2,772 research outputs found
Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations
In this paper we obtain the orthogonality relations for the supergroup
U(m|n), which are remarkably different from the ones for the U(N) case. We
extend our results for ordinary representations, obtained some time ago, to the
case of complex conjugated and mixed representations. Our results are expressed
in terms of the Young tableaux notation for irreducible representations. We use
the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character
expansion technique as mathematical tools for deriving these relations. As a
byproduct we also obtain closed expressions for the supercharacters and
dimensions of some particular irreducible U(m|n) representations. A new way of
labeling the U(m|n) irreducible representations in terms of m + n numbers is
proposed. Finally, as a corollary of our results, new identities among the
dimensions of the irreducible representations of the unitary group U(N) are
presented.Comment: 56 pages, LaTeX, changes only in the writing of the titl
Currents between tethered electrodes in a magnetized laboratory plasma
Laboratory experiments on important plasma physics issues of electrodynamic tethers were performed. These included current propagation, formation of wave wings, limits of current collection, nonlinear effects and instabilities, charging phenomena, and characteristics of transmission lines in plasmas. The experiments were conducted in a large afterglow plasma. The current system was established with a small electron-emitting hot cathode tethered to an electron-collecting anode, both movable across the magnetic field and energized by potential difference up to V approx.=100 T(sub e). The total current density in space and time was obtained from complete measurements of the perturbed magnetic field. The fast spacecraft motion was reproduced in the laboratory by moving the tethered electrodes in small increments, applying delayed current pulses, and reconstructing the net field by a linear superposition of locally emitted wavelets. With this technique, the small-amplitude dc current pattern is shown to form whistler wings at each electrode instead of the generally accepted Alfven wings. For the beam electrode, the whistler wing separates from the field-aligned beam which carries no net current. Large amplitude return currents to a stationary anode generate current-driven microinstabilities, parallel electric fields, ion depletions, current disruptions and time-varying electrode charging. At appropriately high potentials and neutral densities, excess neutrals are ionized near the anode. The anode sheath emits high-frequency electron transit-time oscillations at the sheath-plasma resonance. The beam generates Langmuir turbulence, ion sound turbulence, electron heating, space charge fields, and Hall currents. An insulated, perfectly conducting transmission line embedded in the plasma becomes lossy due to excitation of whistler waves and magnetic field diffusion effects. The implications of the laboratory observations on electrodynamic tethers in space are discussed
A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity
After a brief summary of Double Special Relativity (DSR), we concentrate on a
five dimensional procedure, which consistently introduce coordinates and
momenta in the corresponding four-dimensional phase space, via a Hamiltonian
approach. For the one particle case, the starting point is a de Sitter momentum
space in five dimensions, with an additional constraint selected to recover the
mass shell condition in four dimensions. Different basis of DSR can be
recovered by selecting specific gauges to define the reduced four dimensional
degrees of freedom. This is shown for the Snyder basis in the one particle
case. We generalize the method to the many particles case and apply it again to
this basis. We show that the energy and momentum of the system, given by the
dynamical variables that are generators of translations in space and time and
which close the Poincar\'e algebra, are additive magnitudes. From this it
results that the rest energy (mass) of a composite object does not have an
upper limit, as opposed to a single component particle which does.Comment: 12 pages, no figures, AIP Conf. Pro
Laboratory experiments on current flow between stationary and moving electrodes in magnetoplasmas
Laboratory experiments were performed in order to investigate the basic physics of current flow between tethered electrodes in magnetoplasmas. The major findings are summarized. The experiments are performed in an effectively very large laboratory plasma in which not only the nonlinear current collection is addressed but also the propagation and spread of currents, the formation of current wings by moving electrodes, the current closure, and radiation from transmission lines. The laboratory plasma consists of a pulsed dc discharge whose Maxwellian afterglow provides a quiescent, current-free uniform background plasma. Electrodes consisting of collectors and electron emitters are inserted into the plasma and a pulsed voltage is applied between two floating electrodes via insulated transmission lines. Besides the applied current in the wire, the total current density in the plasma is obtained from space and time resolved magnetic probe measurements via Maxwell's law. Langmuir probes yield the plasma parameters
An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement
This paper presents a modified grand canonical ensemble which provides a new
simple and efficient scheme to study few-body fluid-like inhomogeneous systems
under confinement. The new formalism is implemented to investigate the exact
thermodynamic properties of a hard sphere (HS) fluid-like system with up to
three particles confined in a spherical cavity. In addition, the partition
function of this system was used to analyze the surface thermodynamic
properties of the many-HS system and to derive the exact curvature dependence
of both the surface tension and adsorption in powers of the density. The
expressions for the surface tension and the adsorption were also obtained for
the many- HS system outside of a fixed hard spherical object. We used these
results to derive the dependence of the fluid-substrate Tolman length up to
first order in density.Comment: 6 figures. The paper includes new exact results about hard spheres
fluid-like system
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