577 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
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
Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper
Dimer decimation scheme is introduced in order to study the kicked quantum
systems exhibiting localization transition. The tight-binding representation of
the model is mapped to a vectorized dimer where an asymptotic dissociation of
the dimer is shown to correspond to the vanishing of the transmission
coefficient thru the system. The method unveils an intricate nesting of
extended and localized phases in two-dimensional parameter space. In addition
to computing transport characteristics with extremely high precision, the
renormalization tools also provide a new method to compute quasienergy
spectrum.Comment: There are five postscript figures. Only half of the figure (3) is
shown to reduce file size. However, missing part is the mirror image of the
part show
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
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
Phonon Localization in One-Dimensional Quasiperiodic Chains
Quasiperiodic long range order is intermediate between spatial periodicity
and disorder, and the excitations in 1D quasiperiodic systems are believed to
be transitional between extended and localized. These ideas are tested with a
numerical analysis of two incommensurate 1D elastic chains: Frenkel-Kontorova
(FK) and Lennard-Jones (LJ). The ground state configurations and the
eigenfrequencies and eigenfunctions for harmonic excitations are determined.
Aubry's "transition by breaking the analyticity" is observed in the ground
state of each model, but the behavior of the excitations is qualitatively
different. Phonon localization is observed for some modes in the LJ chain on
both sides of the transition. The localization phenomenon apparently is
decoupled from the distribution of eigenfrequencies since the spectrum changes
from continuous to Cantor-set-like when the interaction parameters are varied
to cross the analyticity--breaking transition. The eigenfunctions of the FK
chain satisfy the "quasi-Bloch" theorem below the transition, but not above it,
while only a subset of the eigenfunctions of the LJ chain satisfy the theorem.Comment: This is a revised version to appear in Physical Review B; includes
additional and necessary clarifications and comments. 7 pages; requires
revtex.sty v3.0, epsf.sty; includes 6 EPS figures. Postscript version also
available at
http://lifshitz.physics.wisc.edu/www/koltenbah/koltenbah_homepage.htm
Cisternal Organization of the Endoplasmic Reticulum during Mitosis
The endoplasmic reticulum (ER) of animal cells is a single, dynamic, and continuous membrane network of interconnected cisternae and tubules spread out throughout the cytosol in direct contact with the nuclear envelope. During mitosis, the nuclear envelope undergoes a major rearrangement, as it rapidly partitions its membrane-bound contents into the ER. It is therefore of great interest to determine whether any major transformation in the architecture of the ER also occurs during cell division. We present structural evidence, from rapid, live-cell, three-dimensional imaging with confirmation from high-resolution electron microscopy tomography of samples preserved by high-pressure freezing and freeze substitution, unambiguously showing that from prometaphase to telophase of mammalian cells, most of the ER is organized as extended cisternae, with a very small fraction remaining organized as tubules. In contrast, during interphase, the ER displays the familiar reticular network of convolved cisternae linked to tubules
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
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
The Short Range RVB State of Even Spin Ladders: A Recurrent Variational Approach
Using a recursive method we construct dimer and nondimer variational ansatzs
of the ground state for the two-legged ladder, and compute the number of dimer
coverings, the energy density and the spin correlation functions. The number of
dimer coverings are given by the Fibonacci numbers for the dimer-RVB state and
their generalization for the nondimer ones. Our method relies on the recurrent
relations satisfied by the overlaps of the states with different lengths, which
can be solved using generating functions. The recurrent relation method is
applicable to other short range systems. Based on our results we make a
conjecture about the bond amplitudes of the 2-leg ladder.Comment: REVTEX file, 32 pages, 10 EPS figures inserted in text with epsf.st
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