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1. Non-Hermitian skin effect as an impurity problem

Author

F. Roccati

Subjects
Physics, Quantum Physics, Spectrum (functional analysis), Lattice (group), FOS: Physical sciences, Mathematical Physics (math-ph), Hermitian matrix, Periodic boundary conditions, Skin effect, Point (geometry), Boundary value problem, Quantum Physics (quant-ph), Mathematical Physics, Eigenvalues and eigenvectors, Mathematical physics
Abstract

A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-Hermitian SSH models and finally we contrast the edge states localization with that of bulk states., Comment: 8 pages, 4 figures

Published
2021
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2. Quantum correlations in PT -symmetric systems

Author

Francesco Ciccarello, Gabriel T. Landi, F. Roccati, G. Massimo Palma, Matteo Brunelli, Salvatore Lorenzo, Roccati F., Lorenzo S., Palma G.M., Landi G.T., Brunelli M., and Ciccarello F.

Subjects
Physics, ENTROPIA, Quantum discord, Physics and Astronomy (miscellaneous), Materials Science (miscellaneous), quantum correlations, quantum discord, Non-Hermitian Hamiltonians, 01 natural sciences, Quantum Optics, Atomic and Molecular Physics, and Optics, 010305 fluids & plasmas, non-Hermitian, PT symmetry, Symmetric systems, Quantum mechanics, 0103 physical sciences, Electrical and Electronic Engineering, 010306 general physics, Quantum
Abstract

We study the dynamics of correlations in a paradigmatic setup to observe PT -symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. Both total and QCs exhibit different scalings of their long-time behavior in the PT -broken/unbroken phase and at the exceptional point (EP). In particular, PT symmetry breaking is accompanied by non-zero stationary QCs. This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration, as classical correlations diverge while QCs vanish.

Published
2021
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3. A no-go result for the quantum damped harmonic oscillator

Author

F. Roccati, Fabio Bagarello, Francesco Gargano, Bagarello F., Gargano F., and Roccati F.

Subjects
Pseudo-boson, Physics, Quantum Physics, Canonical quantization, FOS: Physical sciences, General Physics and Astronomy, 01 natural sciences, 010305 fluids & plasmas, Set (abstract data type), Quantum damped harmonic oscillator, symbols.namesake, Classical mechanics, Ladder operator, Square-integrable function, Go/no go, 0103 physical sciences, symbols, Quantum Physics (quant-ph), 010306 general physics, Settore MAT/07 - Fisica Matematica, Quantum, Lagrangian, Harmonic oscillator
Abstract

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

Published
2019
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4. High-resolution spectroscopy of gaseous $^\mathrm{83m}$Kr conversion electrons with the KATRIN experiment

Author

A. Off, N. Haußmann, Ralph Engel, M. Schrank, A. Huber, N. Titov, S. Bobien, L. Schimpf, M. Suesser, V. Sibille, Andreas Kopmann, E. L. Martin, Reiner Vianden, Helmut H. Telle, T. Bergmann, S. Dyba, M. Korzeczek, F. Roccati, M. A. Howe, W. Q. Choi, Susanne Mertens, M. Fedkevych, M. Ryšavý, D. Eversheim, Stefan Welte, Suren Chilingaryan, K. Schlösser, F. Edzards, B. Krasch, N. Trost, S. Zadoroghny, M. Hackenjos, Marcus Beck, O. Rest, K. Schönung, A. Pollithy, M. Suchopar, Thierry Lasserre, P. C-O Ranitzsch, F. M. Fränkle, A. I. Berlev, W.-J. Baek, J. Sentkerestiová, S. Hickford, R. Grössle, K. Helbing, Matthias Arenz, F. Heizmann, Lutz Bornschein, Magnus Schlösser, Klaus Blaum, M. Deffert, Guido Drexlin, Alexey Lokhov, Sanshiro Enomoto, C. Rodenbeck, M. Klein, N. Buzinsky, D. Hilk, Ondřej Lebeda, Sebastian Mirz, J. F. Wilkerson, Diana Parno, M. Steidl, Florian Priester, J. Letnev, Igor Tkachev, E. Ellinger, L. Kippenbrock, A. Kovalík, Kathrin Valerius, J. Wendel, Marc Weber, M. Kraus, Joachim Wolf, R. Gumbsheimer, G. B. Franklin, Steffen Grohmann, K. Eitel, W. Gil, R. G. H. Robertson, Joseph A. Formaggio, H. Seitz-Moskaliuk, Michael Sturm, T. Brunst, D. Hinz, T. Bode, D. Vénos, M. Slezák, Thomas Thümmler, Alejandro Saenz, Marco Röllig, C. Röttele, Beate Bornschein, Sascha Wüstling, A. González Ureña, U. Besserer, J. Kellerer, F. Block, P. Plischke, A. Beglarian, A. Fulst, A. W. P. Poon, A. Osipowicz, Benjamin Monreal, Holger Neumann, Ernst W. Otten, O. Dragoun, J. Behrens, K. Altenmüller, R. Sack, Ch. Weinheimer, N. Kernert, N. Steinbrink, S. Niemes, G. P. Zeller, A. Marsteller, F. Friedel, L. A. Thorne, M. Machatschek, F. Harms, A. P. Vizcaya Hernández, Volker Hannen, P. J. Doe, A. Jansen, Ferenc Glück, D. Hillesheimer, Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay

Subjects
Nuclear and High Energy Physics, Speichertechnik - Abteilung Blaum, Physics - Instrumentation and Detectors, Resolution (mass spectrometry), Physics::Instrumentation and Detectors, energy resolution, FOS: Physical sciences, Electron, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], KATRIN, 7. Clean energy, 01 natural sciences, Atomic, neutrino mass, Nuclear physics, Particle and Plasma Physics, conversion electrons, Metastability, 0103 physical sciences, Nuclear, ddc:530, [PHYS.PHYS.PHYS-INS-DET]Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], Nuclear Experiment (nucl-ex), 010306 general physics, Spectroscopy, Nuclear Experiment, Physics, Spectrometer, electrostatic spectrometer, 010308 nuclear & particles physics, krypton: decay, Molecular, Instrumentation and Detectors (physics.ins-det), krypton: nuclide, 530 Physik, calibration, Nuclear & Particles Physics, ddc, 3. Good health, Beamline, electron: energy spectrum, Neutrino, performance
Abstract

In this work, we present the first spectroscopic measurements of conversion electrons originating from the decay of metastable gaseous $^\mathrm{83m}$Kr with the Karlsruhe Tritium Neutrino (KATRIN) experiment. The results obtained in this calibration measurement represent a major commissioning milestone for the upcoming direct neutrino mass measurement with KATRIN. The successful campaign demonstrates the functionalities of the full KATRIN beamline. The KATRIN main spectrometer's excellent energy resolution of ~ 1 eV made it possible to determine the narrow K-32 and L$_3$-32 conversion electron line widths with an unprecedented precision of ~ 1 %., Fixed affiliation of the corresponding author

Published
2019
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5. Modeling epidemics through ladder operators

Author

F. Roccati, Fabio Bagarello, Francesco Gargano, Bagarello F., Gargano F., and Roccati F.

Subjects
operatorial model, Coronavirus disease 2019 (COVID-19), Computer science, Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), General Mathematics, General Physics and Astronomy, 01 natural sciences, Measure (mathematics), Quantitative Biology::Other, Article, 010305 fluids & plasmas, Operator (computer programming), Simple (abstract algebra), 0103 physical sciences, Applied mathematics, Quantitative Biology::Populations and Evolution, Limit (mathematics), Quantitative Biology - Populations and Evolution, 010301 acoustics, Settore MAT/07 - Fisica Matematica, Applied Mathematics, Populations and Evolution (q-bio.PE), Statistical and Nonlinear Physics, Computer Science::Social and Information Networks, Transformation (function), Ladder operator, spreading of news, FOS: Biological sciences, ( H, ρ ) -induced dynamic
Abstract

Highlights • We propose an operatorial model to describe epidemics. • The model describes well the asymptotic numbers of the epidemics. • Ladder operators are used to model exchanges between the “actors” of the system., We propose a simple model of spreading of some infection in an originally healthy population which is different from other models existing in the literature. In particular, we use an operator technique which allows us to describe in a natural way the possible interactions between healthy and un-healthy populations, and their transformation into recovered and to dead people. After a rather general discussion, we apply our method to the analysis of Chinese data for the SARS-2003 (Severe acute respiratory syndrome; SARS-CoV-1) and the Coronavirus COVID-19 (Corona Virus Disease; SARS-CoV-2) and we show that the model works very well in reproducing the long-time behaviour of the disease, and in particular in finding the number of affected and dead people in the limit of large time. Moreover, we show how the model can be easily modified to consider some lockdown measure, and we deduce that this procedure drastically reduces the asymptotic value of infected individuals, as expected, and observed in real life.

Published
2020

6. Some remarks on few recent results on the damped quantum harmonic oscillator

Author

F. Roccati, Francesco Gargano, Fabio Bagarello, Bagarello F., Gargano F., and Roccati F.

Subjects
Physics, Annihilation, 010308 nuclear & particles physics, General Physics and Astronomy, Damped quantum harmonic oscillator, 01 natural sciences, Ladder operator, Square-integrable function, Simple (abstract algebra), Quantum harmonic oscillator, 0103 physical sciences, 010306 general physics, Settore MAT/07 - Fisica Matematica, Mathematical physics
Abstract

In a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example clarifying the core of the problem.

Published
2020
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7. First transmission of electrons and ions through the KATRIN beamline

Author

A. Pollithy, M. Steidl, Ch. Weinheimer, Alejandro Saenz, Beate Bornschein, Sascha Wüstling, K. Schlösser, Volker Hannen, Stefan Welte, D. Hilk, Suren Chilingaryan, N. Kernert, S. Hickford, A. I. Berlev, W.-J. Baek, Ralph Engel, Marcus Beck, M. Kleesiek, A. Off, O. Rest, C. Rodenbeck, A. Beglarian, T. Bode, M. Suchopar, W. Herz, Kathrin Valerius, Magnus Schlösser, Florian Priester, Ernst W. Otten, R. Sack, Diana Parno, L. Kippenbrock, Helmut H. Telle, Matthias Arenz, Marc Weber, A. W. P. Poon, Joseph A. Formaggio, J. Wendel, W. Q. Choi, T. Brunst, N. Steinbrink, Ondřej Lebeda, S. Zadoroghny, J. Sentkerestiová, Steffen Grohmann, M. Erhard, L. Kuckert, C. Weiss, S. Niemes, P. J. Doe, S. Fischer, D. Vénos, A. Marsteller, J. Letnev, E. Ellinger, B. Krasch, M. Kraus, Thierry Lasserre, Andreas Kopmann, F. Friedel, M. Machatschek, F. Harms, Sanshiro Enomoto, A. Kovalík, L. Bornschein, A. Jansen, K. Eitel, R. G. H. Robertson, Ferenc Glück, T. Thümmler, D. Hillesheimer, Guido Drexlin, M. Fedkevych, N. Trost, U. Besserer, A. P. Vizcaya Hernández, W. Gil, M. Suesser, M. Slezák, K. Helbing, F. Edzards, A. González Ureña, L. A. Thorne, N. Titov, D. Eversheim, R. Grössle, H.-W. Ortjohann, V. Sibille, H. Seitz-Moskaliuk, J. F. Wilkerson, Marco Röllig, C. Röttele, K. Schönung, Holger Neumann, R. Gumbsheimer, G. B. Franklin, M. A. Howe, M. Schrank, J. Behrens, L. Schimpf, N. Buzinsky, T. Bergmann, Klaus Blaum, M. Deffert, M. Klein, F. Roccati, M. Ryšavý, M. Hackenjos, F. Heizmann, Sebastian Mirz, A. Osipowicz, E. L. Martin, Reiner Vianden, P. C.-O. Ranitzsch, Benjamin Monreal, F. M. Fränkle, M. Korzeczek, O. Dragoun, Susanne Mertens, N. Haußmann, A. Huber, Igor Tkachev, J. Kellerer, A. Fulst, U. Naumann, Michael Sturm, Joachim Wolf, S. Dyba, Alexey Lokhov, Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, KATRIN, Institut de Recherches sur les lois Fondamentales de l'Univers ( IRFU ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay, Massachusetts Institute of Technology. Department of Physics, Massachusetts Institute of Technology. Laboratory for Nuclear Science, Buzinsky, Nicholas Gregory, and Formaggio, Joseph A

Subjects
Physics - Instrumentation and Detectors, Ion beam, FOS: Physical sciences, beam transport, ion: beam, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], KATRIN, 7. Clean energy, 01 natural sciences, Ion, Nuclear physics, 0103 physical sciences, [PHYS.PHYS.PHYS-INS-DET]Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], Nuclear Experiment (nucl-ex), [ PHYS.NEXP ] Physics [physics]/Nuclear Experiment [nucl-ex], electron: beam, 010306 general physics, Instrumentation, [ PHYS.PHYS.PHYS-INS-DET ] Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], Nuclear Experiment, Mathematical Physics, activity report, Physics, 010308 nuclear & particles physics, photoelectron: emission, Instrumentation and Detectors (physics.ins-det), Photoelectric effect, stability, sensitivity, Ion source, ddc, Beamline, Cathode ray, Neutrino, performance
Abstract

The Karlsruhe Tritium Neutrino (KATRIN) experiment is a large-scale effort to probe the absolute neutrino mass scale with a sensitivity of 0.2 eV (90% confidence level), via a precise measurement of the endpoint spectrum of tritium β-decay. This work documents several KATRIN commissioning milestones: the complete assembly of the experimental beamline, the successful transmission of electrons from three sources through the beamline to the primary detector, and tests of ion transport and retention. In the First Light commissioning campaign of autumn 2016, photoelectrons were generated at the rear wall and ions were created by a dedicated ion source attached to the rear section; in July 2017, gaseous83mKr was injected into the KATRIN source section, and a condensed83mKr source was deployed in the transport section. In this paper we describe the technical details of the apparatus and the configuration for each measurement, and give first results on source and system performance. We have successfully achieved transmission from all four sources, established system stability, and characterized many aspects of the apparatus., United States. Department of Energy (Grant DEFG02-97ER41020), United States. Department of Energy (Grant DE-FG02-94ER40818), United States. Department of Energy (Grant DE-SC0004036), United States. Department of Energy (Grant DE-FG02-97ER41033), United States. Department of Energy (Grant DE-FG02- 97ER41041), United States. Department of Energy (Grant DE-AC02-05CH11231), United States. Department of Energy (Grant DE-SC0011091)

Published
2018
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8. Reduction of stored-particle background by a magnetic pulse method at the KATRIN experiment

Author

A. Kovalík, R. G. H. Robertson, R. Grössle, K. Helbing, S. Hickford, F. Edzards, Stefan Welte, M. Steidl, Suren Chilingaryan, Alejandro Saenz, V. Sibille, Andreas Kopmann, A. P. Vizcaya Hernández, D. Furse, D. Vénos, D. Hilk, K. Schlösser, Benjamin Monreal, L. Kuckert, N. Titov, U. Besserer, Kathrin Valerius, O. Dragoun, M. Kleesiek, M. Suchopar, Beate Bornschein, Sascha Wüstling, J. F. Wilkerson, J. Behrens, Ralph Engel, C. Weiss, Klaus Blaum, M. Deffert, K. Eitel, L. Kippenbrock, R. Gumbsheimer, B. Krasch, M. Erhard, J. Sentkerestiová, M. Klein, P. C.-O. Ranitzsch, F. Roccati, Thierry Lasserre, M. Ryšavý, T. Bergmann, G. B. Franklin, A. Beglarian, Holger Neumann, Guido Drexlin, J. Letnev, Helmut H. Telle, A. I. Berlev, E. Ellinger, S. Zadoroghny, W.-J. Baek, Ernst W. Otten, W. Q. Choi, N. Buzinsky, N. Haußmann, Marcus Beck, M. A. Howe, N. Steinbrink, Ondřej Lebeda, K. Schönung, S. Niemes, A. Osipowicz, Florian Priester, F. M. Fränkle, Joachim Wolf, T. Brunst, Marc Weber, M. Slezák, W. Gil, Sanshiro Enomoto, A. Marsteller, F. Friedel, M. Schrank, M. Kraus, M. Machatschek, F. Harms, J. Kellerer, L. Schimpf, S. Bauer, H. Seitz-Moskaliuk, Thomas Thümmler, Volker Hannen, A. Fulst, Marco Röllig, C. Röttele, D. Eversheim, N. Wandkowsky, A. González Ureña, T. Bode, R. Berendes, E. L. Martin, Magnus Schlösser, Reiner Vianden, Diana Parno, J. Wendel, M. Korzeczek, Susanne Mertens, Steffen Grohmann, A. Pollithy, P. J. Doe, Lutz Bornschein, W. Herz, A. Jansen, Ferenc Glück, M. Arenz, W. Buglak, A. Off, M. Hackenjos, R. Sack, Ch. Weinheimer, F. Heizmann, Sebastian Mirz, N. Trost, Alan Poon, M. Fedkevych, N. Kernert, A. Huber, S. Dyba, L. A. Thorne, O. Rest, Alexey Lokhov, Igor Tkachev, Joseph A. Formaggio, Michael Sturm, C. Rodenbeck, Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, KATRIN, Massachusetts Institute of Technology. Department of Physics, Massachusetts Institute of Technology. Laboratory for Nuclear Science, Buzinsky, Nicholas Gregory, Formaggio, Joseph A, Furse, Daniel Lawrence, and Sibille, Valerian

Subjects
Speichertechnik - Abteilung Blaum, Physics - Instrumentation and Detectors, Physics and Astronomy (miscellaneous), Field (physics), Physics::Instrumentation and Detectors, FOS: Physical sciences, lcsh:Astrophysics, Electron, KATRIN, 01 natural sciences, radon: nuclide, Neutrino mass, 0103 physical sciences, lcsh:QB460-466, coil, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, ddc:530, Sensitivity (control systems), [PHYS.PHYS.PHYS-INS-DET]Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], 010306 general physics, numerical calculations, Engineering (miscellaneous), background: radioactivity, background: suppression, Physics, Spectrometer, 010308 nuclear & particles physics, Order (ring theory), Monte Carlo methods, Instrumentation and Detectors (physics.ins-det), Radon background, Pulse (physics), 13. Climate action, Background reduction methods, Partículas, lcsh:QC770-798, spectrometer, Atomic physics, Electricidad, Electron neutrino
Abstract

Arenz, M., et al. “Reduction of Stored-Particle Background by a Magnetic Pulse Method at the KATRIN Experiment.” The European Physical Journal C, vol. 78, no. 9, Sept. 2018. © 2018 The Authors, United States. Department of Energy (DE-FG02-97ER41020), United States. Department of Energy (DE-FG02-94ER40818), United States. Department of Energy (DE-SC0004036), United States. Department of Energy (DE-FG02-97ER41033), United States. Department of Energy (DE-FG02-97ER41041), United States. Department of Energy (DEAC02-05CH11231), United States. Department of Energy (DE-SC0011091)

Published
2018
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9. Calibration of high voltages at the ppm level by the difference of $^{83\mathrm{m}}$Kr conversion electron lines at the KATRIN experiment

Author

P. J. Doe, A. Jansen, Ferenc Glück, D. Hillesheimer, F. M. Fränkle, A. Pollithy, M. Kleesiek, M. Suesser, Magnus Schlösser, M. Suchopar, Matthias Arenz, L. Kuckert, N. Trost, W. Herz, Ondřej Lebeda, K. Eitel, Diana Parno, J. Wendel, Steffen Grohmann, M. Kraus, N. Buzinsky, A. I. Berlev, W.-J. Baek, Joachim Wolf, N. Titov, A. Off, M. Erhard, Christian Weinheimer, L. A. Thorne, M. Fedkevych, A. Osipowicz, D. Eversheim, V. Sibille, Andreas Kopmann, J. Kellerer, T. Bode, F. Roccati, M. Ryšavý, B. Krasch, A. Fulst, Thierry Lasserre, U. Besserer, Marcus Beck, Guido Drexlin, Benjamin Monreal, O. Dragoun, P. C.-O. Ranitzsch, M. A. Howe, M. Schrank, M. Hackenjos, E. L. Martin, N. Haußmann, J. Behrens, Thomas Thümmler, L. Schimpf, Ernst W. Otten, Igor Tkachev, F. Heizmann, Sebastian Mirz, Joseph A. Formaggio, A. González Ureña, Reiner Vianden, D. Hilk, S. Hickford, H. Seitz-Moskaliuk, Kathrin Valerius, M. Korzeczek, M. Steidl, J. F. Wilkerson, J. Sentkerestiová, Michael Sturm, Susanne Mertens, Marco Röllig, C. Röttele, K. Schlösser, A. W. P. Poon, C. Weiss, T. Bergmann, K. Schönung, R. Gumbsheimer, J. Letnev, G. B. Franklin, E. Ellinger, W. Gil, Alejandro Saenz, Klaus Blaum, M. Deffert, S. Zadoroghny, Lutz Bornschein, Beate Bornschein, Sascha Wüstling, A. Huber, A. Beglarian, M. Klein, Florian Priester, Marc Weber, S. Dyba, R. Sack, M. Slezák, Alexey Lokhov, Stefan Welte, Suren Chilingaryan, N. Kernert, Holger Neumann, D. Vénos, Sanshiro Enomoto, Volker Hannen, Helmut H. Telle, W. Q. Choi, Ralph Engel, O. Rest, A. P. Vizcaya Hernández, N. Steinbrink, S. Niemes, A. Marsteller, F. Friedel, M. Machatschek, F. Harms, L. Kippenbrock, C. Rodenbeck, A. Kovalík, T. Brunst, S. Fischer, R. G. H. Robertson, F. Edzards, R. Grössle, K. Helbing, Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Institut de Recherches sur les lois Fondamentales de l'Univers ( IRFU ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay, Massachusetts Institute of Technology. Department of Physics, Buzinsky, Nicholas Gregory, Formaggio, Joseph A, and Sibille, Valerian

Subjects
Speichertechnik - Abteilung Blaum, Physics - Instrumentation and Detectors, Physics and Astronomy (miscellaneous), FOS: Physical sciences, 7. Clean energy, 01 natural sciences, Nuclear physics, 0103 physical sciences, Calibration, ddc:530, [PHYS.PHYS.PHYS-INS-DET]Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], 010306 general physics, Engineering (miscellaneous), [ PHYS.PHYS.PHYS-INS-DET ] Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], Physics, Teoría de los quanta, Spectrometer, 010308 nuclear & particles physics, Voltage divider, Instrumentation and Detectors (physics.ins-det), Metrology, Neutrino, Energy (signal processing), Voltage, KATRIN
Abstract

The neutrino mass experiment KATRIN requires a stability of 3 ppm for the retarding potential at − 18.6 kV of the main spectrometer. To monitor the stability, two custom-made ultra-precise high-voltage dividers were developed and built in cooperation with the German national metrology institute Physikalisch-Technische Bundesanstalt (PTB). Until now, regular absolute calibration of the voltage dividers required bringing the equipment to the specialised metrology laboratory. Here we present a new method based on measuring the energy difference of two [superscript 83m]Kr conversion electron lines with the KATRIN setup, which was demonstrated during KATRIN’s commissioning measurements in July 2017. The measured scale factor M = 1972.449(10) of the high-voltage divider K35 is in agreement with the last PTB calibration 4 years ago. This result demonstrates the utility of the calibration method, as well as the long-term stability of the voltage divider., United States. Department of Energy (Grant DEFG02- 97ER41020), United States. Department of Energy (Grant DE-FG02-94ER40818), United States. Department of Energy (Grant DE-SC0004036), United States. Department of Energy (Grant DEFG02-97ER 41033), United States. Department of Energy (Grant DE-FG02-97ER41041), United States. Department of Energy (Grant DE-AC02-05CH11231), United States. Department of Energy (Grant DE-SC00 11091)

Published
2018
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10. Tridiagonality, supersymmetry and non self-adjoint Hamiltonians

Author

Francesco Gargano, F. Roccati, Fabio Bagarello, Bagarello, F, Gargano, F, and Roccati, F

Subjects
Statistics and Probability, FOS: Physical sciences, General Physics and Astronomy, 01 natural sciences, Factorization, 0103 physical sciences, 010306 general physics, Settore MAT/07 - Fisica Matematica, Mathematical Physics, Eigenvalues and eigenvectors, Mathematics, Quantum Physics, Tridiagonal matrix, 010308 nuclear & particles physics, Recursion (computer science), Statistical and Nonlinear Physics, tridiagonal matrice, Mathematical Physics (math-ph), Supersymmetry, Connection (mathematics), non self-adjoint Hamiltonian, Algebra, biorthogonal bases, Modeling and Simulation, Biorthogonal system, Quantum Physics (quant-ph), Self-adjoint operator
Abstract

In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.

Published
2019
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