22,787 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
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
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
Two-Electron Photon Emission From Metallic Quantum Wells
Unusual emission of visible light is observed in scanning tunneling
microscopy of the quantum well system Na on Cu(111). Photons are emitted at
energies exceeding the energy of the tunneling electrons. Model calculations of
two-electron processes which lead to quantum well transitions reproduce the
experimental fluorescence spectra, the quantum yield, and the power-law
variation of the intensity with the excitation current.Comment: revised version, as published; 4 pages, 3 figure
Liquid-liquid interfacial tension of electrolyte solutions
It is theoretically shown that the excess liquid-liquid interfacial tension
between two electrolyte solutions as a function of the ionic strength I behaves
asymptotically as O(- I^0.5) for small I and as O(+- I) for large I. The former
regime is dominated by the electrostatic potential due to an unequal
partitioning of ions between the two liquids whereas the latter regime is
related to a finite interfacial thickness. The crossover between the two
asymptotic regimes depends sensitively on material parameters suggesting that,
depending on the actual system under investigation, the experimentally
accessible range of ionic strengths can correspond to either the small or the
large ionic strength regime. In the limiting case of a liquid-gas surface where
ion partitioning is absent, the image chage interaction can dominate the
surface tension for small ionic strength I such that an Onsager-Samaras
limiting law O(- I ln(I)) is expected. The proposed picture is consistent with
more elaborate models and published measurements.Comment: Accepted for publication in Physical Review Letter
Polynuclear growth model, GOE and random matrix with deterministic source
We present a random matrix interpretation of the distribution functions which
have appeared in the study of the one-dimensional polynuclear growth (PNG)
model with external sources. It is shown that the distribution, GOE, which
is defined as the square of the GOE Tracy-Widom distribution, can be obtained
as the scaled largest eigenvalue distribution of a special case of a random
matrix model with a deterministic source, which have been studied in a
different context previously. Compared to the original interpretation of the
GOE as ``the square of GOE'', ours has an advantage that it can also
describe the transition from the GUE Tracy-Widom distribution to the GOE.
We further demonstrate that our random matrix interpretation can be obtained
naturally by noting the similarity of the topology between a certain
non-colliding Brownian motion model and the multi-layer PNG model with an
external source. This provides us with a multi-matrix model interpretation of
the multi-point height distributions of the PNG model with an external source.Comment: 27pages, 4 figure
Aperiodic tumbling of microrods advected in a microchannel flow
We report on an experimental investigation of the tumbling of microrods in
the shear flow of a microchannel (40 x 2.5 x 0.4 mm). The rods are 20 to 30
microns long and their diameters are of the order of 1 micron. Images of the
centre-of-mass motion and the orientational dynamics of the rods are recorded
using a microscope equipped with a CCD camera. A motorised microscope stage is
used to track individual rods as they move along the channel. Automated image
analysis determines the position and orientation of a tracked rods in each
video frame. We find different behaviours, depending on the particle shape, its
initial position, and orientation. First, we observe periodic as well as
aperiodic tumbling. Second, the data show that different tumbling trajectories
exhibit different sensitivities to external perturbations. These observations
can be explained by slight asymmetries of the rods. Third we observe that after
some time, initially periodic trajectories lose their phase. We attribute this
to drift of the centre of mass of the rod from one to another stream line of
the channel flow.Comment: 14 pages, 8 figures, as accepted for publicatio
KPZ equation in one dimension and line ensembles
For suitably discretized versions of the Kardar-Parisi-Zhang equation in one
space dimension exact scaling functions are available, amongst them the
stationary two-point function. We explain one central piece from the technology
through which such results are obtained, namely the method of line ensembles
with purely entropic repulsion.Comment: Proceedings STATPHYS22, Bangalore, 200
Average characteristic polynomials in the two-matrix model
The two-matrix model is defined on pairs of Hermitian matrices of
size by the probability measure where
and are given potential functions and \tau\in\er. We study averages
of products and ratios of characteristic polynomials in the two-matrix model,
where both matrices and may appear in a combined way in both
numerator and denominator. We obtain determinantal expressions for such
averages. The determinants are constructed from several building blocks: the
biorthogonal polynomials and associated to the two-matrix
model; certain transformed functions and \Q_n(v); and finally
Cauchy-type transforms of the four Eynard-Mehta kernels , ,
and . In this way we generalize known results for the
-matrix model. Our results also imply a new proof of the Eynard-Mehta
theorem for correlation functions in the two-matrix model, and they lead to a
generating function for averages of products of traces.Comment: 28 pages, references adde
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