1,015 research outputs found
Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems
We prove rigorously that the one-particle density matrix of three dimensional
interacting Bose systems with a short-scale repulsive pair interaction
converges to the solution of the cubic non-linear Schr\"odinger equation in a
suitable scaling limit. The result is extended to -particle density matrices
for all positive integer .Comment: 72 pages, 17 figures. Final versio
Rate of Convergence Towards Hartree Dynamics
We consider a system of N bosons interacting through a two-body potential
with, possibly, Coulomb-type singularities. We show that the difference between
the many-body Schr\"odinger evolution in the mean-field regime and the
effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed
time. The N-dependence of the bound is optimal.Comment: 26 page
Dynamical formation of correlations in a Bose-Einstein condensate
We consider the evolution of bosons interacting with a repulsive short
range pair potential in three dimensions. The potential is scaled according to
the Gross-Pitaevskii scaling, i.e. it is given by . We
monitor the behavior of the solution to the -particle Schr\"odinger equation
in a spatial window where two particles are close to each other. We prove that
within this window a short scale interparticle structure emerges dynamically.
The local correlation between the particles is given by the two-body zero
energy scattering mode. This is the characteristic structure that was expected
to form within a very short initial time layer and to persist for all later
times, on the basis of the validity of the Gross-Pitaevskii equation for the
evolution of the Bose-Einstein condensate. The zero energy scattering mode
emerges after an initial time layer where all higher energy modes disperse out
of the spatial window. We can prove the persistence of this structure up to
sufficiently small times before three-particle correlations could develop.Comment: 36 pages, latex fil
Local semicircle law and complete delocalization for Wigner random matrices
We consider Hermitian random matrices with independent identical
distributed entries. The matrix is normalized so that the average spacing
between consecutive eigenvalues is of order 1/N. Under suitable assumptions on
the distribution of the single matrix element, we prove that, away from the
spectral edges, the density of eigenvalues concentrates around the Wigner
semicircle law on energy scales . Up to the
logarithmic factor, this is the smallest energy scale for which the semicircle
law may be valid. We also prove that for all eigenvalues away from the spectral
edges, the -norm of the corresponding eigenvectors is of order
, modulo logarithmic corrections. The upper bound
implies that every eigenvector is completely delocalized, i.e., the maximum
size of the components of the eigenvector is of the same order as their average
size. In the Appendix, we include a lemma by J. Bourgain which removes one of
our assumptions on the distribution of the matrix elements.Comment: 14 pages, LateX file. An appendix by J. Bourgain was added. Final
version, to appear in Comm. Math. Phy
Dynamical Collapse of Boson Stars
We study the time evolution in system of bosons with a relativistic
dispersion law interacting through an attractive Coulomb potential with
coupling constant . We consider the mean field scaling where tends to
infinity, tends to zero and remains fixed. We investigate
the relation between the many body quantum dynamics governed by the
Schr\"odinger equation and the effective evolution described by a
(semi-relativistic) Hartree equation. In particular, we are interested in the
super-critical regime of large (the sub-critical case has been
studied in \cite{ES,KP}), where the nonlinear Hartree equation is known to have
solutions which blow up in finite time. To inspect this regime, we need to
regularize the Coulomb interaction in the many body Hamiltonian with an
dependent cutoff that vanishes in the limit . We show, first, that
if the solution of the nonlinear equation does not blow up in the time interval
, then the many body Schr\"odinger dynamics (on the level of the
reduced density matrices) can be approximated by the nonlinear Hartree
dynamics, just as in the sub-critical regime. Moreover, we prove that if the
solution of the nonlinear Hartree equation blows up at time (in the sense
that the norm of the solution diverges as time approaches ), then
also the solution of the linear Schr\"odinger equation collapses (in the sense
that the kinetic energy per particle diverges) if and,
simultaneously, sufficiently fast. This gives the first
dynamical description of the phenomenon of gravitational collapse as observed
directly on the many body level.Comment: 40 page
Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite
dimensional Hilbert space and generated by unbounded Hamiltonians. In
particular, we consider quantum harmonic and certain anharmonic lattice
systems
Factorization and Scaling in Hadronic Diffraction
In standard Regge theory with a pomeron intercept a(0)=1+\epsilon, the
contribution of the tripe-pomeron amplitude to the t=0 differential cross
section for single diffraction dissociation has the form d\sigma/dM^2(t=0) \sim
s^{2\epsilon}/(M^2)^{1+\epsilon}. For \epsilon>0, this form, which is based on
factorization, does not scale with energy. From an analysis of p-p and p-pbar
data from fixed target to collider energies, we find that such scaling actually
holds, signaling a breakdown of factorization. Phenomenologically, this result
can be obtained from a scaling law in diffraction, which is embedded in the
hypothesis of pomeron flux renormalization introduced to unitarize the triple
pomeron amplitude.Comment: 39 pages, Latex, 16 figure
Experimental Tests of Quantum Chromodynamics in High-p_â„ Jet Production in 200-GeV/c Hadron-Proton Collisions
Data on inclusive jet production in the transverse-momentum (p_â„) range 0-8 GeV/c for 200-GeV/c p, Ï^-, Ï^+, K^-, K^+, and p incident on a hydrogen target are presented. The jet cross section is fully corrected for losses and biases, and compared with the predictions of a model based on quantum chromodynamics. Both the absolute cross section and the inclusive charged-particle distributions inside and outside the jet are in qualitative agreement with the model
Observation of the Production of Jets of Particles at High Transverse Momentum and Comparison with Inclusive Single-Particle Reactions
Data are presented on production by 200-GeV/c hadrons incident on beryllium of both single particles and jets (groups of particles) with high p_T (transverse momentum). The experiment was performed in a wide-aperture multiparticle spectrometer at Fermilab. The jet and single-particle cross sections have a similar shape from p_T=3 to 5 GeV/c but the jet cross section is over two orders of magnitude larger. The distributions of charged-particle momenta show striking similarities to those observed in lepton-induced processes
Genetic, serological and biochemical characterization of Leishmania tropica from foci in northern Palestine and discovery of zymodeme MON-307
Background
Many cases of cutaneous leishmaniasis (CL) have been recorded in the Jenin District based on their clinical appearance. Here, their parasites have been characterized in depth.
Methods
Leishmanial parasites isolated from 12 human cases of CL from the Jenin District were cultured as promastigotes, whose DNA was extracted. The ITS1 sequence and the 7SL RNA gene were analysed as was the kinetoplast minicircle DNA (kDNA) sequence. Excreted factor (EF) serotyping and multilocus enzyme electrophoresis (MLEE) were also applied.
Results
This extensive characterization identified the strains as Leishmania tropica of two very distinct sub-types that parallel the two sub-groups discerned by multilocus microsatellite typing (MLMT) done previously. A high degree of congruity was displayed among the results generated by the different analytical methods that had examined various cellular components and exposed intra-specific heterogeneity among the 12 strains.
Three of the ten strains subjected to MLEE constituted a new zymodeme, zymodeme MON-307, and seven belonged to the known zymodeme MON-137. Ten of the 15 enzymes in the profile of zymodeme MON-307 displayed different electrophoretic mobilities compared with the enzyme profile of the zymodeme MON-137. The closest profile to that of zymodeme MON-307 was that of the zymodeme MON-76 known from Syria.
Strains of the zymodeme MON-307 were EF sub-serotype A2 and those of the zymodeme MON-137 were either A9 or A9B4. The sub-serotype B4 component appears, so far, to be unique to some strains of L. tropica of zymodeme MON-137. Strains of the zymodeme MON-137 displayed a distinctive fragment of 417 bp that was absent in those of zymodeme MON-307 when their kDNA was digested with the endonuclease RsaI. kDNA-RFLP after digestion with the endonuclease MboI facilitated a further level of differentiation that partially coincided with the geographical distribution of the human cases from which the strains came.
Conclusions
The Palestinian strains that were assigned to different genetic groups differed in their MLEE profiles and their EF types. A new zymodeme, zymodeme MON-307 was discovered that seems to be unique to the northern part of the Palestinian West Bank. What seemed to be a straight forward classical situation of L. tropica causing anthroponotic CL in the Jenin District might be a more complex situation, owing to the presence of two separate sub-types of L. tropica that, possibly, indicates two separate transmission cycles involving two separate types of phlebotomine sand fly vector
- âŠ