PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set

PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras

Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie triple structure is found and an interpretation as PT-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space related J-selfadjoint extensions for PTQM setups with ultra-localized potentials.Comment: 11 page

Quantum oscillator as 1D anyon

It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe

Performance of the Beetle readout chip for LHCb

Beetle is a 128-channel readout chip, which will be used in the silicon vertex detector, the pile-up veto counters and the silicon tracker of the LHCb experiment at CERN. A further application of the Beetle chip is the readout of the LHCb RICH, in case it is equipped with multi-anode PMTs. The scope of this paper is the design changes leading to the latest version 1.3 of the Beetle readout chip. In addition, measurements on earlier versions and simulation results driving these changes are shown

Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models

This is the third paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we analyze models which, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper: These are systems with an SL(2,\Rl) gauge symmetry and the complications arise because non -- compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads to severe obstacles in the refined algebraic quantization programme (group averaging) and we see a trace of that in the fact that the spectrum of the Master Constraint does not contain the point zero. However, the minimum of the spectrum is of order $\hbar^2$ which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to $\hbar$ normal ordering constants). The physical Hilbert space can then be be obtained after subtracting this normal ordering correction.Comment: 33 pages, no figure

The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space

We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge new, non -- trivial solution to the representation problem. This solution exists 1. for any target space dimension, 2. for Minkowski signature of the target space, 3. without tachyons, 4. manifestly ghost -- free (no negative norm states), 5. without fixing a worldsheet or target space gauge, 6. without (Virasoro) anomalies (zero central charge), 7. while preserving manifest target space Poincar\'e invariance and 8. without picking up UV divergences. The existence of this stable solution is exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. Moreover, these new representations could solve some of the major puzzles of string theory such as the cosmological constant problem. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper we treat the more complicated case of curved target spaces.Comment: 46 p., LaTex2e, no figure

Undulator design for Laser Plasma Based Free electron laser

The fourth generation of synchrotron radiation sources, commonly referred to as the Free Electron Laser (FEL), provides an intense source of brilliant X-ray beams enabling the investigation of matter at the atomic scale with unprecedented time resolution. These sources require the use of conventional linear accelerators providing high electron beam performance. The achievement of chirped pulse amplification allowing lasers to be operated at the Terawatt range, opened the way for the Laser Plasma Acceleration (LPA) technique where high energy electron bunches with high current can be produced within a very short centimeter-scale distance. Such an advanced acceleration concept is of great interest to be qualified by an FEL application for compact X-ray light sources. We explore in this paper what the LPA specificities imply on the design of the undulator, part of the gain medium. First, the LPA concept and state-of-art are presented showing the different operation regimes and what electron beam parameters are likely to be achieved. The LPA scaling laws are discussed afterwards to better understand what laser or plasma parameters have to be adjusted in order to improve electron beam quality. The FEL is secondly discussed starting with the spontaneous emission, followed by the different FEL configurations, the electron beam transport to the undulator and finally the scaling laws and correction terms in the high gain case. Then, the different types of compact undulators that can be implemented for an LPA based FEL application are analyzed. Finally, examples of relevant experiments are reported by describing the transport beamline, presenting the spontaneous emission characteristics achieved so far and the future prospects

Developing a 50 MeV LPA-based Injector at ATHENA for a Compact Storage Ring

The laser-driven generation of relativistic electron beams in plasma and their acceleration to high energies with GV/m-gradients has been successfully demonstrated. Now, it is time to focus on the application of laser-plasma accelerated (LPA) beams. The "Accelerator Technology HElmholtz iNfrAstructure" (ATHENA) of the Helmholtz Association fosters innovative particle accelerators and high-power laser technology. As part of the ATHENAe pillar several different applications driven by LPAs are to be developed, such as a compact FEL, medical imaging and the first realization of LPA-beam injection into a storage ring. The latter endeavour is conducted in close collaboration between Deutsches Elektronen-Synchrotron (DESY), Karlsruhe Institute of Technology (KIT) and Helmholtz Institute Jena (HIJ). In the cSTART project at KIT, a compact storage ring optimized for short bunches and suitable to accept LPA-based electron bunches is in preparation. In this conference contribution we will introduce the 50 MeV LPA-based injector and give an overview about the project goals. The key parameters of the plasma injector will be presented. Finally, the current status of the project will be summarized

First observation of Bs -> D_{s2}^{*+} X mu nu decays

Using data collected with the LHCb detector in proton-proton collisions at a centre-of-mass energy of 7 TeV, the semileptonic decays Bs -> Ds+ X mu nu and Bs -> D0 K+ X mu nu are detected. Two structures are observed in the D0 K+ mass spectrum at masses consistent with the known D^+_{s1}(2536) and $D^{*+}_{s2}(2573) mesons. The measured branching fractions relative to the total Bs semileptonic rate are B(Bs -> D_{s2}^{*+} X mu nu)/B(Bs -> X mu nu)= (3.3\pm 1.0\pm 0.4)%, and B(Bs -> D_{s1}^+ X munu)/B(Bs -> X mu nu)= (5.4\pm 1.2\pm 0.5)%, where the first uncertainty is statistical and the second is systematic. This is the first observation of the D_{s2}^{*+} state in Bs decays; we also measure its mass and width.Comment: 8 pages 2 figures. Published in Physics Letters