21,774 research outputs found
Can Plane Wave Modes be Physical Modes in Soliton Models?
I show that plane waves may not be used as asymptotic states in soliton
models because they describe unphysical states. When asymptotic states are
taken to be physical there is no T-matrix of \cO(1).Comment: Latex. Published in Phys. Lett.
Asymmetric Evaluations of Erasure and Undetected Error Probabilities
The problem of channel coding with the erasure option is revisited for
discrete memoryless channels. The interplay between the code rate, the
undetected and total error probabilities is characterized. Using the
information spectrum method, a sequence of codes of increasing blocklengths
is designed to illustrate this tradeoff. Furthermore, for additive discrete
memoryless channels with uniform input distribution, we establish that our
analysis is tight with respect to the ensemble average. This is done by
analysing the ensemble performance in terms of a tradeoff between the code
rate, the undetected and the total errors. This tradeoff is parametrized by the
threshold in a generalized likelihood ratio test. Two asymptotic regimes are
studied. First, the code rate tends to the capacity of the channel at a rate
slower than corresponding to the moderate deviations regime. In this
case, both error probabilities decay subexponentially and asymmetrically. The
precise decay rates are characterized. Second, the code rate tends to capacity
at a rate of . In this case, the total error probability is
asymptotically a positive constant while the undetected error probability
decays as for some . The proof techniques involve
applications of a modified (or "shifted") version of the G\"artner-Ellis
theorem and the type class enumerator method to characterize the asymptotic
behavior of a sequence of cumulant generating functions.Comment: 28 pages, no figures in IEEE Transactions on Information Theory, 201
Minimum Rates of Approximate Sufficient Statistics
Given a sufficient statistic for a parametric family of distributions, one
can estimate the parameter without access to the data. However, the memory or
code size for storing the sufficient statistic may nonetheless still be
prohibitive. Indeed, for independent samples drawn from a -nomial
distribution with degrees of freedom, the length of the code scales as
. In many applications, we may not have a useful notion of
sufficient statistics (e.g., when the parametric family is not an exponential
family) and we also may not need to reconstruct the generating distribution
exactly. By adopting a Shannon-theoretic approach in which we allow a small
error in estimating the generating distribution, we construct various {\em
approximate sufficient statistics} and show that the code length can be reduced
to . We consider errors measured according to the
relative entropy and variational distance criteria. For the code constructions,
we leverage Rissanen's minimum description length principle, which yields a
non-vanishing error measured according to the relative entropy. For the
converse parts, we use Clarke and Barron's formula for the relative entropy of
a parametrized distribution and the corresponding mixture distribution.
However, this method only yields a weak converse for the variational distance.
We develop new techniques to achieve vanishing errors and we also prove strong
converses. The latter means that even if the code is allowed to have a
non-vanishing error, its length must still be at least .Comment: To appear in the IEEE Transactions on Information Theor
Collective Coordinates and the Absence of Yukawa Coupling in the Classical Skyrme Model
In systems with constraints, physical states must be annihilated by the
constraints. We make use of this rule to construct physical asymptotic states
in the Skyrme model. The standard derivation of the Born terms with asymptotic
physical states shows that there is no Yukawa coupling for the Skyrmion. We
propose a remedy tested in other solitonic models: A Wilsonian action obtained
after integrating the energetic mesons and where the Skyrmion is a quantum
state should have a Yukawa coupling.Comment: LATE
Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential
We theoretically study Langevin systems with a tilted periodic potential. It
has been known that the ratio of the diffusion constant to the
differential mobility is not equal to the temperature of the environment
(multiplied by the Boltzmann constant), except in the linear response regime,
where the fluctuation dissipation theorem holds. In order to elucidate the
physical meaning of far from equilibrium, we analyze a modulated
system with a slowly varying potential. We derive a large scale description of
the probability density for the modulated system by use of a perturbation
method. The expressions we obtain show that plays the role of the
temperature in the large scale description of the system and that can
be determined directly in experiments, without measurements of the diffusion
constant and the differential mobility
Single-molecule stochastic resonance
Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It
consists of the amplification and optimization of the response of a system
assisted by stochastic noise. Here we carry out the first experimental study of
SR in single DNA hairpins which exhibit cooperatively folding/unfolding
transitions under the action of an applied oscillating mechanical force with
optical tweezers. By varying the frequency of the force oscillation, we
investigated the folding/unfolding kinetics of DNA hairpins in a periodically
driven bistable free-energy potential. We measured several SR quantifiers under
varied conditions of the experimental setup such as trap stiffness and length
of the molecular handles used for single-molecule manipulation. We find that
the signal-to-noise ratio (SNR) of the spectral density of measured
fluctuations in molecular extension of the DNA hairpins is a good quantifier of
the SR. The frequency dependence of the SNR exhibits a peak at a frequency
value given by the resonance matching condition. Finally, we carried out
experiments in short hairpins that show how SR might be useful to enhance the
detection of conformational molecular transitions of low SNR.Comment: 11 pages, 7 figures, supplementary material
(http://prx.aps.org/epaps/PRX/v2/i3/e031012/prx-supp.pdf
Interplay of the Chiral and Large N_c Limits in pi N Scattering
Light-quark hadronic physics admits two useful systematic expansions, the
chiral and 1/N_c expansions. Their respective limits do not commute, making
such cases where both expansions may be considered to be especially
interesting. We first study pi N scattering lengths, showing that (as expected
for such soft-pion quantities) the chiral expansion converges more rapidly than
the 1/N_c expansion, although the latter nevertheless continues to hold. We
also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of pi N
scattering, finding that both fail if the large N_c limit is taken prior to the
chiral limit.Comment: 10 pages, ReVTe
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