Precision heat forming of tetrafluoroethylene tubing

An invention that provides a method of altering the size of tetrafluoroethylene tubing which is only available in limited combination of wall thicknesses and diameter are discussed. The method includes the steps of sliding the tetrafluoroethylene tubing onto an aluminum mandrel and clamping the ends of the tubing to the mandrel by means of clamps. The tetrafluorethylene tubing and mandrel are then placed in a supporting coil which with the mandrel and tetrafluorethylene tubing are then positioned in a insulated steel pipe which is normally covered with a fiber glass insulator to smooth out temperature distribution therein. The entire structure is then placed in an event which heats the tetrafluorethylene tubing which is then shrunk by the heat to the outer dimension of the aluminum mandrel. After cooling the aluminum mandrel is removed from the newly sized tetrafluorethylene tubing by a conventional chemical milling process

Physical interpretation of NUT solution

We show that the well-known NUT solution can be correctly interpreted as describing the exterior field of two counter-rotating semi-infinite sources possessing negative masses and infinite angular momenta which are attached to the poles of a static finite rod of positive mass.Comment: 7 pages, 1 figure, submitted to Classical and Quantum Gravit

Polyakov loop in chiral quark models at finite temperature

We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponentially small with the pion mass. To illustrate the point we compute some low energy observables at finite temperature and show that the finite temperature corrections to the low energy coefficients are $N_c$ suppressed due to color average of the Polyakov loop. Our analysis also shows how the phenomenology of chiral quark models at finite temperature can be made compatible with the expectations of chiral perturbation theory. The implications for the simultaneous center symmetry breaking-chiral symmetry restoration phase transition are also discussed.Comment: 24 pages, 8 ps figures. Figure and appendix added. To appear in Physical Review

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Harmonic states for the free particle

Different families of states, which are solutions of the time-dependent free Schr\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined.Comment: 21 pages, 3 figures. Title changed, content added, references adde

Large quantum nonlinear dynamic susceptibility of single-molecule magnets

The nonlinear dynamical response of Mn$_{12}$ single-molecule magnets is experimentally found to be very large, quite insensitive to the spin-lattice coupling constant, and displaying peaks reversed with respect to classical superparamagnets. It is shown that these features are caused by the strong field dependence of the relaxation rate due to the detuning of energy levels between which tunneling takes place. The nonlinear susceptibility technique, previously overlooked, is thus proposed as a privileged probe to ascertain the occurrence of quantum effects in mesoscopic magnetic systems.Comment: 4 pages, 4 figure

How can exact and approximate solutions of Einstein's field equations be compared?

The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate solution whose form on the symmetry axis is subsequently used for the identification of the exact solution possessing the same multipole structure, and (ii) the generation of approximate solutions from exact ones by expanding the latter in series of powers of a small parameter. The central result of our paper is the derivation of the correct approximate analogues of the double-Kerr solution possessing the physically meaningful equilibrium configurations. We also show that the interpretation of an approximate solution originally attributed to it on the basis of some general physical suppositions may not coincide with its true nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure

Global Partial Density of States: Statistics and Localization Length in Quasi-one Dimensional disordered systems

We study the distributions functions for global partial density of states (GPDOS) in quasi-one-dimensional (Q1D) disordered wires as a function of disorder parameter from metal to insulator. We consider two different models for disordered Q1D wire: a set of two dimensional $\delta$ potentials with an arbitrary signs and strengths placed randomly, and a tight-binding Hamiltonian with several modes and on-site disorder. The Green functions (GF) for two models were calculated analytically and it was shown that the poles of GF can be presented as determinant of the rank $N\times N$, where $N$ is the number of scatters. We show that the variances of partial GPDOS in the metal to insulator crossover regime are crossing. The critical value of disorder $w_c$ where we have crossover can be used for calculation a localization length in Q1D systems.Comment: RevTex4 8 .eps figure