4,122 research outputs found
Some remarks on quasi-Hermitian operators
A quasi-Hermitian operator is an operator that is similar to its adjoint in
some sense, via a metric operator, i.e., a strictly positive self-adjoint
operator. Whereas those metric operators are in general assumed to be bounded,
we analyze the structure generated by unbounded metric operators in a Hilbert
space. Following our previous work, we introduce several generalizations of the
notion of similarity between operators. Then we explore systematically the
various types of quasi-Hermitian operators, bounded or not. Finally we discuss
their application in the so-called pseudo-Hermitian quantum mechanics.Comment: 18page
Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces
We compute the Green's function for the Hodge Laplacian on the symmetric
spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or
Lorentzian manifold of constant curvature and \Sigma is a simply connected
Riemannian surface of constant curvature. Our approach is based on a
generalization to the case of differential forms of the method of spherical
means and on the use of Riesz distributions on manifolds. The radial part of
the Green's function is governed by a fourth order analogue of the Heun
equation.Comment: 18 page
One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities
A one-dimensional discrete Stark Hamiltonian with a continuous electric field
is constructed by extension theory methods. In absence of the impurities the
model is proved to be exactly solvable, the spectrum is shown to be simple,
continuous, filling the real axis; the eigenfunctions, the resolvent and the
spectral measure are constructed explicitly. For this (unperturbed) system the
resonance spectrum is shown to be empty. The model considering impurity in a
single node is also constructed using the operator extension theory methods.
The spectral analysis is performed and the dispersion equation for the
resolvent singularities is obtained. The resonance spectrum is shown to contain
infinite discrete set of resonances. One-to-one correspondence of the
constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure
A note on maximal estimates for stochastic convolutions
In stochastic partial differential equations it is important to have pathwise
regularity properties of stochastic convolutions. In this note we present a new
sufficient condition for the pathwise continuity of stochastic convolutions in
Banach spaces.Comment: Minor correction
The quantized Hall effect in the presence of resistance fluctuations
We present an experimental study of mesoscopic, two-dimensional electronic
systems at high magnetic fields. Our samples, prepared from a low-mobility
InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance
fluctuations. Focusing on the lowest Landau level we find that, while the
diagonal resistivity displays strong fluctuations, the Hall resistivity is free
of fluctuations and remains quantized at its value, . This is
true also in the insulating phase that terminates the quantum Hall series.
These results extend the validity of the semicircle law of conductivity in the
quantum Hall effect to the mesoscopic regime.Comment: Includes more data, changed discussio
New mobilities across the lifecourse: A framework for analysing demographically-linked drivers of migration
Date of acceptance: 17/02/2015Taking the life course as the central concern, the authors set out a conceptual framework and define some key research questions for a programme of research that explores how the linked lives of mobile people are situated in time–space within the economic, social, and cultural structures of contemporary society. Drawing on methodologically innovative techniques, these perspectives can offer new insights into the changing nature and meanings of migration across the life course.Publisher PDFPeer reviewe
The geometry of a vorticity model equation
We provide rigorous evidence of the fact that the modified
Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics
describes the geodesic flow on the subgroup of orientation-preserving
diffeomorphisms fixing one point, with respect to right-invariant metric
induced by the homogeneous Sobolev norm and show the local existence
of the geodesics in the extended group of diffeomorphisms of Sobolev class
with .Comment: 24 page
Magnetoresistivity in a Tilted Magnetic Field in p-Si/SiGe/Si Heterostructures with an Anisotropic g-Factor: Part II
The magnetoresistance components and were measured in
two p-Si/SiGe/Si quantum wells that have an anisotropic g-factor in a tilted
magnetic field as a function of temperature, field and tilt angle. Activation
energy measurements demonstrate the existence of a ferromagnetic-paramagnetic
(F-P) transition for a sample with a hole density of
=2\,cm. This transition is due to crossing of the
0 and 1 Landau levels. However, in another sample, with
=7.2\,cm, the 0 and 1 Landau
levels coincide for angles =0-70. Only for >
70 do the levels start to diverge which, in turn, results in the
energy gap opening.Comment: 5 pages, 6 figure
Breit Equation with Form Factors in the Hydrogen Atom
The Breit equation with two electromagnetic form-factors is studied to obtain
a potential with finite size corrections. This potential with proton structure
effects includes apart from the standard Coulomb term, the Darwin term,
retarded potentials, spin-spin and spin-orbit interactions corresponding to the
fine and hyperfine structures in hydrogen atom. Analytical expressions for the
hyperfine potential with form factors and the subsequent energy levels
including the proton structure corrections are given using the dipole form of
the form factors. Numerical results are presented for the finite size
corrections in the 1S and 2S hyperfine splittings in the hydrogen atom, the
Sternheim observable and the 2S and 2P hyperfine splittings in muonic
hydrogen. Finally, a comparison with some other existing methods in literature
is presented.Comment: 24 pages, Latex, extended version, title change
Inextendible Schwarzschild black hole with a single exterior: How thermal is the Hawking radiation?
Several approaches to Hawking radiation on Schwarzschild spacetime rely in
some way or another on the fact that the Kruskal manifold has two causally
disconnected exterior regions. We investigate the Hawking(-Unruh) effect for a
real scalar field on the \RPthree geon: an inextendible, globally hyperbolic,
space and time orientable eternal black hole spacetime that is locally
isometric to Kruskal but contains only one exterior region. The
Hartle-Hawking-like vacuum~\hhvacgeon, which can be characterized
alternatively by the positive frequency properties along the horizons or by the
complex analytic properties of the Feynman propagator, turns out to contain
exterior region Boulware modes in correlated pairs, and any operator in the
exterior that only couples to one member of each correlated Boulware pair has
thermal expectation values in the usual Hawking temperature. Generic operators
in the exterior do not have this special form; however, we use a Bogoliubov
transformation, a particle detector analysis, and a particle
emission-absorption analysis that invokes the analytic properties of the
Feynman propagator, to argue that \hhvacgeon appears as a thermal bath with
the standard Hawking temperature to any exterior observer at asymptotically
early and late Schwarzschild times. A~(naive) saddle-point estimate for the
path-integral-approach partition function yields for the geon only half of the
Bekenstein-Hawking entropy of a Schwarzschild black hole with the same ADM
mass: possible implications of this result for the validity of path-integral
methods or for the statistical interpretation of black-hole entropy are
discussed. Analogous results hold for a Rindler observer in a flat spacetime
whose global properties mimic those of the geon.Comment: 53 pages, REVTex v3.1 with amsfonts and epsf, includes 5 eps figures.
(v2: Title and abstract expanded, minor comments added. v3: Minor typos
corrected.
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