1,142 research outputs found
Unsharp Degrees of Freedom and the Generating of Symmetries
In quantum theory, real degrees of freedom are usually described by operators
which are self-adjoint. There are, however, exceptions to the rule. This is
because, in infinite dimensional Hilbert spaces, an operator is not necessarily
self-adjoint even if its expectation values are real. Instead, the operator may
be merely symmetric. Such operators are not diagonalizable - and as a
consequence they describe real degrees of freedom which display a form of
"unsharpness" or "fuzzyness". For example, there are indications that this type
of operators could arise with the description of space-time at the string or at
the Planck scale, where some form of unsharpness or fuzzyness has long been
conjectured.
A priori, however, a potential problem with merely symmetric operators is the
fact that, unlike self-adjoint operators, they do not generate unitaries - at
least not straightforwardly. Here, we show for a large class of these operators
that they do generate unitaries in a well defined way, and that these operators
even generate the entire unitary group of the Hilbert space. This shows that
merely symmetric operators, in addition to describing unsharp physical
entities, may indeed also play a r{\^o}le in the generation of symmetries, e.g.
within a fundamental theory of quantum gravity.Comment: 23 pages, LaTe
On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions
The Dirac equation has been studied in which the Dirac matrices
\hat{\boldmath\alpha}, \hat\beta have space factors, respectively and
, dependent on the particle's space coordinates. The function deforms
Heisenberg algebra for the coordinates and momenta operators, the function
being treated as a dependence of the particle mass on its position. The
properties of these functions in the transition to the Schr\"odinger equation
are discussed. The exact solution of the Dirac equation for the particle motion
in the Coulomnb field with a linear dependence of the function on the
distance to the force centre and the inverse dependence on for the
function has been found.Comment: 13 page
First Calorimetric Measurement of OI-line in the Electron Capture Spectrum of Ho
The isotope Ho undergoes an electron capture process with a
recommended value for the energy available to the decay, , of about
2.5 keV. According to the present knowledge, this is the lowest
value for electron capture processes. Because of that, Ho is the best
candidate to perform experiments to investigate the value of the electron
neutrino mass based on the analysis of the calorimetrically measured spectrum.
We present for the first time the calorimetric measurement of the atomic
de-excitation of the Dy daughter atom upon the capture of an electron
from the 5s shell in Ho, OI-line. The measured peak energy is 48 eV.
This measurement was performed using low temperature metallic magnetic
calorimeters with the Ho ion implanted in the absorber.
We demonstrate that the calorimetric spectrum of Ho can be measured
with high precision and that the parameters describing the spectrum can be
learned from the analysis of the data. Finally, we discuss the implications of
this result for the Electron Capture Ho experiment, ECHo, aiming to
reach sub-eV sensitivity on the electron neutrino mass by a high precision and
high statistics calorimetric measurement of the Ho spectrum.Comment: 5 pages, 3 figure
Coherent States for the Non-Linear Harmonic Oscillator
Wave packets for the Quantum Non-Linear Oscillator are considered in the
Generalized Coherent State framerwork. To first order in the non-linearity
parameter the Coherent State behaves very similarly to its classical
counterpart. The position expectation value oscillates in a simple harmonic
manner. The energy-momentum uncertainty relation is time independent as in a
harmonic oscillator. Various features, (such as the Squeezed State nature), of
the Coherent State have been discussed
Asymptotically maximal families of hypersurfaces in toric varieties
A real algebraic variety is maximal (with respect to the Smith-Thom
inequality) if the sum of the Betti numbers (with coefficients)
of the real part of the variety is equal to the sum of Betti numbers of its
complex part. We prove that there exist polytopes that are not Newton polytopes
of any maximal hypersurface in the corresponding toric variety. On the other
hand we show that for any polytope there are families of hypersurfaces
with the Newton polytopes that are
asymptotically maximal when tends to infinity. We also show that
these results generalize to complete intersections.Comment: 18 pages, 1 figur
Casimir Effect in the Presence of Minimal Lengths
It is expected that the implementation of minimal length in quantum models
leads to a consequent lowering of Planck's scale. In this paper, using the
quantum model with minimal length of Kempf et al \cite{kempf0}, we examine the
effect of the minimal length on the Casimir force between parallel plates.Comment: 10 pages, 2 figure
WKB approximation in deformed space with minimal length
The WKB approximation for deformed space with minimal length is considered.
The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in
presence of deformation is that the WKB approximation is valid for intermediate
quantum numbers and can be invalid for small as well as very large quantum
numbers. The correctness of the rule is verified by comparing obtained results
with exact expressions for corresponding spectra.Comment: 13 pages Now it is avaible at http://stacks.iop.org/0305-4470/39/37
Cryogenic micro-calorimeters for mass spectrometric identification of neutral molecules and molecular fragments
We have systematically investigated the energy resolution of a magnetic
micro-calorimeter (MMC) for atomic and molecular projectiles at impact energies
ranging from to 150 keV. For atoms we obtained absolute energy
resolutions down to eV and relative energy resolutions
down to . We also studied in detail the MMC
energy-response function to molecular projectiles of up to mass 56 u. We have
demonstrated the capability of identifying neutral fragmentation products of
these molecules by calorimetric mass spectrometry. We have modeled the MMC
energy-response function for molecular projectiles and conclude that
backscattering is the dominant source of the energy spread at the impact
energies investigated. We have successfully demonstrated the use of a detector
absorber coating to suppress such spreads. We briefly outline the use of MMC
detectors in experiments on gas-phase collision reactions with neutral
products. Our findings are of general interest for mass spectrometric
techniques, particularly for those desiring to make neutral-particle mass
measurements
Online Demodulation and Trigger for Flux-ramp Modulated SQUID Signals
Due to the periodic characteristics of SQUIDs, a suitable linearization technique is required for SQUID-based readout. Flux-ramp modulation is a common linearization technique and is typically applied for the readout of a microwave SQUID multiplexer as well as since recently also for dc-SQUIDs. Flux-ramp modulation requires another stage in the signal processing chain to demodulate the SQUID output signal before further processing. For cryogenic microcalorimeters, the signal contains events that are given by a fast exponentially rising and slowly exponentially decaying pulses shape. The events shall be detected by a trigger engine and recorded by a storage logic. Since the data rate can be decreased significantly by demodulation and event detection, it is desirable to do both steps on the deployed fast FPGA logic during measurement before passing the data to a general-purpose processor. In this contribution, we show the implementation of efficient multi-channel flux-ramp demodulation computed at run-time on a SoC-FPGA. Furthermore, a concept and implementation for an online trigger and buffer mechanism with its theoretical trigger loss rates depending on buffer size is presented. Both FPGA modules can be operated with up to 500 MHz clock frequency and can efficiently process 32 channels. Correct functionality and data reduction capability of the modules are demonstrated in measurements utilizing magnetic microcalorimeter irradiated with an Iron-55 source for event generation and read out by a microwave SQUID multiplexer
SDR-Based Readout Electronics for the ECHo Experiment
Due to their excellent energy resolution, the intrinsically fast signal rise time, the huge energy dynamic range, and the almost ideally linear detector response, metallic magnetic calorimeters (MMC)s are very well suited for a variety of applications in physics. In particular, the ECHo experiment aims to utilize large-scale MMC-based detector arrays to investigate the mass of the electron neutrino. Reading out such arrays is a challenging task which can be tackled using microwave SQUID multiplexing. Here, the detector signals are transduced into frequency shifts of superconducting microwave resonators, which can be deduced using a high-end software-defined radio (SDR) system. The ECHo SDR system is a custom-made modular electronics, which provides 400 channels equally distributed in a 4 to 8 GHz frequency band. The system consists of a superheterodyne RF frequency converter with two successive mixers, a modular conversion, and an FPGA board. For channelization, a novel heterogeneous approach, utilizing the integrated digital down conversion (DDC) of the ADC, a polyphase channelizer, and another DDC for demodulation, is proposed. This approach has excellent channelization properties while being resource-efficient at the same time. After signal demodulation, on-FPGA flux-ramp demodulation processes the signals before streaming it to the data processing and storage backend
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