27,310 research outputs found
Interlaced particle systems and tilings of the Aztec diamond
Motivated by the problem of domino tilings of the Aztec diamond, a weighted
particle system is defined on lines, with line containing
particles. The particles are restricted to lattice points from 0 to , and
particles on successive lines are subject to an interlacing constraint. It is
shown that marginal distributions for this particle system can be computed
exactly. This in turn is used to give unified derivations of a number of
fundamental properties of the tiling problem, for example the evaluation of the
number of distinct configurations and the relation to the GUE minor process. An
interlaced particle system associated with the domino tiling of a certain half
Aztec diamond is similarly defined and analyzed.Comment: 17 pages, 4 figure
Fermi distribution of semicalssical non-eqilibrium Fermi states
When a classical device suddenly perturbs a degenerate Fermi gas a
semiclassical non-equilibrium Fermi state arises. Semiclassical Fermi states
are characterized by a Fermi energy or Fermi momentum that slowly depends on
space or/and time. We show that the Fermi distribution of a semiclassical Fermi
state has a universal nature. It is described by Airy functions regardless of
the details of the perturbation. In this letter we also give a general
discussion of coherent Fermi states
Edge scaling limits for a family of non-Hermitian random matrix ensembles
A family of random matrix ensembles interpolating between the GUE and the
Ginibre ensemble of matrices with iid centered complex Gaussian
entries is considered. The asymptotic spectral distribution in these models is
uniform in an ellipse in the complex plane, which collapses to an interval of
the real line as the degree of non-Hermiticity diminishes. Scaling limit
theorems are proven for the eigenvalue point process at the rightmost edge of
the spectrum, and it is shown that a non-trivial transition occurs between
Poisson and Airy point process statistics when the ratio of the axes of the
supporting ellipse is of order . In this regime, the family of
limiting probability distributions of the maximum of the real parts of the
eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page
Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat
initial condition and no extra constraints. The joint distributions of surface
height at finitely many points at a fixed time moment are given as marginals of
a signed determinantal point process. The long time scaling limit of the
surface height is shown to coincide with the Airy_1 process. This result holds
more generally for the observation points located along any space-like path in
the space-time plane. We also obtain the corresponding results for the discrete
time TASEP (totally asymmetric simple exclusion process) with parallel update.Comment: 39 pages,6 figure
Quasiperiodic localized oscillating solutions in the discrete nonlinear Schr\"odinger equation with alternating on-site potential
We present what we believe to be the first known example of an exact
quasiperiodic localized stable solution with spatially symmetric
large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The
model is a one-dimensional discrete nonlinear Schr\"odinger equation with
alternating on-site energies, modelling e.g. an array of optical waveguides
with alternating widths. The solution bifurcates from a stationary discrete gap
soliton, and in a regime of large oscillations its intensity oscillates
periodically between having one peak at the central site, and two symmetric
peaks at the neighboring sites with a dip in the middle. Such solutions, termed
'pulsons', are found to exist in continuous families ranging arbitrarily close
both to the anticontinuous and continuous limits. Furthermore, it is shown that
they may be linearly stable also in a regime of large oscillations.Comment: 4 pages, 4 figures, to be published in Phys. Rev. E. Revised version:
change of title, added Figs. 1(b),(c), 4 new references + minor
clarification
- …