285 research outputs found
Mutual Information of Population Codes and Distance Measures in Probability Space
We studied the mutual information between a stimulus and a large system
consisting of stochastic, statistically independent elements that respond to a
stimulus. The Mutual Information (MI) of the system saturates exponentially
with system size. A theory of the rate of saturation of the MI is developed. We
show that this rate is controlled by a distance function between the response
probabilities induced by different stimuli. This function, which we term the
{\it Confusion Distance} between two probabilities, is related to the Renyi
-Information.Comment: 11 pages, 3 figures, accepted to PR
Large time off-equilibrium dynamics of a manifold in a random potential
We study the out of equilibrium dynamics of an elastic manifold in a random
potential using mean-field theory. We find two asymptotic time regimes: (i)
stationary dynamics, (ii) slow aging dynamics with violation of equilibrium
theorems. We obtain an analytical solution valid for all large times with
universal scalings of two-time quantities with space. A non-analytic scaling
function crosses over to ultrametricity when the correlations become
long-range. We propose procedures to test numerically or experimentally the
extent to which this scenario holds for a given system.Comment: 12 page
A Solvable Model of a Glass
An analytically tractable model is introduced which exhibits both, a
glass--like freezing transition, and a collection of double--well
configurations in its zero--temperature potential energy landscape. The latter
are generally believed to be responsible for the anomalous low--temperature
properties of glass-like and amorphous systems via a tunneling mechanism that
allows particles to move back and forth between adjacent potential energy
minima. Using mean--field and replica methods, we are able to compute the
distribution of asymmetries and barrier--heights of the double--well
configurations {\em analytically}, and thereby check various assumptions of the
standard tunneling model. We find, in particular, strong correlations between
asymmetries and barrier--heights as well as a collection of single--well
configurations in the potential energy landscape of the glass--forming system
--- in contrast to the assumptions of the standard model. Nevertheless, the
specific heat scales linearly with temperature over a wide range of low
temperatures.Comment: 11 pages, latex, including 5 figures, talk presented at the XIV
Sitges Conferenc
Plasticity and learning in a network of coupled phase oscillators
A generalized Kuramoto model of coupled phase oscillators with slowly varying
coupling matrix is studied. The dynamics of the coupling coefficients is driven
by the phase difference of pairs of oscillators in such a way that the coupling
strengthens for synchronized oscillators and weakens for non-synchronized
pairs. The system possesses a family of stable solutions corresponding to
synchronized clusters of different sizes. A particular cluster can be formed by
applying external driving at a given frequency to a group of oscillators. Once
established, the synchronized state is robust against noise and small
variations in natural frequencies. The phase differences between oscillators
within the synchronized cluster can be used for information storage and
retrieval.Comment: 10 page
Phase variance of squeezed vacuum states
We consider the problem of estimating the phase of squeezed vacuum states
within a Bayesian framework. We derive bounds on the average Holevo variance
for an arbitrary number of uncorrelated copies. We find that it scales with
the mean photon number, , as dictated by the Heisenberg limit, i.e., as
, only for . For this fundamental scaling breaks down
and it becomes . Thus, a single squeezed vacuum state performs worse
than a single coherent state with the same energy. We find the optimal
splitting of a fixed given energy among various copies. We also compute the
variance for repeated individual measurements (without classical communication
or adaptivity) and find that the standard Heisenberg-limited scaling
is recovered for large samples.Comment: Minor changes, version to appear in PRA, 8 pages, 2 figure
Schwinger-Keldysh Approach to Disordered and Interacting Electron Systems: Derivation of Finkelstein's Renormalization Group Equations
We develop a dynamical approach based on the Schwinger-Keldysh formalism to
derive a field-theoretic description of disordered and interacting electron
systems. We calculate within this formalism the perturbative RG equations for
interacting electrons expanded around a diffusive Fermi liquid fixed point, as
obtained originally by Finkelstein using replicas. The major simplifying
feature of this approach, as compared to Finkelstein's is that instead of replicas, we only need to consider N=2 species. We compare the dynamical
Schwinger-Keldysh approach and the replica methods, and we present a simple and
pedagogical RG procedure to obtain Finkelstein's RG equations.Comment: 22 pages, 14 figure
Large times off-equilibrium dynamics of a particle in a random potential
We study the off-equilibrium dynamics of a particle in a general
-dimensional random potential when . We demonstrate the
existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it
ii.} slow aging dynamics with violation of equilibrium theorems. We derive the
equations obeyed by the slowly varying part of the two-times correlation and
response functions and obtain an analytical solution of these equations. For
short-range correlated potentials we find that: {\it i.} the scaling function
is non analytic at similar times and this behaviour crosses over to
ultrametricity when the correlations become long range, {\it ii.} aging
dynamics persists in the limit of zero confining mass with universal features
for widely separated times. We compare with the numerical solution to the
dynamical equations and generalize the dynamical equations to finite by
extending the variational method to the dynamics.Comment: 70 pages, 7 figures included, uuencoded Z-compressed .tar fil
Langevin description of speckle dynamics in nonlinear disordered media
We formulate a Langevin description of dynamics of a speckle pattern
resulting from the multiple scattering of a coherent wave in a nonlinear
disordered medium. The speckle pattern exhibits instability with respect to
periodic excitations at frequencies below some
, provided that the nonlinearity exceeds some
-dependent threshold. A transition of the speckle pattern from a
stationary state to the chaotic evolution is predicted upon increasing
nonlinearity. The shortest typical time scale of chaotic intensity fluctuations
is of the order of .Comment: 6 pages, 3 figure
Dynamics of relaxor ferroelectrics
We study a dynamic model of relaxor ferroelectrics based on the spherical
random-bond---random-field model and the Langevin equations of motion. The
solution to these equations is obtained in the long-time limit where the system
reaches an equilibrium state in the presence of random local electric fields.
The complex dynamic linear and third-order nonlinear susceptibilities
and , respectively, are calculated as
functions of frequency and temperature. In analogy with the static case, the
dynamic model predicts a narrow frequency dependent peak in ,
which mimics a transition into a glass-like state.Comment: 15 pages, Revtex plus 5 eps figure
Equilibrium and dynamical properties of the ANNNI chain at the multiphase point
We study the equilibrium and dynamical properties of the ANNNI (axial
next-nearest-neighbor Ising) chain at the multiphase point. An interesting
property of the system is the macroscopic degeneracy of the ground state
leading to finite zero-temperature entropy. In our equilibrium study we
consider the effect of softening the spins. We show that the degeneracy of the
ground state is lifted and there is a qualitative change in the low temperature
behaviour of the system with a well defined low temperature peak of the
specific heat that carries the thermodynamic ``weight'' of the ground state
entropy. In our study of the dynamical properties, the stochastic Kawasaki
dynamics is considered. The Fokker-Planck operator for the process corresponds
to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with
constraints on allowed states. This leads to a number of differences in its
properties which are obtained through exact numerical diagonalization,
simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E
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