topological defect in the order parameter field that dominates the energy. We
also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended,
REVISED --- rearranged and clarified, new paragraph on naive dimensional
analysis at end of section I
Dentine Oxygn Isotopes (δ18O) as a Proxy for Odontocete Distributions and Movements.
Spatial variation in marine oxygen isotope ratios ( δ18O) resulting from differential evaporation rates and precipitation inputs is potentially useful for characterizing marine mammal distributions and tracking movements across δ18O gradients. Dentine hydroxyapatite contains carbonate and phosphate that precipitate in oxygen isotopic equilibrium with body water, which in odontocetes closely tracks the isotopic composition of ambient water. To test whether dentine oxygen isotope composition reliably records that of ambient water and can therefore serve as a proxy for odontocete distribution and movement patterns, we measured δ18O values of dentine structural carbonate (δ18OSC) and phosphate (δ18OP) of seven odontocete species (n = 55 individuals) from regional marine water bodies spanning a surface water δ18O range of several per mil. Mean dentine δ18OSC (range +21.2 to +25.5‰ VSMOW) and δ18OP (+16.7 to +20.3‰) values were strongly correlated with marine surface water δ18O values, with lower dentine δ18OSC and δ18OP values in high-latitude regions (Arctic and Eastern North Pacific) and higher values in the Gulf of California, Gulf of Mexico, and Mediterranean Sea. Correlations between dentine δ18OSC and δ18OP values with marine surface water δ18O values indicate that sequential δ18O measurements along dentine, which grows incrementally and archives intra- and interannual isotopic composition over the lifetime of the animal, would be useful for characterizing residency within and movements among water bodies with strong δ18O gradients, particularly between polar and lower latitudes, or between oceans and marginal basins
InCoB2010 - 9thInternational Conference on Bioinformatics at Tokyo, Japan, September 26-28, 2010
10.1186/1471-2105-11-S7-S1BMC Bioinformatics11SUPPL. 7-BBMI
One-dimensional fermions with incommensuration
We study the spectrum of fermions hopping on a chain with a weak
incommensuration close to dimerization; both q, the deviation of the wave
number from pi, and delta, the strength of the incommensuration, are small. For
free fermions, we use a continuum Dirac theory to show that there are an
infinite number of bands which meet at zero energy as q approaches zero. In the
limit that the ratio q/ \delta --> 0, the number of states lying inside the q=0
gap is nonzero and equal to 2 \delta /\pi^2. Thus the limit q --> 0 differs
from q=0; this can be seen clearly in the behavior of the specific heat at low
temperature. For interacting fermions or the XXZ spin-1/2 chain close to
dimerization, we use bosonization to argue that similar results hold; as q -->
0, we find a nontrivial density of states near zero energy. However, the limit
q --> 0 and q=0 give the same results near commensurate wave numbers which are
different from pi. We apply our results to the Azbel-Hofstadter problem of
electrons hopping on a two-dimensional lattice in the presence of a magnetic
field. Finally, we discuss the complete energy spectrum of noninteracting
fermions with incommensurate hopping by going up to higher orders in delta.Comment: Revtex, 23 pages including 7 epsf figures; this is a greatly expanded
version of cond-mat/981133
Nonequilibrium Steady States of Driven Periodic Media
We study a periodic medium driven over a random or periodic substrate. Our
work is based on nonequilibrium continuum hydrodynamic equations of motion,
which we derive microscopically. We argue that in the random case instabilities
will always destroy the LRO of the lattice. In most, if not all, cases, the
stable driven ordered state is a transverse smectic, with ordering wavevector
perpendicular to the velocity. It consists of a periodic array of flowing
liquid channels, with transverse displacements and density (``permeation
mode'') as hydrodynamic variables. We present dynamic functional
renormalization group calculations in two and three dimensions for an
approximate model of the smectic. The finite temperature behavior is much less
glassy than in equilibrium, owing to a disorder-driven effective ``heating''
(allowed by the absence of the fluctuation-dissipation theorem). This, in
conjunction with the permeation mode, leads to a fundamentally analytic
transverse response for . Our results are compared to recent experiments
and other theoretical work.Comment: 39 PRB pages, RevTex and 9 postscript figures, uses multicol.st
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