44 research outputs found
Monte Carlo simulation of a two-field effective Hamiltonian of complete wetting
Recent work on the complete wetting transition for three dimensional systems
with short-ranged forces has emphasized the role played by the coupling of
order-parameter fluctuations near the wall and depinning interface. It has been
proposed that an effective two-field Hamiltonian, which predicts a
renormalisation of the wetting parameter, could explain the controversy between
RG analysis of the capillary-wave model and Monte Carlo simulations on the
Ising model. In this letter results of extensive Monte Carlo simulations of the
two-field model are presented. The results are in agreement with prediction of
a renormalized wetting parameter .Comment: To appear in Europhysics Letters. Latex file, 6 pages, 2 figure
Measurement Theory in Lax-Phillips Formalism
It is shown that the application of Lax-Phillips scattering theory to quantum
mechanics provides a natural framework for the realization of the ideas of the
Many-Hilbert-Space theory of Machida and Namiki to describe the development of
decoherence in the process of measurement. We show that if the quantum
mechanical evolution is pointwise in time, then decoherence occurs only if the
Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in
Liouville space), then the decoherence may occur even for closed systems. These
conclusions apply as well to the general problem of mixing of states.Comment: 14 pages, IASSNS-HEP 93/6
Fresh look at randomly branched polymers
We develop a new, dynamical field theory of isotropic randomly branched
polymers, and we use this model in conjunction with the renormalization group
(RG) to study several prominent problems in the physics of these polymers. Our
model provides an alternative vantage point to understand the swollen phase via
dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of
the model that describes the collapse (-)transition to compact
polymer-conformations, and calculate the critical exponents to 2-loop order. It
turns out that the long-standing 1-loop results for these exponents are not
entirely correct. A runaway of the RG flow indicates that the so-called
-transition could be a fluctuation induced first order
transition.Comment: 4 page
Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space
We discuss the quantum Lax-Phillips theory of scattering and unstable
systems. In this framework, the decay of an unstable system is described by a
semigroup. The spectrum of the generator of the semigroup corresponds to the
singularities of the Lax-Phillips -matrix. In the case of discrete (complex)
spectrum of the generator of the semigroup, associated with resonances, the
decay law is exactly exponential. The states corresponding to these resonances
(eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips
Hilbert space, and therefore all physical properties of the resonant states can
be computed.
We show that the Lax-Phillips -matrix is unitarily related to the
-matrix of standard scattering theory by a unitary transformation
parametrized by the spectral variable of the Lax-Phillips theory.
Analytic continuation in has some of the properties of a method
developed some time ago for application to dilation analytic potentials.
We work out an illustrative example using a Lee-Friedrichs model for the
underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision
Collapsing lattice animals and lattice trees in two dimensions
We present high statistics simulations of weighted lattice bond animals and
lattice trees on the square lattice, with fugacities for each non-bonded
contact and for each bond between two neighbouring monomers. The simulations
are performed using a newly developed sequential sampling method with
resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used
for linear chain polymers. We determine with high precision the line of second
order transitions from an extended to a collapsed phase in the resulting
2-dimensional phase diagram. This line includes critical bond percolation as a
multicritical point, and we verify that this point divides the line into two
different universality classes. One of them corresponds to the collapse driven
by contacts and includes the collapse of (weakly embeddable) trees, but the
other is {\it not yet} bond driven and does not contain the Derrida-Herrmann
model as special point. Instead it ends at a multicritical point where a
transition line between two collapsed phases (one bond-driven and the other
contact-driven) sparks off. The Derrida-Herrmann model is representative for
the bond driven collapse, which then forms the fourth universality class on the
transition line (collapsing trees, critical percolation, intermediate regime,
and Derrida-Herrmann). We obtain very precise estimates for all critical
exponents for collapsing trees. It is already harder to estimate the critical
exponents for the intermediate regime. Finally, it is very difficult to obtain
with our method good estimates of the critical parameters of the
Derrida-Herrmann universality class. As regards the bond-driven to
contact-driven transition in the collapsed phase, we have some evidence for its
existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl
Approximate resonance states in the semigroup decomposition of resonance evolution
The semigroup decomposition formalism makes use of the functional model for
class contractive semigroups for the description of the time evolution
of resonances. For a given scattering problem the formalism allows for the
association of a definite Hilbert space state with a scattering resonance. This
state defines a decomposition of matrix elements of the evolution into a term
evolving according to a semigroup law and a background term. We discuss the
case of multiple resonances and give a bound on the size of the background
term. As an example we treat a simple problem of scattering from a square
barrier potential on the half-line.Comment: LaTex 22 pages 3 figure
Experimental simulation of quantum graphs by microwave networks
We present the results of experimental and theoretical study of irregular,
tetrahedral microwave networks consisting of coaxial cables (annular
waveguides) connected by T-joints. The spectra of the networks were measured in
the frequency range 0.0001-16 GHz in order to obtain their statistical
properties such as the integrated nearest neighbor spacing distribution and the
spectral rigidity. The comparison of our experimental and theoretical results
shows that microwave networks can simulate quantum graphs with time reversal
symmetry. In particular, we use the spectra of the microwave networks to study
the periodic orbits of the simulated quantum graphs. We also present
experimental study of directional microwave networks consisting of coaxial
cables and Faraday isolators for which the time reversal symmetry is broken. In
this case our experimental results indicate that spectral statistics of
directional microwave networks deviate from predictions of Gaussian orthogonal
ensembles (GOE) in random matrix theory approaching, especially for small
eigenfrequency spacing s, results for Gaussian unitary ensembles (GUE).
Experimental results are supported by the theoretical analysis of directional
graphs.Comment: 16 pages, 7 figures, to be published in Phys. Rev.
Ozone, aerosols and polar stratospheric clouds measurements during the EASOE Campaign
Preliminary results are presented of observations obtained during the EASOE campaign, with an airborne backscatter lidar and a ground-based DIAL ozone lidar system. Although the main signature observed on the lidar signals was due to the Pinatubo cloud which erupted in June 1991, distinct PSC events were detected on several occasions by the airborne lidar often in relation with orographic wave activity over the norvegian mountains. The ozone profiles obtained in Sodankyla with the ground based lidar are locally perturbed by the presence of the volcanic cloud. After a first correction of the aerosols effect, they present however a reasonably good agreement with the ozone sondes profiles performed on the same site
Arctic polar stratospheric cloud measurements by means of a four wavelength depolarization lidar
A four wavelength depolarization backscattering lidar has been operated during the European Arctic Stratospheric Ozone Experiment (EASOE) in Sodankyl, in the Finnish Arctic. The lidar performed measurements during the months of December 1991, January, February and March 1992. The Finnish Meteorological Institute during the same period launched regularly three Radiosondes per day, and three Ozone sondes per week. Both Mt. Pinatubo aerosols and Polar Stratospheric Clouds were measured. The use of four wavelengths, respectively at 355 nm, 532 nm , 750 nm, and 850 nm permits an inversion of the lidar data to determine aerosol particle size. The depolarization technique permits the identification of Polar Stratospheric Clouds. Frequent correlation between Ozone minima and peaks in the Mt. Pinatubo aerosol maxima were detected. Measurements were carried out both within and outside the Polar Vortex