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 $D\geq 2$ results in the supercooled liquid regime above the glass transition. As $D$ increases, the radial distribution functions reflect reduced geometric constraints. Nearest-neighbor distances become smaller with increasing $D$ 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 $D$ crystallization becomes increasingly more difficult.Comment: 26 pages, 13 figure

Magnetic shape-memory effect in SrRuO3_3

Like most perovskites, SrRuO$_3$ exhibits structural phase transitions associated with rotations of the RuO$_6$ 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]$_c$ 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 $V(r)=(a^2\omega^2/4)sinh(r/a)^2$ where $a$ is the curvature radius and $r$ 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, $m$, equals 0.Comment: to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler