14,833 research outputs found
On amenability and co-amenability of algebraic quantum groups and their corepresentations
We introduce and study several amenability properties for unitary
corepresentations and *-representations of algebraic quantum groups, which may
be used to characterize amenability or co-amenability of such groups. As a
background for this study, we also investigate the involved tensor
C*-categories.Comment: 46 pages, (some misprints corrected, a couple of remarks and a new
reference added
Measurement of scaling laws for shock waves in thermal nonlocal media
We are able to detect the details of spatial optical collisionless
wave-breaking through the high aperture imaging of a beam suffering shock in a
fluorescent nonlinear nonlocal thermal medium. This allows us to directly
measure how nonlocality and nonlinearity affect the point of shock formation
and compare results with numerical simulations.Comment: 4 pages, 4 figure
Phase diagram and complexity of mode-locked lasers: from order to disorder
We investigate mode-locking processes in lasers displaying a variable degree
of structural randomness, from standard optical cavities to multiple-scattering
media. By employing methods mutuated from spin-glass theory, we analyze the
mean-field Hamiltonian and derive a phase-diagram in terms of the pumping rate
and the degree of disorder. Three phases are found: i) paramagnetic,
corresponding to a noisy continuous wave emission, ii) ferromagnetic, that
describes the standard passive mode-locking, and iii) the spin-glass in which
the phases of the electromagnetic field are frozen in a exponentially large
number of configurations. The way the mode-locking threshold is affected by the
amount of disorder is quantified. The results are also relevant for other
physical systems displaying a random Hamiltonian, like Bose-Einstein
condensates and nonlinear optical beams.Comment: 4 pages, 2 figure
Light diffusion and localization in 3D nonlinear disordered media
Using a 3D Finite-Difference Time-Domain parallel code, we report on the
linear and nonlinear propagation of light pulses in a disordered assembly of
scatterers, whose spatial distribution is generated by a Molecular Dynamics
code; refractive index dispersion is also taken into account. We calculate the
static and dynamical diffusion constant of light, while considering a pulsed
excitation. Our results are in quantitative agreement with reported
experiments, also furnishing evidence of a non-exponential decay of the
transmitted pulse in the linear regime and in the presence of localized modes.
By using an high power excitation, we numerically demonstrate the
``modulational instability random laser'': at high peak input powers energy is
transferred to localized states from the input pulse, via third-order
nonlinearity and optical parametric amplification, and this process is signed
by a power-dependent non-exponential time-decay of the transmitted pulse.Comment: 5 pages, 4 figures. Revised version with new figure 4 with localized
state
Room temperature GW bar detector with opto-mechanical readout
We present the full implementation of a room-temperature gravitational wave
bar detector equipped with an opto-mechanical readout. The mechanical
vibrations are read by a Fabry--Perot interferometer whose length changes are
compared with a stable reference optical cavity by means of a resonant laser.
The detector performance is completely characterized in terms of spectral
sensitivity and statistical properties of the fluctuations in the system output
signal. The new kind of readout technique allows for wide-band detection
sensitivity and we can accurately test the model of the coupled oscillators for
thermal noise. Our results are very promising in view of cryogenic operation
and represent an important step towards significant improvements in the
performance of massive gravitational wave detectors.Comment: 7 figures, submitted to Phys. Rev.
Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions
We make use of continuum elasticity theory to investigate the collective
modes that propagate along the edge of a two-dimensional electron liquid or
crystal in a magnetic field. An exact solution of the equations of motion is
obtained with the following simplifying assumptions: (i) The system is {\it
macroscopically} homogeneous and isotropic in the half-plane delimited by the
edge (ii) The electron-electron interaction is of finite range due to screening
by external electrodes (iii) The system is nearly incompressible. At
sufficiently small wave vector we find a universal dispersion curve independent of the shear modulus. At larger wave vectors the dispersion
can change its form in a manner dependent on the comparison of various length
scales. We obtain analytical formulas for the dispersion and damping of the
modes in various physical regimes.Comment: 3 figure
A microscopic model for solidification
We present a novel picture of a non isothermal solidification process
starting from a molecular level, where the microscopic origin of the basic
mechanisms and of the instabilities characterizing the approach to equilibrium
is rendered more apparent than in existing approaches based on coarse grained
free energy functionals \`a la Landau.
The system is composed by a lattice of Potts spins, which change their state
according to the stochastic dynamics proposed some time ago by Creutz. Such a
method is extended to include the presence of latent heat and thermal
conduction.
Not only the model agrees with previous continuum treatments, but it allows
to introduce in a consistent fashion the microscopic stochastic fluctuations.
These play an important role in nucleating the growing solid phase in the melt.
The approach is also very satisfactory from the quantitative point of view
since the relevant growth regimes are fully characterized in terms of scaling
exponents.Comment: 7 pages Latex +3 figures.p
Experimental measurement of photothermal effect in Fabry-Perot cavities
We report the experimental observation of the photothermal effect. The
measurements are performed by modulating the laser power absorbed by the
mirrors of two high-finesse Fabry-Perot cavities. The results are very well
described by a recently proposed theoretical model [M. Cerdonio, L. Conti, A.
Heidmann and M. Pinard, Phys. Rev. D 63 (2001) 082003], confirming the
correctness of such calculations. Our observations and quantitative
characterization of the photothermal effect demonstrate its critical importance
for high sensitivity interferometric displacement measurements, as those
necessary for gravitational wave detection.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Selective readout and back-action reduction for wideband acoustic gravitational wave detectors
We present the concept of selective readout for broadband resonant mass
gravitational wave detectors. This detection scheme is capable of specifically
selecting the signal from the contributions of the vibrational modes sensitive
to the gravitational waves, and efficiently rejecting the contribution from non
gravitationally sensitive modes. Moreover this readout, applied to a dual
detector, is capable to give an effective reduction of the back-action noise
within the frequency band of interest. The overall effect is a significant
enhancement in the predicted sensitivity, evaluated at the standard quantum
limit for a dual torus detector. A molybdenum detector, 1 m in diameter and
equipped with a wide area selective readout, would reach spectral strain
sensitivities 2x10^{-23}/sqrt{Hz} between 2-6 kHz.Comment: 9 pages, 4 figure
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