Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincar\'e groups in arbitrary dimension. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre Delign

Progress in the ITER neutral beam test facility

Heating neutral beam (HNB) injectors, necessary to achieve burning conditions and to control plasma instabilities in ITER, are characterized by such demanding parameters that a neutral beam test facility (NBTF) dedicated to their development and optimization is being realized in Padua (Italy) with direct contributions from the Italian government (through Consorzio RFX as the host entity) and the ITER international organization (with kind contributions from the ITER domestic agencies of Europe, Japan and India) and technical and scientific support from various European laboratories and universities. The NBTF hosts two experiments: SPIDER, devoted to ion source optimization for the required source performance, and MITICA, the full-size prototype of the ITER HNB, with an ion source identical to SPIDER. This paper gives an overview of the progress towards NBTF realization, with particular emphasis on issues discovered during this phase of activity and on solutions adopted to minimize the impact on the schedule and maintain the goals of the facilities. The realization of MITICA is well advanced; operation is expected to start in 2023 due to the long procurement time of the in-vessel mechanical components. The beam source power supplies, operating at 1 MV, are in an advanced phase of realization; all high-voltage components have been installed and the complex insulation test phase began in 2018. At the same time, construction and installation of SPIDER plant systems was successfully completed with their integration into the facility. The mechanical components of the SPIDER ion source were installed inside the vessel and connected to the plants. Integrated commissioning with the control, protection and safety systems ended positively and the first experimental phase has begun. The first results of the SPIDER experiment, with data from operational diagnostics, and the plans for the 1 MV insulation tests on the MITICA high-voltage components are presented

The ITER Neutral Beam Test Facility towards SPIDER operation

SPIDER is one of two projects of the ITER Neutral Beam Test Facility under construction in Padova, Italy, at the Consorzio RFX premises. It will have a 100 keV beam source with a full-size prototype of the radiofrequency ion source for the ITER neutral beam injector (NBI) and also, similar to the ITER diagnostic neutral beam, it is designed to operate with a pulse length of up to 3600 s, featuring an ITER-like magnetic filter field configuration (for high extraction of negative ions) and caesium oven (for high production of negative ions) layout as well as a wide set of diagnostics. These features will allow a reproduction of the ion source operation in ITER, which cannot be done in any other existing test facility. SPIDER realization is well advanced and the first operation is expected at the beginning of 2018, with the mission of achieving the ITER heating and diagnostic NBI ion source requirements and of improving its performance in terms of reliability and availability. This paper mainly focuses on the preparation of the first SPIDER operations - integration and testing of SPIDER components, completion and implementation of diagnostics and control and formulation of operation and research plan, based on a staged strategy

Normal completely positive maps on the space of quantum operations

Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quantum superinstruments, namely measures with values in the set of quantum supermaps, and derive a dilation theorem for them that is analogue to Ozawa's theorem for quantum instruments. The three dilation theorems presented here show that all the supermaps defined in this paper can be implemented by connecting devices in quantum circuits.Comment: 47 pages (in one-column format), including new results about quantum operations on separable von Neumann algebra

Effects of Axial Vorticity in Elongated Mixtures of Bose-Einstein Condensates

We consider a meniscus between rotating and nonrotating species in the Bose-Einstein condensate (BEC) with repulsive inter-atomic interactions, confined to a pipe-shaped trap. In this setting, we derive a system of coupled one-dimensional (1D) nonpolynomial Schrodinger equations (NPSEs) for two mean-field wave functions. Using these equations, we analyze the phase separation/mixing in the pipe with periodic axial boundary conditions, i.e. in a toroidal configuration. We find that the onset of the mixing, in the form of suction, i.e., filling the empty core in the vortical component by its nonrotating counterpart, crucially depends on the vorticity of the first component, and on the strengths of the inter-atomic interactions.Comment: 4 pages, 3 figure

Light scattering from an amplifying medium bounded by a randomly rough surface: A numerical study

We study by numerical simulations the scattering of $s$-polarized light from a rough dielectric film deposited on the planar surface of a semi-infinite perfect conductor. The dielectric film is allowed to be either active or passive, situations that we model by assigning negative and positive values, respectively, to the imaginary part $\epsilon_2$ of the dielectric constant of the film. We study the reflectance ${\cal R}$ and the total scattered energy ${\cal U}$ for the system as functions of both $\epsilon_2$ and the angle of incidence of the light. Furthermore, the positions and widths of the enhanced backscattering and satellite peaks are discussed. It is found that these peaks become narrower and higher when the amplification of the system is increased, and that their widths scale linearly with $\epsilon_2$. The positions of the backscattering peaks are found to be independent of $\epsilon_2$, while we find a weak dependence on this quantity in the positions of the satellite peaks.Comment: Revtex, 9 pages, 9 figure

A complete characterization of phase space measurements

We characterize all the phase space measurements for a non-relativistic particle.Comment: 11 pages, latex, no figures, iopart styl

Dynamic correlations of the Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.Comment: 11 pages, 3 figures, submitted to PR