1,291 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
Glass transitions in 1, 2, 3, and 4 dimensional binary Lennard-Jones systems
We investigate the calorimetric liquid-glass transition by performing
simulations of a binary Lennard-Jones mixture in one through four dimensions.
Starting at a high temperature, the systems are cooled to T=0 and heated back
to the ergodic liquid state at constant rates. Glass transitions are observed
in two, three and four dimensions as a hysteresis between the cooling and
heating curves. This hysteresis appears in the energy and pressure diagrams,
and the scanning-rate dependence of the area and height of the hysteresis can
be described by power laws. The one dimensional system does not experience a
glass transition but its specific heat curve resembles the shape of the results in the supercooled liquid regime above the glass transition. As
increases, the radial distribution functions reflect reduced geometric
constraints. Nearest-neighbor distances become smaller with increasing due
to interactions between nearest and next-nearest neighbors. Simulation data for
the glasses are compared with crystal and melting data obtained with a
Lennard-Jones system with only one type of particle and we find that with
increasing crystallization becomes increasingly more difficult.Comment: 26 pages, 13 figure
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 number of bound states for weak perturbations of spin-orbit Hamiltonians
We give a variational proof of the existence of infinitely many bound states
below the continuous spectrum for some weak perturbations of a class of
spin-orbit Hamiltonians including the Rashba and Dresselhaus Hamiltonians
Real-time determination of laser beam quality by modal decomposition
We present a real-time method to determine the beam propagation ratio M2 of
laser beams. The all-optical measurement of modal amplitudes yields M2
parameters conform to the ISO standard method. The experimental technique is
simple and fast, which allows to investigate laser beams under conditions
inaccessible to other methods.Comment: 8 pages, 4 figures, published in Optics Expres
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.
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
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