4,427 research outputs found
Soliton-dynamical approach to a noisy Ginzburg-Landau model
We present a dynamical description and analysis of non-equilibrium
transitions in the noisy Ginzburg-Landau equation based on a canonical phase
space formulation. The transition pathways are characterized by nucleation and
subsequent propagation of domain walls or solitons. We also evaluate the
Arrhenius factor in terms of an associated action and find good agreement with
recent numerical optimization studies.Comment: 4 pages (revtex4), 3 figures (eps
Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
Electron-electron interactions can induce Fermi surface deformations which
break the point-group symmetry of the lattice structure of the system. In the
vicinity of such a "Pomeranchuk instability" the Fermi surface is easily
deformed by anisotropic perturbations, and exhibits enhanced collective
fluctuations. We show that critical Fermi surface fluctuations near a d-wave
Pomeranchuk instability in two dimensions lead to large anisotropic decay rates
for single-particle excitations, which destroy Fermi liquid behavior over the
whole surface except at the Brillouin zone diagonal.Comment: 12 pages, 2 figures, revised version as publishe
Noisy regression and classification with continuous multilayer networks
We investigate zero temperature Gibbs learning for two classes of
unrealizable rules which play an important role in practical applications of
multilayer neural networks with differentiable activation functions:
classification problems and noisy regression problems. Considering one step of
replica symmetry breaking, we surprisingly find that for sufficiently large
training sets the stable state is replica symmetric even though the target rule
is unrealizable. Further, the classification problem is shown to be formally
equivalent to the noisy regression problem.Comment: 7 pages, including 2 figure
Ionisation by quantised electromagnetic fields: The photoelectric effect
In this paper we explain the photoelectric effect in a variant of the
standard model of non relativistic quantum electrodynamics, which is in some
aspects more closely related to the physical picture, than the one studied in
[BKZ]: Now we can apply our results to an electron with more than one bound
state and to a larger class of electron-photon interactions. We will specify a
situation, where ionisation probability in second order is a weighted sum of
single photon terms. Furthermore we will see, that Einstein's equality
for the maximal kinetic energy of
the electron, energy of the photon and ionisation gap
is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2
A Hierarchically-Organized Phase Diagram near a Quantum Critical Point in URu2Si2
A comprehensive transport study, as a function of both temperature and
magnetic field in continuous magnetic fields up to 45 T reveals that URu2Si2
possesses all the essential hallmarks of quantum criticality at temperatures
above 5.5 K and fields around 38 T, but then collapses into multiple low
temperature phases in a hierarchically-organized phase diagram as the
temperature is reduced. Although certain generic features of the phase diagram
are very similar to those in the cuprates and heavy fermion superconductors,
the existence of multiple ordered hysteretic phases near the field-tuned
quantum critical point is presently unique to URu2Si2. This finding suggests
the existence of many competing order parameters separated by small energy
difference in URu2Si2.Comment: 6 pages, twocolum texts, 3 coloured figure included, submitted to PR
Reconstructing the Hopfield network as an inverse Ising problem
We test four fast mean field type algorithms on Hopfield networks as an
inverse Ising problem. The equilibrium behavior of Hopfield networks is
simulated through Glauber dynamics. In the low temperature regime, the
simulated annealing technique is adopted. Although performances of these
network reconstruction algorithms on the simulated network of spiking neurons
are extensively studied recently, the analysis of Hopfield networks is lacking
so far. For the Hopfield network, we found that, in the retrieval phase favored
when the network wants to memory one of stored patterns, all the reconstruction
algorithms fail to extract interactions within a desired accuracy, and the same
failure occurs in the spin glass phase where spurious minima show up, while in
the paramagnetic phase, albeit unfavored during the retrieval dynamics, the
algorithms work well to reconstruct the network itself. This implies that, as a
inverse problem, the paramagnetic phase is conversely useful for reconstructing
the network while the retrieval phase loses all the information about
interactions in the network except for the case where only one pattern is
stored. The performances of algorithms are studied with respect to the system
size, memory load and temperature, sample-to-sample fluctuations are also
considered.Comment: 8 pages, 3 figure
Entropy and typical properties of Nash equilibria in two-player games
We use techniques from the statistical mechanics of disordered systems to
analyse the properties of Nash equilibria of bimatrix games with large random
payoff matrices. By means of an annealed bound, we calculate their number and
analyse the properties of typical Nash equilibria, which are exponentially
dominant in number. We find that a randomly chosen equilibrium realizes almost
always equal payoffs to either player. This value and the fraction of
strategies played at an equilibrium point are calculated as a function of the
correlation between the two payoff matrices. The picture is complemented by the
calculation of the properties of Nash equilibria in pure strategies.Comment: 6 pages, was "Self averaging of Nash equilibria in two player games",
main section rewritten, some new results, for additional information see
http://itp.nat.uni-magdeburg.de/~jberg/games.htm
Analysis of ensemble learning using simple perceptrons based on online learning theory
Ensemble learning of nonlinear perceptrons, which determine their outputs
by sign functions, is discussed within the framework of online learning and
statistical mechanics. One purpose of statistical learning theory is to
theoretically obtain the generalization error. This paper shows that ensemble
generalization error can be calculated by using two order parameters, that is,
the similarity between a teacher and a student, and the similarity among
students. The differential equations that describe the dynamical behaviors of
these order parameters are derived in the case of general learning rules. The
concrete forms of these differential equations are derived analytically in the
cases of three well-known rules: Hebbian learning, perceptron learning and
AdaTron learning. Ensemble generalization errors of these three rules are
calculated by using the results determined by solving their differential
equations. As a result, these three rules show different characteristics in
their affinity for ensemble learning, that is ``maintaining variety among
students." Results show that AdaTron learning is superior to the other two
rules with respect to that affinity.Comment: 30 pages, 17 figure
Thermodynamic picture of the glassy state
A picture for thermodynamics of the glassy state is introduced. It assumes
that one extra parameter, the effective temperature, is needed to describe the
glassy state. This explains the classical paradoxes concerning the Ehrenfest
relations and the Prigogine-Defay ratio. As a second part, the approach
connects the response of macroscopic observables to a field change with their
temporal fluctuations, and with the fluctuation-dissipation relation, in a
generalized non-equilibrium way.Comment: Proceedings of the Conference "Unifying Concepts in Glass Physics",
ICTP, Trieste, 15 - 18 September 199
Drying and cracking mechanisms in a starch slurry
Starch-water slurries are commonly used to study fracture dynamics. Drying
starch-cakes benefit from being simple, economical, and reproducible systems,
and have been used to model desiccation fracture in soils, thin film fracture
in paint, and columnar joints in lava. In this paper, the physical properties
of starch-water mixtures are studied, and used to interpret and develop a
multiphase transport model of drying. Starch-cakes are observed to have a
nonlinear elastic modulus, and a desiccation strain that is comparable to that
generated by their maximum achievable capillary pressure. It is shown that a
large material porosity is divided between pore spaces between starch grains,
and pores within starch grains. This division of pore space leads to two
distinct drying regimes, controlled by liquid and vapor transport of water,
respectively. The relatively unique ability for drying starch to generate
columnar fracture patterns is shown to be linked to the unusually strong
separation of these two transport mechanisms.Comment: 9 pages, 8 figures [revised in response to reviewer comments
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