59 research outputs found
Energy Landscape and Overlap Distribution of Binary Lennard-Jones Glasses
We study the distribution of overlaps of glassy minima, taking proper care of
residual symmetries of the system. Ensembles of locally stable, low lying
glassy states are efficiently generated by rapid cooling from the liquid phase
which has been equilibrated at a temperature . Varying , we
observe a transition from a regime where a broad range of states are sampled to
a regime where the system is almost always trapped in a metastable glassy
state. We do not observe any structure in the distribution of overlaps of
glassy minima, but find only very weak correlations, comparable in size to
those of two liquid configurations.Comment: 7 pages, 5 figures, uses europhys-style. Minor notational changes,
typos correcte
Thermal Equilibrium with the Wiener Potential: Testing the Replica Variational Approximation
We consider the statistical mechanics of a classical particle in a
one-dimensional box subjected to a random potential which constitutes a Wiener
process on the coordinate axis. The distribution of the free energy and all
correlation functions of the Gibbs states may be calculated exactly as a
function of the box length and temperature. This allows for a detailed test of
results obtained by the replica variational approximation scheme. We show that
this scheme provides a reasonable estimate of the averaged free energy.
Furthermore our results shed more light on the validity of the concept of
approximate ultrametricity which is a central assumption of the replica
variational method.Comment: 6 pages, 1 file LaTeX2e generating 2 eps-files for 2 figures
automaticall
Comment on ``Critical behavior of a two-species reaction-diffusion problem''
In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented
simulational results for the critical exponents of the two-species
reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In
particular, the correlation length exponent was found as \nu = 2.21(5) in
contradiction to the exact relation \nu = 2/d. In this Comment, the symmetry
arguments leading to exact critical exponents for the universality class of
this reaction-diffusion system are concisely reconsidered
Influence of Collision Cascade Statistics on Pattern Formation of Ion-Sputtered Surfaces
Theoretical continuum models that describe the formation of patterns on
surfaces of targets undergoing ion-beam sputtering, are based on Sigmund's
formula, which describes the spatial distribution of the energy deposited by
the ion. For small angles of incidence and amorphous or polycrystalline
materials, this description seems to be suitable, and leads to the classic BH
morphological theory [R.M. Bradley and J.M.E. Harper, J. Vac. Sci. Technol. A
6, 2390 (1988)]. Here we study the sputtering of Cu crystals by means of
numerical simulations under the binary-collision approximation. We observe
significant deviations from Sigmund's energy distribution. In particular, the
distribution that best fits our simulations has a minimum near the position
where the ion penetrates the surface, and the decay of energy deposition with
distance to ion trajectory is exponential rather than Gaussian. We provide a
modified continuum theory which takes these effects into account and explores
the implications of the modified energy distribution for the surface
morphology. In marked contrast with BH's theory, the dependence of the
sputtering yield with the angle of incidence is non-monotonous, with a maximum
for non-grazing incidence angles.Comment: 12 pages, 13 figures, RevTe
Phase Transitions in Operational Risk
In this paper we explore the functional correlation approach to operational
risk. We consider networks with heterogeneous a-priori conditional and
unconditional failure probability. In the limit of sparse connectivity,
self-consistent expressions for the dynamical evolution of order parameters are
obtained. Under equilibrium conditions, expressions for the stationary states
are also obtained. The consequences of the analytical theory developed are
analyzed using phase diagrams. We find co-existence of operational and
non-operational phases, much as in liquid-gas systems. Such systems are
susceptible to discontinuous phase transitions from the operational to
non-operational phase via catastrophic breakdown. We find this feature to be
robust against variation of the microscopic modelling assumptions.Comment: 13 pages, 7 figures. Accepted in Physical Review
Low energy excitations in crystalline perovskite oxides: Evidence from noise experiments
In this paper we report measurements of 1/f noise in a crystalline metallic
oxide with perovskite structure down to 4.2K. The results show existence of
localized excitations with average activation energy 70-80 meV which
produce peak in the noise at T 35-40K. In addition, it shows clear
evidence of tunnelling type two-level-systems (as in glasses) which show up in
noise measurements below 30K.Comment: 11 pages, 4 figures, to appear in Phys Rev B, vol 58, 1st Dec issu
Field theory for a reaction-diffusion model of quasispecies dynamics
RNA viruses are known to replicate with extremely high mutation rates. These
rates are actually close to the so-called error threshold. This threshold is in
fact a critical point beyond which genetic information is lost through a
second-order phase transition, which has been dubbed the ``error catastrophe.''
Here we explore this phenomenon using a field theory approximation to the
spatially extended Swetina-Schuster quasispecies model [J. Swetina and P.
Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape.
In analogy with standard absorbing-state phase transitions, we develop a
reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model.
The field theory representation of the reaction-diffusion system is
constructed. The proposed field theory belongs to the same universality class
than a conserved reaction-diffusion model previously proposed [F. van Wijland
{\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we
obtain the full set of exponents that characterize the critical behavior at the
error threshold. Our results present the error catastrophe from a new point of
view and suggest that spatial degrees of freedom can modify several mean field
predictions previously considered, leading to the definition of characteristic
exponents that could be experimentally measurable.Comment: 13 page
The signal-to-noise analysis of the Little-Hopfield model revisited
Using the generating functional analysis an exact recursion relation is
derived for the time evolution of the effective local field of the fully
connected Little-Hopfield model. It is shown that, by leaving out the feedback
correlations arising from earlier times in this effective dynamics, one
precisely finds the recursion relations usually employed in the signal-to-noise
approach. The consequences of this approximation as well as the physics behind
it are discussed. In particular, it is pointed out why it is hard to notice the
effects, especially for model parameters corresponding to retrieval. Numerical
simulations confirm these findings. The signal-to-noise analysis is then
extended to include all correlations, making it a full theory for dynamics at
the level of the generating functional analysis. The results are applied to the
frequently employed extremely diluted (a)symmetric architectures and to
sequence processing networks.Comment: 26 pages, 3 figure
Bosonization method for second super quantization
A bosonic-fermionic correspondence allows an analytic definition of
functional super derivative, in particular, and a bosonic functional calculus,
in general, on Bargmann- Gelfand triples for the second super quantization. A
Feynman integral for the super transformation matrix elements in terms of
bosonic anti-normal Berezin symbols is rigorously constructed.Comment: In memoriam of F. A. Berezin, accepted in Journal of Nonlinear
Mathematical Physics, 15 page
Statistical properties of phases and delay times of the one-dimensional Anderson model with one open channel
We study the distribution of phases and of Wigner delay times for a
one-dimensional Anderson model with one open channel. Our approach, based on
classical Hamiltonian maps, allows us an analytical treatment. We find that the
distribution of phases depends drastically on the parameter where is the variance of the disorder distribution and
the wavevector. It undergoes a transition from uniformity to singular
behaviour as increases. The distribution of delay times shows
universal power law tails , while the short time behaviour is
- dependent.Comment: 4 pages, 2 figures, Submitted to PR
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