A General Approach of Quasi-Exactly Solvable Schroedinger Equations with Three Known Eigenstates

We propose a general method for constructing quasi-exactly solvable potentials with three analytic eigenstates. These potentials can be real or complex functions but the spectrum is real. A comparison with other methods is also performed

Calculations of Energy Losses due to Atomic Processes in Tokamaks with Applications to the ITER Divertor

Reduction of the peak heat loads on the plasma facing components is essential for the success of the next generation of high fusion power tokamaks such as the International Thermonuclear Experimental Reactor (ITER) 1 . Many present concepts for accomplishing this involve the use of atomic processes to transfer the heat from the plasma to the main chamber and divertor chamber walls and much of the experimental and theoretical physics research in the fusion program is directed toward this issue. The results of these experiments and calculations are the result of a complex interplay of many processes. In order to identify the key features of these experiments and calculations and the relative role of the primary atomic processes, simple quasi-analytic models and the latest atomic physics rate coefficients and cross sections have been used to assess the relative roles of central radiation losses through bremsstrahlung, impurity radiation losses from the plasma edge, charge exchange and hydrogen radiation losses from the scrape-off layer and divertor plasma and impurity radiation losses from the divertor plasma. This anaysis indicates that bremsstrahlung from the plasma center and impurity radiation from the plasma edge and divertor plasma can each play a significant role in reducing the power to the divertor plates, and identifies many of the factors which determine the relative role of each process. For instance, for radiation losses in the divertor to be large enough to radiate the power in the divertor for high power experiments, a neutral fraction of 10-3 to 10-2 and an impurity recycling rate of netrecycle of ~ 10^16 s m^-3 will be required in the divertor.Comment: Preprint for the 1994 APSDPP meeting, uuencoded and gzipped postscript with 22 figures, 40 pages

A generalized photon propagator

A covariant gauge independent derivation of the generalized dispersion relation of electromagnetic waves in a medium with local and linear constitutive law is presented. A generalized photon propagator is derived. For Maxwell constitutive tensor, the standard light cone structure and the standard Feynman propagator are reinstated

Effective Theories for Circuits and Automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure

Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

The Constitutive Relations and the Magnetoelectric Effect for Moving Media

In this paper the constitutive relations for moving media with homogeneous and isotropic electric and magnetic properties are presented as the connections between the generalized magnetization-polarization bivector $$ and the electromagnetic field F. Using the decompositions of F and $\mathcal{M}$, it is shown how the polarization vector P(x) and the magnetization vector M(x) depend on E, B and two different velocity vectors, u - the bulk velocity vector of the medium, and v - the velocity vector of the observers who measure E and B fields. These constitutive relations with four-dimensional geometric quantities, which correctly transform under the Lorentz transformations (LT), are compared with Minkowski's constitutive relations with the 3-vectors and several essential differences are pointed out. They are caused by the fact that, contrary to the general opinion, the usual transformations of the 3-vectors $$, $\mathbf{B}$, $\mathbf{P}$, $\mathbf{M}$, etc. are not the LT. The physical explanation is presented for the existence of the magnetoelectric effect in moving media that essentially differs from the traditional one.Comment: 18 pages, In Ref. [10] here, which corresponds to Ref. [18] in the published paper in IJMPB, Z. Oziewicz's published paper is added. arXiv admin note: text overlap with arXiv:1101.329

Persistent detwinning of iron pnictides by small magnetic fields

Our comprehensive study on EuFe$_2$As$_2$ reveals a dramatic reduction of magnetic detwinning fields compared to other AFe$_2$As$_2$ (A = Ba, Sr, Ca) iron pnictides by indirect magneto-elastic coupling of the Eu$^{2+}$ ions. We find that only 0.1T are sufficient for persistent detwinning below the local Eu$^{2+}$ ordering; above $T_\text{Eu}$ = 19K, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetrybreaking external force.Comment: accepted by Physical Review Letter

An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page