Search results for "Mathematical physics"

Trivial S-Matrices, Wigner-Von Neumann Resonances and Positon Solutions of the Integrable Nonlinear Evolution Equations

1996

It is well known that the scattering matrix is different from the unit matrix in the case of 1-dimensional Schrodinger operator with smooth rapidly decreasing nonzero potential. This no more true in the case of the slowly decreasing and oscillating potentials for which the absence of scattering is accompanied by the occurrence of the Wigner-von Neumann resonances embedded in the positive absolutely continuous spectrum. Taken as initial conditions in the KdV like integrable partial differential equations these potentials generate interesting family of explicit solutions. Below we will call them positon or multipositon solutions. The interaction of an arbitrary finite number of positons and s…

The Maximum Entropy Formalism.

1980

The AD and ELENA orbit, trajectory and intensity measurement systems

2017

This paper describes the new Antiproton Decelerator (AD) orbit measurement system and the Extra Low ENergy Antiproton ring (ELENA) orbit, trajectory and intensity measurement system. The AD machine at European Organization for Nuclear Research (CERN) is presently being used to decelerate antiprotons from 3.57 GeV/c to 100 MeV/c for matter vs anti-matter comparative studies. The ELENA machine, presently under commissioning, has been designed to provide an extra deceleration stage down to 13.7 MeV/c. The AD orbit system is based on 32 horizontal and 27 vertical electrostatic Beam Position Monitor (BPM) fitted with existing low noise front-end amplifiers while the ELENA system consists of 24 \…

Applications of wavelets to quantum mechanics: A pedagogical example

1995

We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models starting from considerations on the numerical results on the energy. We conclude that wavelet theory can be conveniently used in the description of the system. Finally we suggest applications of our results to the Fractional Quantum Hall Effect.

A covariant constituent-quark formalism for mesons

2014

Using the framework of the Covariant Spectator Theory (CST) [1] we are developing a covariant model formulated in Minkowski space to study mesonic structure and spectra. Treating mesons as effective $q\bar{q}$ states, we focused in [2] on the nonrelativistic bound-state problem in momentum space with a linear confining potential. Although integrable, this kernel has singularities which are difficult to handle numerically. In [2] we reformulate it into a form in which all singularities are explicitely removed. The resulting equations are then easier to solve and yield accurate and stable solutions. In the present work, the same method is applied to the relativistic case, improving upon the r…

Nonlocal random motions: The trapping problem

2014

L\'evy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a particular L\'evy process may be subject to physically implementable manipulations, whose ultimate goal is to confine the random motion in a spatially finite, possibly mesoscopic trap. We analyze thisissue for an exemplary case of the Cauchy process in a finiteinterval. Qualitatively, our observations extend to general jump-type processes that are driven by non-gaussian noises, classified by the integral part of the L\'evy-Khintchine formula.For clarity of arguments we discuss, as a reference model, the classic …

RPA in wavefunction representation

1992

The RPA is formulated in subspaces of coordinate-like and momentum-like I ph operators. This allows to embed a large class of approximative schemes into a generalized RPA treatment. We give a detailed formulation in terms of wavefunctions in coordinate space which is ideally suited to practical programming. In particular, we work out the reduction to spherical tensors in the case of spherical symmetry which is most often the starting point in finite Fermion systems.

Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity

2022

AbstractWe study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal diffe…

Optical response of highly reflective film used in the water Cherenkov muon veto of the XENON1T dark matter experiment

2017

The XENON1T experiment is the most recent stage of the XENON Dark Matter Search, aiming for the direct detection of Weakly Interacting Massive Particles (WIMPs). To reach its projected sensitivity, the background has to be reduced by two orders of magnitude compared to its predecessor XENON100. This requires a water Cherenkov muon veto surrounding the XENON1T TPC, both to shield external backgrounds and to tag muon-induced energetic neutrons through detection of a passing muon or the secondary shower induced by a muon interacting in the surrounding rock. The muon veto is instrumented with $84$ $8"$ PMTs with high quantum efficiency (QE) in the Cherenkov regime and the walls of the watertank…

Performance of the large scale HV-CMOS pixel sensor MuPix8

2019

The Mu3e experiment is searching for the charged lepton flavour violating decay $ ��^+\rightarrow e^+ e^- e^+ $, aiming for an ultimate sensitivity of one in $10^{16}$ decays. In an environment of up to $10^9$ muon decays per second the detector needs to provide precise vertex, time and momentum information to suppress accidental and physics background. The detector consists of cylindrical layers of $50\, ��\text{m}$ thin High Voltage Monolithic Active Pixel Sensors (HV-MAPS) placed in a $1\,\text{T}$ magnetic field. The measurement of the trajectories of the decay particles allows for a precise vertex and momentum reconstruction. Additional layers of fast scintillating fibre and tile detec…