440 research outputs found
Universal criterion for the breakup of invariant tori in dissipative systems
The transition from quasiperiodicity to chaos is studied in a two-dimensional
dissipative map with the inverse golden mean rotation number. On the basis of a
decimation scheme, it is argued that the (minimal) slope of the critical
iterated circle map is proportional to the effective Jacobian determinant.
Approaching the zero-Jacobian-determinant limit, the factor of proportion
becomes a universal constant. Numerical investigation on the dissipative
standard map suggests that this universal number could become observable in
experiments. The decimation technique introduced in this paper is readily
applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page
Role of phason-defects on the conductance of a 1-d quasicrystal
We have studied the influence of a particular kind of phason-defect on the
Landauer resistance of a Fibonacci chain. Depending on parameters, we sometimes
find the resistance to decrease upon introduction of defect or temperature, a
behavior that also appears in real quasicrystalline materials. We demonstrate
essential differences between a standard tight-binding model and a full
continuous model. In the continuous case, we study the conductance in relation
to the underlying chaotic map and its invariant. Close to conducting points,
where the invariant vanishes, and in the majority of cases studied, the
resistance is found to decrease upon introduction of a defect. Subtle
interference effects between a sudden phason-change in the structure and the
phase of the wavefunction are also found, and these give rise to resistive
behaviors that produce exceedingly simple and regular patterns.Comment: 12 pages, special macros jnl.tex,reforder.tex, eqnorder.tex. arXiv
admin note: original tex thoroughly broken, figures missing. Modified so that
tex compiles, original renamed .tex.orig in source
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
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
Glassiness Vs. Order in Densely Frustrated Josephson Arrays
We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the
uniformly frustrated two dimensional XY model, for a sequence of frustrations f
converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp
first order equilibrium phase transition to an ordered vortex structure at a
T_c which varies only slightly with f. This ordered vortex structure remains in
general phase incoherent until a lower pinning transition T_p(f) that varies
with f. We argue that the glassy behaviors reported for this model in earlier
simulations are dynamic effects.Comment: 4 pages, 4 eps figure
Hidden dimers and the matrix maps: Fibonacci chains re-visited
The existence of cycles of the matrix maps in Fibonacci class of lattices is
well established. We show that such cycles are intimately connected with the
presence of interesting positional correlations among the constituent `atoms'
in a one dimensional quasiperiodic lattice. We particularly address the
transfer model of the classic golden mean Fibonacci chain where a six cycle of
the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys.
Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far
been provided, to the best of our knowledge. In addition, we show that our
prescription leads to a determination of other energy values for a mixed model
of the Fibonacci chain, for which the full matrix map may have similar cyclic
behaviour. Apart from the standard transfer-model of a golden mean Fibonacci
chain, we address a variant of it and the silver mean lattice, where the
existence of four cycles of the matrix map is already known to exist. The
underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review
Disturbance spreading in incommensurate and quasiperiodic systems
The propagation of an initially localized excitation in one dimensional
incommensurate, quasiperiodic and random systems is investigated numerically.
It is discovered that the time evolution of variances of atom
displacements depends on the initial condition. For the initial condition with
nonzero momentum, goes as with and 0 for
incommensurate Frenkel-Kontorova (FK) model at below and above
respectively; and for uniform, quasiperiodic and random chains. It
is also found that with the exponent of distribution
function of frequency at zero frequency, i.e., (as ). For the initial condition with zero
momentum, for all systems studied. The underlying physical meaning
of this diffusive behavior is discussed.Comment: 8 Revtex Pages, 5 PS figures included, to appear in Phys. Rev. B
April 200
Mapping the spatiotemporal dynamics of calcium signaling in cellular neural networks using optical flow
An optical flow gradient algorithm was applied to spontaneously forming net-
works of neurons and glia in culture imaged by fluorescence optical microscopy
in order to map functional calcium signaling with single pixel resolution.
Optical flow estimates the direction and speed of motion of objects in an image
between subsequent frames in a recorded digital sequence of images (i.e. a
movie). Computed vector field outputs by the algorithm were able to track the
spatiotemporal dynamics of calcium signaling pat- terns. We begin by briefly
reviewing the mathematics of the optical flow algorithm, and then describe how
to solve for the displacement vectors and how to measure their reliability. We
then compare computed flow vectors with manually estimated vectors for the
progression of a calcium signal recorded from representative astrocyte
cultures. Finally, we applied the algorithm to preparations of primary
astrocytes and hippocampal neurons and to the rMC-1 Muller glial cell line in
order to illustrate the capability of the algorithm for capturing different
types of spatiotemporal calcium activity. We discuss the imaging requirements,
parameter selection and threshold selection for reliable measurements, and
offer perspectives on uses of the vector data.Comment: 23 pages, 5 figures. Peer reviewed accepted version in press in
Annals of Biomedical Engineerin
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
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
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