1,595 research outputs found
Fermionic field theory for directed percolation in (1+1) dimensions
We formulate directed percolation in (1+1) dimensions in the language of a
reaction-diffusion process with exclusion taking place in one space dimension.
We map the master equation that describes the dynamics of the system onto a
quantum spin chain problem. From there we build an interacting fermionic field
theory of a new type. We study the resulting theory using renormalization group
techniques. This yields numerical estimates for the critical exponents and
provides a new alternative analytic systematic procedure to study
low-dimensional directed percolation.Comment: 20 pages, 2 figure
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Hot electron cooling by acoustic phonons in graphene
We have investigated the energy loss of hot electrons in metallic graphene by
means of GHz noise thermometry at liquid helium temperature. We observe the
electronic temperature T / V at low bias in agreement with the heat diffusion
to the leads described by the Wiedemann-Franz law. We report on
behavior at high bias, which corresponds to a T4 dependence
of the cooling power. This is the signature of a 2D acoustic phonon cooling
mechanism. From a heat equation analysis of the two regimes we extract accurate
values of the electron-acoustic phonon coupling constant in monolayer
graphene. Our measurements point to an important effect of lattice disorder in
the reduction of , not yet considered by theory. Moreover, our study
provides a strong and firm support to the rising field of graphene bolometric
detectors.Comment: 5 figure
Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagom\'e Compound ZnCu(OH)Cl
We report the determination of the Dzyaloshinsky-Moriya interaction, the
dominant magnetic anisotropy term in the \kagome spin-1/2 compound {\herbert}.
Based on the analysis of the high-temperature electron spin resonance (ESR)
spectra, we find its main component K to be perpendicular to the
\kagome planes. Through the temperature dependent ESR line-width we observe a
building up of nearest-neighbor spin-spin correlations below 150 K.Comment: 4 pages, 3 figures, minor modification
Finite-size and correlation-induced effects in Mean-field Dynamics
The brain's activity is characterized by the interaction of a very large
number of neurons that are strongly affected by noise. However, signals often
arise at macroscopic scales integrating the effect of many neurons into a
reliable pattern of activity. In order to study such large neuronal assemblies,
one is often led to derive mean-field limits summarizing the effect of the
interaction of a large number of neurons into an effective signal. Classical
mean-field approaches consider the evolution of a deterministic variable, the
mean activity, thus neglecting the stochastic nature of neural behavior. In
this article, we build upon two recent approaches that include correlations and
higher order moments in mean-field equations, and study how these stochastic
effects influence the solutions of the mean-field equations, both in the limit
of an infinite number of neurons and for large yet finite networks. We
introduce a new model, the infinite model, which arises from both equations by
a rescaling of the variables and, which is invertible for finite-size networks,
and hence, provides equivalent equations to those previously derived models.
The study of this model allows us to understand qualitative behavior of such
large-scale networks. We show that, though the solutions of the deterministic
mean-field equation constitute uncorrelated solutions of the new mean-field
equations, the stability properties of limit cycles are modified by the
presence of correlations, and additional non-trivial behaviors including
periodic orbits appear when there were none in the mean field. The origin of
all these behaviors is then explored in finite-size networks where interesting
mesoscopic scale effects appear. This study leads us to show that the
infinite-size system appears as a singular limit of the network equations, and
for any finite network, the system will differ from the infinite system
Statistical mechanics of systems with heterogeneous agents: Minority Games
We study analytically a simple game theoretical model of heterogeneous
interacting agents. We show that the stationary state of the system is
described by the ground state of a disordered spin model which is exactly
solvable within the simple replica symmetric ansatz. Such a stationary state
differs from the Nash equilibrium where each agent maximizes her own utility.
The latter turns out to be characterized by a replica symmetry broken
structure. Numerical results fully agree with our analytic findings.Comment: 4 pages, 1 Postscript figure. Revised versio
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