1,583 research outputs found
Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations
An operator Riccati equation from systems theory is considered in the case
that all entries of the associated Hamiltonian are unbounded. Using a certain
dichotomy property of the Hamiltonian and its symmetry with respect to two
different indefinite inner products, we prove the existence of nonnegative and
nonpositive solutions of the Riccati equation. Moreover, conditions for the
boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to
appear in Journal of Evolution Equation
Glasslike Arrest in Spinodal Decomposition as a Route to Colloidal Gelation
Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich
and colloid-poor regions. Gelation results when interconnected colloid-rich
regions solidify. We show that this occurs when these regions undergo a glass
transition, leading to dynamic arrest of the spinodal decomposition. The
characteristic length scale of the gel decreases with increasing quench depth,
and the nonergodicity parameter exhibits a pronounced dependence on scattering
vector. Mode coupling theory gives a good description of the dynamics, provided
we use the full static structure as input.Comment: 14 pages, 4 figures; replaced with published versio
A note on the uniqueness of D=4 N=1 Supergravity
We investigate in 4 spacetime dimensions, all the consistent deformations of
the lagrangian , which is the sum of the
Pauli-Fierz lagrangian for a free massless spin 2 field and the
Rarita-Schwinger lagrangian for a free massless spin 3/2
field. Using BRST cohomogical techniques, we show, under the assumptions of
locality, Poincar\'e invariance, conservation of the number of gauge symmetries
and the number of derivatives on each fields, that N=1 D=4 supergravity is the
only consistent interaction between a massless spin 2 and a massless spin 3/2
field. We do not assume general covariance. This follows automatically, as does
supersymmetry invariance. Various cohomologies related to conservations laws
are also given.Comment: 22+1 pages, LaTeX. References adde
The Borrego Mountain, California, earthquake of 9 April 1968: A preliminary report
The largest earthquake to hit California in more than 15 years occurred at
02:28:58.9 GCT on 9 April 1968 near Borrego Mountain, on the western edge of
the Imperial Valley. The Seismological Laboratory at Pasadena has tentatively
assigned the shock a magnitude of 6.5, an epicentral location of 33 ° 08.8' N, 116 °
07.5' W, and a focal depth of 20 km. The earthquake was felt throughout most
of southern California and adjacent areas, but the absence of severe damage and
casualties was in large part due to the relatively undeveloped nature of the epicentral
region. Indeed, it would have been difficult to pick a location in the southernmost
part of the State more remote from centers of population
Linear Relaxation Processes Governed by Fractional Symmetric Kinetic Equations
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski
kinetic equations, which describe evolution of the systems influenced by
stochastic forces distributed with stable probability laws. These equations
generalize known kinetic equations of the Brownian motion theory and contain
symmetric fractional derivatives over velocity and space, respectively. With
the help of these equations we study analytically the processes of linear
relaxation in a force - free case and for linear oscillator. For a weakly
damped oscillator we also get kinetic equation for the distribution in slow
variables. Linear relaxation processes are also studied numerically by solving
corresponding Langevin equations with the source which is a discrete - time
approximation to a white Levy noise. Numerical and analytical results agree
quantitatively.Comment: 30 pages, LaTeX, 13 figures PostScrip
Orbifold projection in supersymmetric QCD at N_f\leq N_c
Supersymmetric orbifold projection of N=1 SQCD with relatively small number
of flavors (not larger than the number of colors) is considered. The purpose is
to check whether orbifolding commutes with the infrared limit. On the one hand,
one considers the orbifold projection of SQCD and obtains the low-energy
description of the resulting theory. On the other hand, one starts with the
low-energy effective theory of the original SQCD, and only then perfoms
orbifolding. It is shown that at finite N_c the two low-energy theories
obtained in these ways are different. However, in the case of stabilized
run-away vacuum these two theories are shown to coincide in the large N_c
limit. In the case of quantum modified moduli space, topological solitons
carrying baryonic charges are present in the orbifolded low-energy theory.
These solitons may restore the correspondence between the two theories provided
that the soliton mass tends to zero in the large N_c limit.Comment: 10 pages; misprint corrected, reference adde
Aharonov-Bohm-Type Oscillations of Thermopower in a Quantum Dot Ring Geometry
We investigate Aharonov-Bohm-type oscillations of the thermopower of a
quantum dot embedded in a ring for the case when the interaction between
electrons can be neglected. The thermopower is shown to be strongly flux
dependent, and typically the amplitude of oscillations exceeds the background
value. It is also shown to be essentially dependent on the phase of the
scattering matrix which is determined by the experimental geometry and is not
known in the given experiment. Two procedures to compare theory and experiment
are proposed.Comment: Revtex, 5 figures include
Local Density Approximation for proton-neutron pairing correlations. I. Formalism
In the present study we generalize the self-consistent
Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the
case which incorporates an arbitrary mixing between protons and neutrons in the
particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define
the HFB density matrices, discuss their spin-isospin structure, and construct
the most general energy density functional that is quadratic in local
densities. The consequences of the local gauge invariance are discussed and the
particular case of the Skyrme energy density functional is studied. By varying
the total energy with respect to the density matrices the self-consistent
one-body HFB Hamiltonian is obtained and the structure of the resulting mean
fields is shown. The consequences of the time-reversal symmetry, charge
invariance, and proton-neutron symmetry are summarized. The complete list of
expressions required to calculate total energy is presented.Comment: 22 RevTeX page
Silicon detectors for γ-ray and β-spectroscopy
Large active volume Si(Li) detectors were successfully developed for Îł-ray spectrometry at room temperature that show a sufficient efficiency and an energy resolution that is better than scintillation detectors. The higher efficiency of the proposed detectors with respect to normal silicon diodes is achieved by increasing the active volume. For this purpose special attention is given to the selection of the initial material which has to show homogeneous electro-physical parameters, low concentration of oxygen impurities and high structural perfection. The technique of using lithium ions is used as these drift into large depths and hence the profile of the impurity distribution is optimized
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