arXiv subjects
Publications and source records attributed to A. Pichler.
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the dispersion analysis, including comparison with the plane wave discontinuous Galerkin method.
The VIP2 (VIolation of the Pauli Exclusion Principle) experiment at the Gran Sasso underground laboratory (LNGS) is searching for possible violations of standard quantum mechanics predictions in atoms at very high sensitivity. We investigate atomic transitions with precision X-ray spectroscopy in order to test the Pauli Exclusion Principle (PEP) and therefore the related spin-statistics theorem. We will present our experimental method for the search for "anomalous" (i.e. Pauli-forbidden) X-ray transitions in copper atoms, produced by "new" electrons, which could have tiny probability to undergo Pauli-forbidden transition to the ground state already occupied by two electrons. We will describe the VIP2 experimental setup, which is taking data at LNGS presently. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10$^{-31}$. We will present current experimental results and discuss implications of a possible violation.
We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecewise constant wave number. With respect to the original approach, we address two additional issues: firstly, we define the coupling of local approximation spaces with piecewise constant wave numbers, secondly, we enrich such local spaces with special functions capturing the physical behaviour of the solution to the target problem. As these two issues are directly related to an increase of the number of degrees of freedom, we use a reduction strategy inspired by arXiv:1807.11237, which allows to mitigate the growth of the dimension of the approximation space when considering $h$- and $p$-refinements. This renders the new method highly competitive in comparison to other Trefftz and quasi-Trefftz technologies tailored for the Helmholtz problem with piecewise constant wave number. A wide range of numerical experiments, including the $p$-version with quasi-uniform meshes and the $hp$-version with isotropic and anisotropic mesh refinements, is presented.
We discuss the implementation details and the numerical performance of the recently introduced nonconforming Trefftz virtual element method for the 2D Helmholtz problem. In particular, we present a strategy to significantly reduce the ill-conditioning of the original method; such a recipe is based on an automatic filtering of the basis functions edge by edge, and therefore allows for a notable reduction of the number of degrees of freedom. A widespread set of numerical experiments, including an application to acoustic scattering, the $h$-, $p$-, and $hp$-versions of the method, is presented. Moreover, a comparison with other Trefftz-based methods for the Helmholtz problem shows that this novel approach results in robust and effective performance.
The VIP2 experiment tests the Pauli Exclusion Principle with high sensitivity, by searching for Pauli-forbidden atomic transitions from the 2p to the 1s shell in copper at about 8keV. The transition energy of Pauli-forbidden K X-rays is shifted by about 300 eV with respect to the normal allowed K line. This energy difference can be resolved using Silicon Drift Detectors. The data for this experiment is taken in the Gran Sasso underground laboratory (LNGS), which provides shielding from cosmic radiation. An overview of the detection system of the VIP2 experiment will be given. This includes the Silicon Drift Detectors used as X-ray detectors which provide an energy resolution of around 150 eV at 6 keV and timing information for active shielding. Furthermore, the low maintenance requirement makes them excellent X-ray detectors for the use in an underground laboratory. The VIP2 setup will be discussed which consists of a high current target system and a passive as well as an active shielding system using plastic scintillators read out by Silicon Photomultipliers.
We introduce a novel virtual element method (VEM) for the two dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefftz functions, i.e., functions belonging to the kernel of the Helmholtz operator. The global trial and test spaces are not fully discontinuous, but rather interelement continuity is imposed in a nonconforming fashion. Although their functions are only implicitly defined, as typical of the VEM framework, they contain discontinuous subspaces made of functions known in closed form and with good approximation properties (plane waves, in our case). We carry out an abstract error analysis of the method, and derive $h$-version error estimates. Moreover, we initiate its numerical investigation by presenting a first test, which demonstrates the theoretical convergence rates.
The VIolation of Pauli exclusion principle -2 experiment, or VIP-2 experiment, at the Laboratori Nazionali del Gran Sasso searches for x-rays from copper atomic transition that are prohibited by the Pauli Exclusion Principle. Candidate direct violation events come from the transition of a $2p$ electron to the ground state that is already occupied by two electrons. From the first data taking campaign in 2016 of VIP-2 experiment, we determined a best upper limit of 3.4 $\times$ 10$^{-29}$ for the probability that such a violation exists. Significant improvement in the control of the experimental systematics was also achieved, although not explicitly reflected in the improved upper limit. By introducing a simultaneous spectral fit of the signal and background data in the analysis, we succeeded in taking into account systematic errors that could not be evaluated previously in this type of measurements.
In the VIP2 (VIolation of the Pauli Exlusion Principle) experiment at the Gran Sasso underground laboratory (LNGS) we are searching for possible violations of standard quantum mechanics predictions. With high precision we investigate the Pauli Exclusion Principle and the collapse of the wave function (collapse models). We will present our experimental method of searching for possible small violations of the Pauli Exclusion Principle for electrons, via the search for "anomalous" X-ray transitions in copper atoms, produced by "new" electrons (brought inside a copper bar by circulating current) which could have the probability to undergo Pauli-forbidden transition to the ground state (1 s level) already occupied by two electrons. We will describe the concept of the VIP2 experiment taking data at LNGS presently. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10$^{-31}$. We will show preliminary experimental results obtained at LNGS and discuss implications of a possible violation.
In this paper, new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models. This study allows the obtainment of the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate $λ$ and the correlation length $r_C$ are mapped, thus allowing the exclusion of a broad range of the parameter space.
By performing X-rays measurements in the "cosmic silence" of the underground laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum mechanics: the Pauli Exclusion Principle (PEP), for electrons. We present the achieved results of the VIP experiment and the ongoing VIP2 measurement aiming to gain two orders of magnitude improvement in testing PEP. We also use a similar experimental technique to search for radiation (X and gamma) predicted by continuous spontaneous localization models, which aim to solve the "measurement problem".
We are experimentally investigating possible violations of standard quantum mechanics predictions in the Gran Sasso underground laboratory in Italy. We test with high precision the Pauli Exclusion Principle and the collapse of the wave function (collapse models). We present our method of searching for possible small violations of the Pauli Exclusion Principle (PEP) for electrons, through the search for anomalous X-ray transitions in copper atoms. These transitions are produced by new electrons (brought inside the copper bar by circulating current) which can have the possibility to undergo Pauli-forbidden transition to the 1s level already occupied by two electrons. We describe the VIP2 (VIolation of the Pauli Exclusion Principle) experimental data taking at the Gran Sasso underground laboratories. The goal of VIP2 is to test the PEP for electrons in agreement with the Messiah-Greenberg superselection rule with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10E-31. We show preliminary experimental results and discuss implications of a possible violation.
The Pauli Exclusion Principle (PEP) was famously discovered in 1925 by the austrian physicist Wolfgang Pauli. Since then, it underwent several experimental tests. Starting in 2006, the VIP (Violation of the Pauli Principle) experiment looked for 2p to 1s X-ray transitions in copper, where 2 electrons are present in the 1s state before the transition happens. These transitions violate the PEP, and the lack of detection of the corresponding X-ray photons lead to a preliminary upper limit for the violation of the PEP of 4.7 * 10^(-29). The follow-up experiment VIP 2 is currently in the testing phase and will be transported to its final destination, the underground laboratory of Gran Sasso in Italy, in autumn 2015. Several improvements compared to its predecessor like the use of new X-ray detectors and active shielding from background gives rise to a goal for the improvement of the upper limit of the probability for the violation of the Pauli Exclusion Principle of 2 orders of magnitude.
The Pauli Exclusion Principle (PEP) was introduced by the austrian physicist Wolfgang Pauli in 1925. Since then, several experiments have checked its validity. From 2006 until 2010, the VIP (VIolation of the Pauli Principle) experiment took data at the LNGS underground laboratory to test the PEP. This experiment looked for electronic 2p to 1s transitions in copper, where 2 electrons are in the 1s state before the transition happens. These transitions violate the PEP. The lack of detection of X-ray photons coming from these transitions resulted in a preliminary upper limit for the violation of the PEP of $4.7 \times 10^{-29}$. Currently, the successor experiment VIP2 is under preparation. The main improvements are, on one side, the use of Silicon Drift Detectors (SDDs) as X-ray photon detectors. On the other side an active shielding is implemented, which consists of plastic scintillator bars read by Silicon Photomultipliers (SiPMs). The employment of these detectors will improve the upper limit for the violation of the PEP by around 2 orders of magnitude.
We present the idea of searching for X-rays as a signature of the mechanism inducing the spontaneous collapse of the wave function. Such a signal is predicted by the continuous spontaneous localization theories, which are solving the "measurement problem" by modifying the Schrodinger equation. We will show some encouraging preliminary results and discuss future plans and strategy.
Many experiments investigated the violation of the Pauli Exclusion Principle (PEP) since its discovery in 1925. The VIP (VIolation of the Pauli Principle) experiment tested the PEP by measuring the probability for an external electron to be captured and undergo a 2p to 1s transition during its cascading process, where the 1s state is already occupied by two electrons. This transition is forbidden by the Pauli Exclusion Principle. The VIP experiment resulted in a preliminary upper limit for the probability of the violation of the PEP of 4.7 x 10^{-29}. Currently a setup for the follow-up experiment VIP 2 is under preparation. The goal of this experiment is to improve the upper limit for the violation of the PEP by two orders of magnitude, by different improvements like enhanced energy resolution of the X-ray detectors and by implementing an active shielding. Here we report currently ongoing performance tests of the new parts of the setup.
The Pauli Exclusion Principle is one of the most fundamental rules of nature and represents a pillar of modern physics. According to many observations the Pauli Exclusion Principle must be extremely well fulfilled. Nevertheless, numerous experimental investigations were performed to search for a small violation of this principle. The VIP experiment at the Gran Sasso underground laboratory searched for Pauli-forbidden X-ray transitions in copper atoms using the Ramberg-Snow method and obtained the best limit so far. The follow-up experiment VIP2 is designed to reach even higher sensitivity. It aims to improve the limit by VIP by orders of magnitude. The experimental method, comparison of different PEP tests based on different assumptions and the developments for VIP2 are presented.