732 research outputs found
Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain
The multifractal properties of the electronic spectrum of a general
quasiperiodic chain are studied in first order in the quasiperiodic potential
strength. Analytical expressions for the generalized dimensions are found and
are in good agreement with numerical simulations. These first order results do
not depend on the irrational incommensurability.Comment: 10 Pages in RevTeX, 2 Postscript figure
Universal statistical properties of poker tournaments
We present a simple model of Texas hold'em poker tournaments which retains
the two main aspects of the game: i. the minimal bet grows exponentially with
time; ii. players have a finite probability to bet all their money. The
distribution of the fortunes of players not yet eliminated is found to be
independent of time during most of the tournament, and reproduces accurately
data obtained from Internet tournaments and world championship events. This
model also makes the connection between poker and the persistence problem
widely studied in physics, as well as some recent physical models of biological
evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament
Persistence exponents for fluctuating interfaces
Numerical and analytic results for the exponent \theta describing the decay
of the first return probability of an interface to its initial height are
obtained for a large class of linear Langevin equations. The models are
parametrized by the dynamic roughness exponent \beta, with 0 < \beta < 1; for
\beta = 1/2 the time evolution is Markovian. Using simulations of
solid-on-solid models, of the discretized continuum equations as well as of the
associated zero-dimensional stationary Gaussian process, we address two
problems: The return of an initially flat interface, and the return to an
initial state with fully developed steady state roughness. The two problems are
shown to be governed by different exponents. For the steady state case we point
out the equivalence to fractional Brownian motion, which has a return exponent
\theta_S = 1 - \beta. The exponent \theta_0 for the flat initial condition
appears to be nontrivial. We prove that \theta_0 \to \infty for \beta \to 0,
\theta_0 \geq \theta_S for \beta
1/2, and calculate \theta_{0,S} perturbatively to first order in an expansion
around the Markovian case \beta = 1/2. Using the exact result \theta_S = 1 -
\beta, accurate upper and lower bounds on \theta_0 can be derived which show,
in particular, that \theta_0 \geq (1 - \beta)^2/\beta for small \beta.Comment: 12 pages, REVTEX, 6 Postscript figures, needs multicol.sty and
epsf.st
A phason disordered two dimensional quantum antiferromagnet
We examine a novel type of disorder in quantum antiferromagnets. Our model
consists of localized spins with antiferromagnetic exchanges on a bipartite
quasiperiodic structure, which is geometrically disordered in such a way that
no frustration is introduced. In the limit of zero disorder, the structure is
the perfect Penrose rhombus tiling. This tiling is progressively disordered by
augmenting the number of random "phason flips" or local tile-reshuffling
operations. The ground state remains N\'eel ordered, and we have studied its
properties as a function of increasing disorder using linear spin wave theory
and quantum Monte Carlo. We find that the ground state energy decreases,
indicating enhanced quantum fluctuations with increasing disorder. The magnon
spectrum is progressively smoothed, and the effective spin wave velocity of low
energy magnons increases with disorder. For large disorder, the ground state
energy as well as the average staggered magnetization tend towards limiting
values characteristic of this type of randomized tilings.Comment: 5 pages, 7 figure
Anomalous Drude Model
A generalization of the Drude model is studied. On the one hand, the free
motion of the particles is allowed to be sub- or superdiffusive; on the other
hand, the distribution of the time delay between collisions is allowed to have
a long tail and even a non-vanishing first moment. The collision averaged
motion is either regular diffusive or L\'evy-flight like. The anomalous
diffusion coefficients show complex scaling laws. The conductivity can be
calculated in the diffusive regime. The model is of interest for the
phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter
Contest based on a directed polymer in a random medium
We introduce a simple one-parameter game derived from a model describing the
properties of a directed polymer in a random medium. At his turn, each of the
two players picks a move among two alternatives in order to maximize his final
score, and minimize opponent's return. For a game of length , we find that
the probability distribution of the final score develops a traveling wave
form, , with the wave profile unusually
decaying as a double exponential for large positive and negative . In
addition, as the only parameter in the game is varied, we find a transition
where one player is able to get his maximum theoretical score. By extending
this model, we suggest that the front velocity is selected by the nonlinear
marginal stability mechanism arising in some traveling wave problems for which
the profile decays exponentially, and for which standard traveling wave theory
applies
Self-gravitating Brownian systems and bacterial populations with two or more types of particles
We study the thermodynamical properties of a self-gravitating gas with two or
more types of particles. Using the method of linear series of equilibria, we
determine the structure and stability of statistical equilibrium states in both
microcanonical and canonical ensembles. We show how the critical temperature
(Jeans instability) and the critical energy (Antonov instability) depend on the
relative mass of the particles and on the dimension of space. We then study the
dynamical evolution of a multi-components gas of self-gravitating Brownian
particles in the canonical ensemble. Self-similar solutions describing the
collapse below the critical temperature are obtained analytically. We find
particle segregation, with the scaling profile of the slowest collapsing
particles decaying with a non universal exponent that we compute perturbatively
in different limits. These results are compared with numerical simulations of
the two-species Smoluchowski-Poisson system. Our model of self-attracting
Brownian particles also describes the chemotactic aggregation of a
multi-species system of bacteria in biology
Scaling laws and vortex profiles in 2D decaying turbulence
We use high resolution numerical simulations over several hundred of turnover
times to study the influence of small scale dissipation onto vortex statistics
in 2D decaying turbulence. A self-similar scaling regime is detected when the
scaling laws are expressed in units of mean vorticity and integral scale, as
predicted by Carnevale et al., and it is observed that viscous effects spoil
this scaling regime. This scaling regime shows some trends toward that of the
Kirchhoff model, for which a recent theory predicts a decay exponent .
In terms of scaled variables, the vortices have a similar profile close to a
Fermi-Dirac distribution.Comment: 4 Latex pages and 4 figures. Submitted to Phys. Rev. Let
Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations
We determine an asymptotic expression of the blow-up time t_coll for
self-gravitating Brownian particles or bacterial populations (chemotaxis) close
to the critical point. We show that t_coll=t_{*}(eta-eta_c)^{-1/2} with
t_{*}=0.91767702..., where eta represents the inverse temperature (for Brownian
particles) or the mass (for bacterial colonies), and eta_c is the critical
value of eta above which the system blows up. This result is in perfect
agreement with the numerical solution of the Smoluchowski-Poisson system. We
also determine the asymptotic expression of the relaxation time close but above
the critical temperature and derive a large time asymptotic expansion for the
density profile exactly at the critical point
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