655 research outputs found
Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
We address the thermodynamics (equilibrium density profiles, phase diagram,
instability analysis...) and the collapse of a self-gravitating gas of Brownian
particles in D dimensions, in both canonical and microcanonical ensembles. In
the canonical ensemble, we derive the analytic form of the density scaling
profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical
ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max}
is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in
the limit of large D. Finally, we solve the problem in D=2, which displays
rather rich and peculiar features
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
Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions
We derive the exact expression of the diffusion coefficient of a
self-gravitating Brownian gas in two dimensions. Our formula generalizes the
usual Einstein relation for a free Brownian motion to the context of
two-dimensional gravity. We show the existence of a critical temperature T_{c}
at which the diffusion coefficient vanishes. For T<T_{c} the diffusion
coefficient is negative and the gas undergoes gravitational collapse. This
leads to the formation of a Dirac peak concentrating the whole mass in a finite
time. We also stress that the critical temperature T_{c} is different from the
collapse temperature T_{*} at which the partition function diverges. These
quantities differ by a factor 1-1/N where N is the number of particles in the
system. We provide clear evidence of this difference by explicitly solving the
case N=2. We also mention the analogy with the chemotactic aggregation of
bacteria in biology, the formation of ``atoms'' in a two-dimensional (2D)
plasma and the formation of dipoles or supervortices in 2D point vortex
dynamics
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
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
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
Smoluchowski's equation for cluster exogenous growth
We introduce an extended Smoluchowski equation describing coagulation
processes for which clusters of mass s grow between collisions with
. A physical example, dropwise condensation is provided, and
its collision kernel K is derived. In the general case, the gelation criterion
is determined. Exact solutions are found and scaling solutions are
investigated. Finally we show how these results apply to nucleation of discs on
a planeComment: Revtex, 4 pages (multicol.sty), 1 eps figures (uses epsfig
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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