Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum

In single Hilbert space, Pauli's well-known theorem implies that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian signifies that the time operator and the Hamiltonian possess completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate to a semibounded or discrete Hamiltonian despite some well-known illustrative counterexamples. In this paper we evaluate Pauli's theorem against the single Hilbert space formulation of quantum mechanics, and consequently show the consistency of assuming a bounded, self-adjoint time operator canonically conjugate to a Hamiltonian with an unbounded, or semibounded, or finite point spectrum. We point out Pauli's implicit assumptions and show that they are not consistent in a single Hilbert space. We demonstrate our analysis by giving two explicit examples. Moreover, we clarify issues sorrounding the different solutions to the canonical commutation relations, and, consequently, expand the class of acceptable canonical pairs beyond the solutions required by Pauli's theorem.Comment: contains corrections to minor typographical errors of the published versio

Coronal bright point statistics I. Lifetime, shape, and coronal co-rotation

Context. The corona of the Sun is the part of the solar atmosphere with temperatures of over one million Kelvin, which needs to be heated internally in order to exist. This heating mechanism remains a mystery; we see large magnetically active regions in the photosphere lead to strong extreme UV (EUV) emission in the corona. On much smaller scales (on the order of tens of Mm), there are bipolar and multipolar regions that can be associated with evenly sized coronal bright points (CBPs). Aims. Our aim was to study the properties of CBPs in a statistical sense and to use continuous data from the SDO spacecraft, which makes it possible to track CBPs over their whole lifetime. Furthermore, we tested various rotation-speed profiles for CBPs in order to find out if the lower corona is co-rotating with the photosphere. Then we compiled a database with about 346 CBPs together with information of their sizes, shapes, appearance and disappearance, and their visibility in the EUV channels of the AIA instrument. We want to verify our methods with similar previous studies. Methods. We used the high-cadence data of the largest continuous SDO observation interval in 2015 to employ an automated tracking algorithm for CBPs. Some of the information (e.g., the total lifetime, the characteristic shape, and the magnetic polarities below the CBPs) still requires human interaction. Results. In this work we present statistics on fundamental properties of CBPs along with some comparison tables that relate, for example, the CBP lifetime with their shape. CBPs that are visible in all AIA channels simultaneously seem to be brighter in total and also have a stronger heating, and hence a higher total radiation flux. We compared the EUV emission visibility in different AIA channels with the CBP's shape and lifetime. ... (full version see pdf)Comment: 8 pages, 11 figures, 3 table, publishe

Resolving the dusty circumstellar environment of the A[e] supergiant HD 62623 with the VLTI/MIDI

B[e] stars are hot stars surrounded by circumstellar gas and dust responsible for the presence of emission lines and IR-excess in their spectra. How dust can be formed in this highly illuminated and diluted environment remains an open issue. HD 62623 is one of the very few A-type supergiants showing the B[e] phenomenon. We obtained nine calibrated visibility measurements using the VLTI/MIDI instrument in SCI-PHOT mode and PRISM spectral dispersion mode with projected baselines ranging from 13 to 71 m and with various position angles. We used geometrical models and physical modeling with a radiative transfer code to analyze these data. The dusty circumstellar environment of HD 62623 is partially resolved by the VLTI/MIDI even with the shortest baselines. The environment is flattened and can be separated into two components: a compact one whose extension grows from 17 mas at 8 microns to 30 mas at 9.6 microns and stays almost constant up to 13 microns, and a more extended one that is over-resolved even with the shortest baselines. Using the radiative transfer code MC3D, we managed to model HD 62623's circumstellar environment as a dusty disk with an inner radius of 3.85+-0.6 AU, an inclination angle of 60+-10 deg, and a mass of 2x10^-7Mo. It is the first time that the dusty disk inner rim of a supergiant star exhibiting the B[e] phenomenon is significantly constrained. The inner gaseous envelope likely contributes up to 20% to the total N band flux and acts like a reprocessing disk. Finally, the hypothesis of a stellar wind deceleration by the companion's gravitational effects remains the most probable case since the bi-stability mechanism does not seem to be efficient for this star.Comment: 13 pages, 11 figures. A&A accepted pape

Tachyon kinks on non BPS D-branes

We consider solitonic solutions of the DBI tachyon effective action for a non-BPS brane. When wrapped on a circle, these solutions are regular and have a finite energy. We show that in the decompactified limit, these solitons give Sen's infinitely thin finite energy kink -- interpreted as a BPS brane -- provided that some conditions on the potential hold. In particular, if for large $T$ the potential is exponential, $V = e^{-T^a}$, then Sen's solution is only found for $a<1$. For power-law potentials $V = 1/T^b$, one must have $b>1$. If these conditions are not satisfied, we show that the lowest energy configuration is the unstable tachyon vacuum with no kinks. We examine the stability of the solitons and the spectrum of small perturbations.Comment: 16 pages, 2 figure

First AMBER/VLTI observations of hot massive stars

AMBER is the first near infrared focal instrument of the VLTI. It combines three telescopes and produces spectrally resolved interferometric measures. This paper discusses some preliminary results of the first scientific observations of AMBER with three Unit Telescopes at medium (1500) and high (12000) spectral resolution. We derive a first set of constraints on the structure of the circumstellar material around the Wolf Rayet Gamma2 Velorum and the LBV Eta Carinae

Quantum Iterated Function Systems

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include

Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World

In this Letter we show that the vacuum polarization of quantum fields in an anti-de Sitter space naturally gives rise to a small but nonzero cosmological constant in a brane world living in it. To explain the extremely small ratio of mass density in the cosmological constant to the Planck mass density in our universe (\approx 10^{-123}) as suggested by cosmological observations, all we need is a four-dimensional brane world (our universe) living in a five-dimensional anti-de Sitter space with a curvature radius r_0 \sim 10^{-3}cm and a fundamental Planck energy M_P \sim 10^9 GeV, and a scalar field with a mass m \sim r_0^{-1}\sim 10^{-2}eV. Probing gravity down to a scale \sim 10^{-3}cm, which is attainable in the near future, will provide a test of the model.Comment: 10 pages, including 1 figur

Classical interventions in quantum systems. I. The measuring process

The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. This description of the measuring process is a substantial generalization of current models in quantum measurement theory. In particular, no ancilla is needed. The final result is represented by a completely positive map of the quantum state $\rho$ (possibly with a change of the dimensions of $\rho$). A continuous limit of the above process leads to Lindblad's equation for the quantum dynamical semigroup.Comment: Final version, 14 pages LaTe

Cosmology and Brane Worlds: A Review

Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hyper--surface (a so--called brane), which is embedded in a higher--dimensional spacetime (the so--called bulk). We begin our review with the simplest consistent brane world model: a single brane embedded in a five--dimensional Anti-de Sitter space--time. Then we include a scalar field in the bulk and discuss in detail the difference with the Anti-de Sitter case. The geometry of the bulk space--time is also analysed in some depth. Finally, we investigate the cosmology of a system with two branes and a bulk scalar field. We comment on brane collisions and summarize some open problems of brane world cosmology.Comment: 37 pages; invited topical review for Classical and Quantum Gravity; to appea

Imaging the spinning gas and dust in the disc around the supergiant A[e] star HD62623

Context. To progress in the understanding of evolution of massive stars one needs to constrain the mass-loss and determine the phenomenon responsible for the ejection of matter an its reorganization in the circumstellar environment Aims. In order to test various mass-ejection processes, we probed the geometry and kinematics of the dust and gas surrounding the A[e] supergiant HD 62623. Methods. We used the combined high spectral and spatial resolution covered by the VLTI/AMBER instrument. Thanks to a new multiwavelength optical/IR interferometry imaging technique, we reconstructed the first velocity-resolved images with a milliarcsecond resolution in the infrared domain. Results. We managed to disentangle the dust and gas emission in the HD 62623 circumstellar disc.We measured the dusty disc inner inner rim, i.e. 6 mas, constrained the inclination angle and the position angle of the major-axis of the disc.We also measured the inner gaseous disc extension (2 mas) and probed its velocity field thanks to AMBER high spectral resolution. We find that the expansion velocity is negligible, and that Keplerian rotation is a favoured velocity field. Such a velocity field is unexpected if fast rotation of the central star alone is the main mechanism of matter ejection. Conclusions. As the star itself seems to rotate below its breakup-up velocity, rotation cannot explain the formation of the dense equatorial disc. Moreover, as the expansion velocity is negligible, radiatively driven wind is also not a suitable explanation to explain the disc formation. Consequently, the most probable hypothesis is that the accumulation of matter in the equatorial plane is due to the presence of the spectroscopic low mass companion.Comment: To be published soon in A\&