966 research outputs found
Instabilities and waves in thin films of living fluids
We formulate the thin-film hydrodynamics of a suspension of polar self-driven
particles and show that it is prone to several instabilities through the
interplay of activity, polarity and the existence of a free surface. Our
approach extends, to self-propelling systems, the work of Ben Amar and Cummings
[Phys Fluids 13 (2001) 1160] on thin-film nematics. Based on our estimates the
instabilities should be seen in bacterial suspensions and the lamellipodium,
and are potentially relevant to the morphology of biofilms. We suggest several
experimental tests of our theory.Comment: 4 pages, pdflatex, accepted for publication in Phys Rev Let
Solution of a Generalized Stieltjes Problem
We present the exact solution for a set of nonlinear algebraic equations
. These
were encountered by us in a recent study of the low energy spectrum of the
Heisenberg ferromagnetic chain \cite{dhar}. These equations are low
(density) ``degenerations'' of more complicated transcendental equation of
Bethe's Ansatz for a ferromagnet, but are interesting in themselves. They
generalize, through a single parameter, the equations of Stieltjes,
, familiar from Random Matrix theory.
It is shown that the solutions of these set of equations is given by the
zeros of generalized associated Laguerre polynomials. These zeros are
interesting, since they provide one of the few known cases where the location
is along a nontrivial curve in the complex plane that is determined in this
work.
Using a ``Green's function'' and a saddle point technique we determine the
asymptotic distribution of zeros.Comment: 19 pages, 4 figure
Anomalous viscous loss in emulsions
We propose a model for concentrated emulsions based on the speculation that a macroscopic shear strain does not produce an affine deformation in the randomly close-packed droplet structure. The model yields an anomalous contribution to the complex dynamic shear modulus that varies as the square root of frequency. We test this prediction using a novel light scattering technique to measure the dynamic shear modulus, and directly observe the predicted behavior over six decades of frequency and a wide range of volume fractions
Order-chaos transitions in field theories with topological terms: a dynamical systems approach
We present a comparative study of the dynamical behaviour of topological
systems of recent interest, namely the non-Abelian Chern-Simons Higgs system
and the Yang-Mills Chern-Simons Higgs system. By reducing the full field
theories to temporal differential systems using the assumption of spatially
homogeneous fields , we study the Lyapunov exponents for two types of initial
conditions. We also examine in minute detail the behaviour of the Lyapunov
spectra as a function of the various coupling parameters in the system. We
compare and contrast our results with those for Abelian Higgs, Yang-Mills Higgs
and Yang-Mills Chern-Simons systems which have been discussed by other authors
recently. The role of the various terms in the Hamiltonians for such systems in
determining the order-disorder transitions is emphasized and shown to be
counter-intuitive in the Yang-Mills Chern-Simons Higgs systems.Comment: 19 pages,15 figures available in hard copy from C. Mukku, and through
e-mail from [email protected]. To appear in J. Phys.
Quantum-Mechanical Position Operator and Localization in Extended Systems
We introduce a fundamental complex quantity, , which allows us to
discriminate between a conducting and non-conducting thermodynamic phase in
extended quantum systems. Its phase can be related to the expectation value of
the position operator, while its modulus provides an appropriate definition of
a localization length. The expressions are valid for {\it any} fractional
particle filling. As an illustration we use to characterize insulator
to ``superconducting'' and Mott transitions in one-dimensional lattice models
with infinite on-site Coulomb repulsion at quarter filling.Comment: 4 pages, REVTEX, 1 ps figure
Extremely Correlated Quantum Liquids
We formulate the theory of an extremely correlated electron liquid,
generalizing the standard Fermi liquid. This quantum liquid has specific
signatures in various physical properties, such as the Fermi surface volume and
the narrowing of electronic bands by spin and density correlation functions.
We use Schwinger's source field idea to generate equations for the Greens
function for the Hubbard operators. A local (matrix) scale transformation in
the time domain to a quasiparticle Greens function, is found to be optimal.
This transformation allows us to generate vertex functions that are guaranteed
to reduce to the bare values for high frequencies, i.e. are ``asymptotically
free''. The quasiparticles are fractionally charged objects, and we find an
exact Schwinger Dyson equation for their Greens function. We find a hierarchy
of equations for the vertex functions, and further we obtain Ward identities so
that systematic approximations are feasible.
An expansion in terms of the density of holes measured from the Mott Hubbard
insulating state follows from the nature of the theory. A systematic
presentation of the formalism is followed by some preliminary explicit
calculations.Comment: 40 pages, typos remove
Superconductivity in CoO Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model
Motivated by the recent discovery of superconductivity in two dimensional
CoO layers, we present some possibly useful results of the RVB mean field
theory applied to the triangular lattice. Away from half filling, the order
parameter is found to be complex, and yields a fully gapped quasiparticle
spectrum. The sign of the hopping plays a crucial role in the analysis, and we
find that superconductivity is as fragile for one sign as it is robust for the
other. NaCoOHO is argued to belong to the robust case, by
comparing the LDA Fermi surface with an effective tight binding model. The high
frequency Hall constant in this system is potentially interesting, since it is
pointed out to increase linearly with temperature without saturation for T
T.Comment: Published in Physical Review B, total 1 tex + 9 eps files. Erratum
added as separate tex file on November 7, 2003, a numerical factor corrected
in the erratum on Dec 3, 200
Correlation between nanomechanical and piezoelectric properties of thin films: an experimental and finite element study
Piezoelectric materials perform mechanical-to-electrical energy conversion and have unique and enhanced properties, particularly in the thin film form. In this work, the nanomechanical properties of strontium-doped lead zirconate titanate thin films are investigated by nanoindentation. Finite element modeling of the nanoindentation process allows for a comparison of the simulated and experimentally measured load-displacement curves. New insights correlating the nanomechanical and piezoelectric properties of thin films have been obtained which will enable more efficient design of piezoelectric energy harvesting devices
A Majorana Fermion t-J Model in One Dimension
We study a rotation invariant Majorana fermion model in one dimension using
diagrammatic perturbation theory and numerical diagonalization of small
systems. The model is inspired by a Majorana representation of the
antiferromagnetic spin-1/2 chain, and it is similar in form to the t-J model of
electrons, except that the Majorana fermions carry spin-1 and Z_2 charge. We
discuss the implications of our results for the low-energy excitations of the
spin-1/2 chain. We also discuss a generalization of our model from 3 species of
Majorana fermions to N species; the SO(4) symmetric model is particularly
interesting.Comment: 29 LaTeX pages, 11 postscript figure
Supersymmetry and Integrability in Planar Mechanical Systems
We present an N=2-supersymmetric mechanical system whose bosonic sector, with
two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory
with the assumption of spatially homogeneous field configurations and a
particular ansatz imposed on the gauge potentials in the dimensional reduction
procedure. The Painleve test is adopted to discuss integrability and we focus
on the role of supersymmetry and parity invariance in two space dimensions for
the attainment of integrable or chaotic models. Our conclusion is that the
relationships among the parameters imposed by supersymmetry seem to drastically
reduce the number of possibilities for integrable interaction potentials of the
mechanical system under consideration.Comment: 20 pages, 3 figure
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