6,791,722 research outputs found
Persistence in the Voter model: continuum reaction-diffusion approach
We investigate the persistence probability in the Voter model for dimensions
d\geq 2. This is achieved by mapping the Voter model onto a continuum
reaction-diffusion system. Using path integral methods, we compute the
persistence probability r(q,t), where q is the number of ``opinions'' in the
original Voter model. We find r(q,t)\sim exp[-f_2(q)(ln t)^2] in d=2;
r(q,t)\sim exp[-f_d(q)t^{(d-2)/2}] for 2<d<4; r(q,t)\sim exp[-f_4(q)t/ln t] in
d=4; and r(q,t)\sim exp[-f_d(q)t] for d>4. The results of our analysis are
checked by Monte Carlo simulations.Comment: 10 pages, 3 figures, Latex, submitted to J. Phys. A (letters
Universal correlations in random matrices: quantum chaos, the integrable model, and quantum gravity
Random matrix theory (RMT) provides a common mathematical formulation of
distinct physical questions in three different areas: quantum chaos, the 1-d
integrable model with the interaction (the Calogero-Sutherland-Moser
system), and 2-d quantum gravity. We review the connection of RMT with these
areas. We also discuss the method of loop equations for determining correlation
functions in RMT, and smoothed global eigenvalue correlators in the 2-matrix
model for gaussian orthogonal, unitary and symplectic ensembles.Comment: 26 pages, LaTe
Critical dynamics of self-gravitating Langevin particles and bacterial populations
We study the critical dynamics of the generalized Smoluchowski-Poisson system
(for self-gravitating Langevin particles) or generalized Keller-Segel model
(for the chemotaxis of bacterial populations). These models [Chavanis & Sire,
PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading
to the Tsallis statistics. The equilibrium states correspond to polytropic
configurations with index similar to polytropic stars in astrophysics. At
the critical index (where is the dimension of space),
there exists a critical temperature (for a given mass) or a
critical mass (for a given temperature). For or
the system tends to an incomplete polytrope confined by the box (in a
bounded domain) or evaporates (in an unbounded domain). For
or the system collapses and forms, in a finite time, a Dirac peak
containing a finite fraction of the total mass surrounded by a halo. This
study extends the critical dynamics of the ordinary Smoluchowski-Poisson system
and Keller-Segel model in corresponding to isothermal configurations with
. We also stress the analogy between the limiting mass of
white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial
populations in the generalized Keller-Segel model of chemotaxis
From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
The numerical simulation of various field theories at non-zero chemical
potential suffers from severe complex action problems. In particular, QCD at
non-zero quark density can presently not be simulated for that reason. A
similar complex action problem arises in the 2-d O(3) model -- a toy model for
QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional
reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The
complex action problem of the 2-d O(3) model manifests itself as a sign problem
of the ladder system. This sign problem is solved completely with a
meron-cluster algorithm.Comment: Based on a talk by U.-J. Wiese, 6 pages, 12 figures, to be published
in computer physics communication
- …