63 research outputs found
Stability of the replica-symmetric saddle-point in general mean-field spin-glass models
Within the replica approach to mean-field spin-glasses the transition from
ergodic high-temperature behaviour to the glassy low-temperature phase is
marked by the instability of the replica-symmetric saddle-point. For general
spin-glass models with non-Gaussian field distributions the corresponding
Hessian is a matrix with the number of replicas tending to
zero eventually. We block-diagonalize this Hessian matrix using representation
theory of the permutation group and identify the blocks related to the
spin-glass susceptibility. Performing the limit within these blocks we
derive expressions for the de~Almeida-Thouless line of general spin-glass
models. Specifying these expressions to the cases of the
Sherrington-Kirkpatrick, Viana-Bray, and the L\'evy spin glass respectively we
obtain results in agreement with previous findings using the cavity approach
Quantifying dynamics of the financial correlations
A novel application of the correlation matrix formalism to study dynamics of
the financial evolution is presented. This formalism allows to quantify the
memory effects as well as some potential repeatable intradaily structures in
the financial time-series. The present study is based on the high-frequency
Deutsche Aktienindex (DAX) data over the time-period between November 1997 and
December 1999 and demonstrates a power of the method. In this way two
significant new aspects of the DAX evolution are identified: (i) the memory
effects turn out to be sizably shorter than what the standard autocorrelation
function analysis seems to indicate and (ii) there exist short term repeatable
structures in fluctuations that are governed by a distinct dynamics. The former
of these results may provide an argument in favour of the market efficiency
while the later one may indicate origin of the difficulty in reaching a
Gaussian limit, expected from the central limit theorem, in the distribution of
returns on longer time-horizons.Comment: 10 pages, 7 PostScript figures, talk presented by the first Author at
the NATO ARW on Econophysics, Prague, February 8-10, 2001; to be published in
proceedings (Physica A
Barkhausen Noise and Critical Scaling in the Demagnetization Curve
The demagnetization curve, or initial magnetization curve, is studied by
examining the embedded Barkhausen noise using the non-equilibrium, zero
temperature random-field Ising model. The demagnetization curve is found to
reflect the critical point seen as the system's disorder is changed. Critical
scaling is found for avalanche sizes and the size and number of spanning
avalanches. The critical exponents are derived from those related to the
saturation loop and subloops. Finally, the behavior in the presence of long
range demagnetizing fields is discussed. Results are presented for simulations
of up to one million spins.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
We analytically compute the spectrum of the Hessian of the Hamiltonian for a
system of N particles interacting via a purely repulsive potential in one
dimension. Our approach is valid in the low density regime, where we compute
the exact spectrum also in the localized sector. We finally perform a numerical
analysis of the localization properties of the eigenfunctions.Comment: 4 RevTeX pages, 4 EPS figures. Revised version to appear on Phys.
Rev. Let
Bending and Base-Stacking Interactions in Double-Stranded Semiflexible Polymer
Simple expressions for the bending and the base-stacking energy of
double-stranded semiflexible biopolymers (such as DNA and actin) are derived.
The distribution of the folding angle between the two strands is obtained by
solving a Schr\"{o}dinger equation variationally. Theoretical results based on
this model on the extension versus force and extension versus degree of
supercoiling relations of DNA chain are in good agreement with the experimental
observations of Cluzel {\it et al.} [Science {\bf 271}, 792 (1996)], Smith {\it
et al.} [{\it ibid.} {\bf 271}, 795 (1996)], and Strick {\it et al.} [{\it
ibid.} {\bf 271}, 1835 (1996)].Comment: 8 pages in Revtex format, with 4 EPS figure
The phase diagram of L\'evy spin glasses
We study the L\'evy spin-glass model with the replica and the cavity method.
In this model each spin interacts through a finite number of strong bonds and
an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses
becomes transparent in our solution: the local field contains a part
propagating along a backbone of strong bonds and a Gaussian noise term due to
weak bonds. Our method allows to determine the complete replica symmetric phase
diagram, the replica symmetry breaking line and the entropy. The results are
compared with simulations and previous calculations using a Gaussian ansatz for
the distribution of fields.Comment: 20 pages, 7 figure
Theory of High-Force DNA Stretching and Overstretching
Single molecule experiments on single- and double stranded DNA have sparked a
renewed interest in the force-extension of polymers. The extensible Freely
Jointed Chain (FJC) model is frequently invoked to explain the observed
behavior of single-stranded DNA. We demonstrate that this model does not
satisfactorily describe recent high-force stretching data. We instead propose a
model (the Discrete Persistent Chain, or ``DPC'') that borrows features from
both the FJC and the Wormlike Chain, and show that it resembles the data more
closely. We find that most of the high-force behavior previously attributed to
stretch elasticity is really a feature of the corrected entropic elasticity;
the true stretch compliance of single-stranded DNA is several times smaller
than that found by previous authors. Next we elaborate our model to allow
coexistence of two conformational states of DNA, each with its own stretch and
bend elastic constants. Our model is computationally simple, and gives an
excellent fit through the entire overstretching transition of nicked,
double-stranded DNA. The fit gives the first values for the elastic constants
of the stretched state. In particular we find the effective bend stiffness for
DNA in this state to be about 10 nm*kbt, a value quite different from either
B-form or single-stranded DNAComment: 33 pages, 11 figures. High-quality figures available upon reques
Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums
We study segregation of granular mixtures in the continuous avalanche regime
(for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory
for surface flows of grains. The theory predicts profiles in agreement with
experiments only when we consider a flux dependent velocity of flowing grains.
We find the segregation of species of different size and surface properties,
with the smallest and roughest grains being found preferentially at the center
of the drum. For a wide difference between the species we find a complete
segregation in agreement with experiments. In addition, we predict a transition
to a smooth segregation regime - with an power-law decay of the concentrations
as a function of radial coordinate - as the size ratio between the grains is
decreased towards one.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmaks
Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices
We study the statistical properties of eigenvalues of the Hessian matrix
(matrix of second derivatives of the potential energy) for a
classical atomic liquid, and compare these properties with predictions for
random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal
Mode or INM spectra) are evaluated numerically for configurations generated by
molecular dynamics simulations. We find that distribution of spacings between
nearest neighbor eigenvalues, s, obeys quite well the Wigner prediction , with the agreement being better for higher densities at fixed
temperature. The deviations display a correlation with the number of localized
eigenstates (normal modes) in the liquid; there are fewer localized states at
higher densities which we quantify by calculating the participation ratios of
the normal modes. We confirm this observation by calculating the spacing
distribution for parts of the INM spectra with high participation ratios,
obtaining greater conformity with the Wigner form. We also calculate the
spectral rigidity and find a substantial dependence on the density of the
liquid.Comment: To appear in Phys. Rev. E; 10 pages, 6 figure
Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
We study statistical properties of the ensemble of large random
matrices whose entries decrease in a power-law fashion
. Mapping the problem onto a nonlinear
model with non-local interaction, we find a transition from localized
to extended states at . At this critical value of the system
exhibits multifractality and spectral statistics intermediate between the
Wigner-Dyson and Poisson one. These features are reminiscent of those typical
for the mobility edge of disordered conductors. We find a continuous set of
critical theories at , parametrized by the value of the coupling
constant of the model. At all states are expected to be
localized with integrable power-law tails. At the same time, for
the wave packet spreading at short time scale is superdiffusive: , which leads to a modification of the
Altshuler-Shklovskii behavior of the spectral correlation function. At
the statistical properties of eigenstates are similar to those
in a metallic sample in dimensions. Finally, the region
is equivalent to the corresponding Gaussian ensemble of random
matrices . The theoretical predictions are compared with results of
numerical simulations.Comment: 19 pages REVTEX, 4 figure
- …