2,318 research outputs found
The AF structure of non commutative toroidal Z/4Z orbifolds
For any irrational theta and rational number p/q such that q|qtheta-p|<1, a
projection e of trace q|qtheta-p| is constructed in the the irrational rotation
algebra A_theta that is invariant under the Fourier transform. (The latter is
the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are
the canonical unitaries generating A_theta.) Further, the projection e is
approximately central, the cut down algebra eA_theta e contains a Fourier
invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are
approximately inside the matrix algebra. (In particular, there are Fourier
invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown
that for all theta the crossed product A_theta rtimes Z_4 satisfies the
Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the
Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of
M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is
an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page
IL LATO OSCURO DELLA COLPA!
Francesco Mancini e Amelia Gangemi propongono una tesi duale
sul senso di colpa delineando le caratteristiche della colpa deontologica – sensazione di avere trasgredito una norma morale senza che vi
sia una vittima – e della colpa altruistica – sensazione di aver violato
un principio altruistico senza la trasgressione di una norma morale.
Gli autori presentano alcune prove comportamentali, cognitive e neurofisiologiche che dimostrano che i due sensi di colpa hanno tratti distintivi divers
Recent Results on the Periodic Lorentz Gas
The Drude-Lorentz model for the motion of electrons in a solid is a classical
model in statistical mechanics, where electrons are represented as point
particles bouncing on a fixed system of obstacles (the atoms in the solid).
Under some appropriate scaling assumption -- known as the Boltzmann-Grad
scaling by analogy with the kinetic theory of rarefied gases -- this system can
be described in some limit by a linear Boltzmann equation, assuming that the
configuration of obstacles is random [G. Gallavotti, [Phys. Rev. (2) vol. 185
(1969), 308]). The case of a periodic configuration of obstacles (like atoms in
a crystal) leads to a completely different limiting dynamics. These lecture
notes review several results on this problem obtained in the past decade as
joint work with J. Bourgain, E. Caglioti and B. Wennberg.Comment: 62 pages. Course at the conference "Topics in PDEs and applications
2008" held in Granada, April 7-11 2008; figure 13 and a misprint in Theorem
4.6 corrected in the new versio
Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot system
A fiber taper waveguide is used to perform direct optical spectroscopy of a
microdisk-quantum-dot system, exciting the system through the photonic (light)
channel rather than the excitonic (matter) channel. Strong coupling, the regime
of coherent quantum interactions, is demonstrated through observation of vacuum
Rabi splitting in the transmitted and reflected signals from the cavity. The
fiber coupling method also allows the examination of the system's steady-state
nonlinear properties, where saturation of the cavity-QD response is observed
for less than one intracavity photon.Comment: adjusted references, added minor clarification
Simple proof of gauge invariance for the S-matrix element of strong-field photoionization
The relationship between the length gauge (LG) and the velocity gauge (VG)
exact forms of the photoionization probability amplitude is considered. Our
motivation for this paper comes from applications of the Keldysh-Faisal-Reiss
(KFR) theory, which describes atoms (or ions) in a strong laser field (in the
nonrelativistic approach, in the dipole approximation). On the faith of a
certain widely-accepted assumption, we present a simple proof that the
well-known LG form of the exact photoionization (or photodetachment)
probability amplitude is indeed the gauge-invariant result. In contrast, to
obtain the VG form of this probability amplitude, one has to either (i) neglect
the well-known Goeppert-Mayer exponential factor (which assures gauge
invariance) during all the time evolution of the ionized electron or (ii) put
some conditions on the vector potential of the laser field.Comment: The paper was initially submitted (in a previous version) on 16
October 2006 to J. Phys. A and rejected. This is the extended version (with 2
figures), which is identical to the paper published online on 12 December
2007 in Physica Script
Photo-production of scalar particles in the field of a circularly polarized laser beam
The photo-production of a pair of scalar particles in the presence of an
intense, circularly polarized laser beam is investigated. Using the optical
theorem within the framework of scalar quantum electrodynamics, explicit
expressions are given for the pair production probability in terms of the
imaginary part of the vacuum polarization tensor. Its leading asymptotic
behavior is determined for various limits of interest. The influence of the
absence of internal spin degrees of freedom is analyzed via a comparison with
the corresponding probabilities for production of spin-1/2 particles; the lack
of spin is shown to suppress the pair creation rate, as compared to the
predictions from Dirac theory. Potential applications of our results for the
search of minicharged particles are indicated.Comment: 6 pages, 2 figure
Cavity QED with Diamond Nanocrystals and Silica Microspheres
Normal mode splitting is observed in a cavity QED system, in which nitrogen
vacancy centers in diamond nanocrystals are coupled to whispering gallery modes
in a silica microsphere. The composite nanocrystal-microsphere system takes
advantage of the exceptional spin properties of nitrogen vacancy centers as
well as the ultra high quality factor of silica microspheres. The observation
of the normal mode splitting indicates that the dipole optical interaction
between the relevant nitrogen vacancy center and whispering gallery mode has
reached the strong coupling regime of cavity QED
Cantor and band spectra for periodic quantum graphs with magnetic fields
We provide an exhaustive spectral analysis of the two-dimensional periodic
square graph lattice with a magnetic field. We show that the spectrum consists
of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum
of a certain discrete operator under the discriminant (Lyapunov function) of a
suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet
eigenvalues the spectrum is a Cantor set for an irrational flux, and is
absolutely continuous and has a band structure for a rational flux. The
Dirichlet eigenvalues can be isolated or embedded, subject to the choice of
parameters. Conditions for both possibilities are given. We show that
generically there are infinitely many gaps in the spectrum, and the
Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte
The MEG detector for decay search
The MEG (Mu to Electron Gamma) experiment has been running at the Paul
Scherrer Institut (PSI), Switzerland since 2008 to search for the decay \meg\
by using one of the most intense continuous beams in the world. This
paper presents the MEG components: the positron spectrometer, including a thin
target, a superconducting magnet, a set of drift chambers for measuring the
muon decay vertex and the positron momentum, a timing counter for measuring the
positron time, and a liquid xenon detector for measuring the photon energy,
position and time. The trigger system, the read-out electronics and the data
acquisition system are also presented in detail. The paper is completed with a
description of the equipment and techniques developed for the calibration in
time and energy and the simulation of the whole apparatus.Comment: 59 pages, 90 figure
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