916 research outputs found
Photon Statistics for Single Molecule Non-Linear Spectroscopy
We consider the theory of the non-linear spectroscopy for a single molecule
undergoing stochastic dynamics and interacting with a sequence of two laser
pulses. General expressions for photon counting statistics are obtained, and an
exact solution to the problem of the Kubo-Anderson process is found. In the
limit of impulsive pulses the information on the photon statistics is contained
in the molecule's dipole correlation function. The selective limit where
temporal resolution is maintained, the semi-classical approximation and the
fast modulation limit exhibit general behaviors of this new type of
spectroscopy. We show how the design of the external field leads to rich
insights on dynamics of individual molecules which are different than those
found for an ensemble
Learning Curves for Mutual Information Maximization
An unsupervised learning procedure based on maximizing the mutual information
between the outputs of two networks receiving different but statistically
dependent inputs is analyzed (Becker and Hinton, Nature, 355, 92, 161). For a
generic data model, I show that in the large sample limit the structure in the
data is recognized by mutual information maximization. For a more restricted
model, where the networks are similar to perceptrons, I calculate the learning
curves for zero-temperature Gibbs learning. These show that convergence can be
rather slow, and a way of regularizing the procedure is considered.Comment: 13 pages, to appear in Phys.Rev.
Towards deterministic equations for Levy walks: the fractional material derivative
Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited
Random Time-Scale Invariant Diffusion and Transport Coefficients
Single particle tracking of mRNA molecules and lipid granules in living cells
shows that the time averaged mean squared displacement of
individual particles remains a random variable while indicating that the
particle motion is subdiffusive. We investigate this type of ergodicity
breaking within the continuous time random walk model and show that
differs from the corresponding ensemble average. In
particular we derive the distribution for the fluctuations of the random
variable . Similarly we quantify the response to a
constant external field, revealing a generalization of the Einstein relation.
Consequences for the interpretation of single molecule tracking data are
discussed.Comment: 4 pages, 4 figures.Article accompanied by a PRL Viewpoint in
Physics1, 8 (2008
Ergodicity Breaking in a Deterministic Dynamical System
The concept of weak ergodicity breaking is defined and studied in the context
of deterministic dynamics. We show that weak ergodicity breaking describes a
weakly chaotic dynamical system: a nonlinear map which generates subdiffusion
deterministically. In the non-ergodic phase non-trivial distribution of the
fraction of occupation times is obtained. The visitation fraction remains
uniform even in the non-ergodic phase. In this sense the non-ergodicity is
quantified, leading to a statistical mechanical description of the system even
though it is not ergodic.Comment: 11 pages, 4 figure
Analytical and Numerical Study of Internal Representations in Multilayer Neural Networks with Binary Weights
We study the weight space structure of the parity machine with binary weights
by deriving the distribution of volumes associated to the internal
representations of the learning examples. The learning behaviour and the
symmetry breaking transition are analyzed and the results are found to be in
very good agreement with extended numerical simulations.Comment: revtex, 20 pages + 9 figures, to appear in Phys. Rev.
Theory of Single File Diffusion in a Force Field
The dynamics of hard-core interacting Brownian particles in an external
potential field is studied in one dimension. Using the Jepsen line we find a
very general and simple formula relating the motion of the tagged center
particle, with the classical, time dependent single particle reflection and transmission coefficients. Our formula describes rich
physical behaviors both in equilibrium and the approach to equilibrium of this
many body problem.Comment: 4 Phys. Rev. page
Investigation of a generalized Obukhov Model for Turbulence
We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys.
6, 113 (1959)] for the description of the joint position-velocity statistics of
a single fluid particle in fully developed turbulence. In the presented model
the velocity is assumed to undergo a continuous time random walk. This takes
into account long time correlations. As a consequence the evolution equation
for the joint position-velocity probability distribution is a Fokker-Planck
equation with a fractional time derivative. We determine the solution of this
equation in the form of an integral transform and derive a relation for
arbitrary single time moments. Analytical solutions for the joint probability
distribution and its moments are given.Comment: 10 page
- …