1,302 research outputs found
Infinite Infrared Regularization and a State Space for the Heisenberg Algebra
We present a method for the construction of a Krein space completion for
spaces of test functions, equipped with an indefinite inner product induced by
a kernel which is more singular than a distribution of finite order. This
generalizes a regularization method for infrared singularities in quantum field
theory, introduced by G. Morchio and F. Strocchi, to the case of singularites
of infinite order. We give conditions for the possibility of this procedure in
terms of local differential operators and the Gelfand- Shilov test function
spaces, as well as an abstract sufficient condition. As a model case we
construct a maximally positive definite state space for the Heisenberg algebra
in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde
On semiclassical dispersion relations of Harper-like operators
We describe some semiclassical spectral properties of Harper-like operators,
i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and
position. The spectral region corresponding to the separatrices of the
classical Hamiltonian is studied for the case of integer flux. We derive
asymptotic formula for the dispersion relations, the width of bands and gaps,
and show how geometric characteristics and the absence of symmetries of the
Hamiltonian influence the form of the energy bands.Comment: 13 pages, 8 figures; final version, to appear in J. Phys. A (2004
Magnetic shape-memory effect in SrRuO
Like most perovskites, SrRuO exhibits structural phase transitions
associated with rotations of the RuO octahedra. The application of moderate
magnetic fields in the ferromagnetically ordered state allows one to fully
control these structural distortions, although the ferromagnetic order occurs
at six times lower temperature than the structural distortion. Our neutron
diffraction and macroscopic measurements unambiguously show that magnetic
fields rearrange structural domains, and that for the field along a cubic
[110] direction a fully detwinned crystal is obtained. Subsequent heating
above the Curie temperature causes a magnetic shape-memory effect, where the
initial structural domains recover
On the discrete spectrum of spin-orbit Hamiltonians with singular interactions
We give a variational proof of the existence of infinitely many bound states
below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba
and Dresselhaus cases) perturbed by measure potentials thus extending the
results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007)
F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics
(memorial volume in honor of Vladimir Geyler). Results improved in this
versio
On the harmonic oscillator on the Lobachevsky plane
We introduce the harmonic oscillator on the Lobachevsky plane with the aid of
the potential where is the curvature
radius and is the geodesic distance from a fixed center. Thus the potential
is rotationally symmetric and unbounded likewise as in the Euclidean case. The
eigenvalue equation leads to the differential equation of spheroidal functions.
We provide a basic numerical analysis of eigenvalues and eigenfunctions in the
case when the value of the angular momentum, , equals 0.Comment: to appear in Russian Journal of Mathematical Physics (memorial volume
in honor of Vladimir Geyler
The Analytic Torsion of the cone over an odd dimensional manifold
We study the analytic torsion of the cone over an orientable odd dimensional
compact connected Riemannian manifold W. We prove that the logarithm of the
analytic torsion of the cone decomposes as the sum of the logarithm of the root
of the analytic torsion of the boundary of the cone, plus a topological term,
plus a further term that is a rational linear combination of local Riemannian
invariants of the boundary. We also prove that this last term coincides with
the anomaly boundary term appearing in the Cheeger Muller theorem for a
manifold with boundary, according to Bruning and Ma, either in the case that W
is an odd sphere or has dimension smaller than six. It follows in particular
that the Cheeger Muller theorem holds for the cone over an odd dimensional
sphere. We also prove Poincare duality for the analytic torsion of a cone
Approximation by point potentials in a magnetic field
We discuss magnetic Schrodinger operators perturbed by measures from the
generalized Kato class. Using an explicit Krein-like formula for their
resolvent, we prove that these operators can be approximated in the strong
resolvent sense by magnetic Schrodinger operators with point potentials. Since
the spectral problem of the latter operators is solvable, one in fact gets an
alternative way to calculate discrete spectra; we illustrate it by numerical
calculations in the case when the potential is supported by a circle.Comment: 16 pages, 2 eps figures, submitted to J. Phys.
Effect of external pressure on the magnetic properties of CoAsO ( = La, Pr, Sm): a SR study
We report on a detailed investigation of the itinerant ferromagnets LaCoAsO,
PrCoAsO and SmCoAsO performed by means of muon spin spectroscopy upon the
application of external hydrostatic pressures up to GPa. These
materials are shown to be magnetically hard in view of the weak dependence of
both critical temperatures and internal fields at the muon site on .
In the cases = La and Sm, the behaviour of the internal field is
substantially unaltered up to GPa. A much richer phenomenology is
detected in PrCoAsO instead, possibly associated with a strong dependence
of the statistical population of the two different crystallographic sites for
the muon. Surprisingly, results are notably different from what is observed in
the case of the isostructural compounds CoPO, where the full As/P
substitution is already inducing a strong chemical pressure within the lattice
but is still very effective in further affecting the magnetic properties.Comment: 8 pages, 9 figure
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