Redshifted X-rays from the material accreting onto TW Hya: evidence of a low-latitude accretion spot

High resolution spectroscopy, providing constraints on plasma motions and temperatures, is a powerful means to investigate the structure of accretion streams in CTTS. In particular, the accretion shock region, where the accreting material is heated to temperatures of a few MK as it continues its inward bulk motion, can be probed by X-ray spectroscopy. To attempt to detect for the first time the motion of this X-ray-emitting post-shock material, we searched for a Doppler shift in the deep Chandra/HETGS observation of the CTTS TW Hya. This test should unveil the nature of this X-ray emitting plasma component in CTTS, and constrain the accretion stream geometry. We searched for a Doppler shift in the X-ray emission from TW Hya with two different methods, by measuring the position of a selected sample of emission lines, and by fitting the whole TW Hya X-ray spectrum, allowing the line-of-sight velocity to vary. We found that the plasma at T~2-4 MK has a line-of-sight velocity of 38.3+/-5.1 km/s with respect to the stellar photosphere. This result definitively confirms that this X-ray-emitting material originates in the post-shock region, at the base of the accretion stream, and not in coronal structures. The comparison of the observed velocity along the line of sight, 38.3+/-5.1 km/s, with the inferred intrinsic velocity of the post shock of TW Hya, v_post~110-120 km/s, indicates that the footpoints of the accretion streams on TW Hya are located at low latitudes on the stellar surface. Our results indicate that complex magnetic field geometries, such as that of TW Hya, permit low-latitude accretion spots. Moreover, since on TW Hya the redshift of the soft X-ray emission is very similar to that of the narrow component of the CIV resonance doublet at 1550 Ang, as found by Ardila et al. (2013), then the plasma at 2-4 MK and that at 0.1 MK likely originate in the same post-shock regions.Comment: Accepted for publication in Astronomy & Astrophysics; 2nd version after language editor corrections; 16 pages, 8 figures, 6 table

From Heisenberg to Goedel via Chaitin

In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the {\it converse} implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a ``formal uncertainty principle'' which implies Chaitin's information-theoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. In fact, the formal uncertainty principle applies to {\it all} systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies randomness not only in mathematics, but also in physics.Comment: Small change

Influence of detector motion in entanglement measurements with photons

We investigate how the polarization correlations of entangled photons described by wave packets are modified when measured by moving detectors. For this purpose, we analyze the Clauser-Horne-Shimony-Holt Bell inequality as a function of the apparatus velocity. Our analysis is motivated by future experiments with entangled photons designed to use satellites. This is a first step towards the implementation of quantum information protocols in a global scale

A perturbative approach to the polaron shift of excitons in transition metal dichalcogeniedes

In this Letter, we study the effect of phonons on the position of the 1s excitonic resonance of the fundamental absorption transition line in two-dimensional transition metal dichalcogenides. We apply our theory to WS2, a two-dimensional material where the shift in the absorption peak position has been measured as a function of temperature. The theory is composed of two ingredients only: (i) the effect of longitudinal optical phonons on the absorption peak position, which we describe with second-order perturbation theory, and (ii) the effect of phonons on the value of the single-particle energy gap, which we describe with the Huang Rhys model. Our results show excellent agreement with the experimentally measured shift of the absorption peak with the temperature.- N.M.R.P. acknowledges support by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. J.C.G.H. acknowledges the Center of Physics for a grant funded by the UIDB/04650/2020 strategic project. N.M.R.P. acknowledges support from the European Commission through the project Graphene-Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3), COMPETE 2020, PORTUGAL 2020, FEDER, and the FCT through Projects No. POCI-01-0145FEDER-028114 and No. PTDC/NAN-OPT/29265/2017

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

Excitons in phosphorene: A semi-analytical perturbative approach

In this paper we develop a semi-analytical perturbation-theory approach to the calculation of the energy levels (binding energies) and wave functions of excitons in phosphorene. Our method gives the exciton wave function in both real and reciprocal spaces with the same ease. This latter aspect is important for the calculation of the nonlinear optical properties of phosphorene. We find that our results are in agreement with calculations based both on the Bethe-Salpeter equation and on Monte Carlo simulations, which are computationally much more demanding. Our approach thus introduces a simple, viable, and accurate method to address the problem of excitons in anisotropic two-dimensional materials.N.M.R.P. acknowledges support from the European Commission through the project "Graphene-Driven Revolutions in ICT and Beyond" (Reference No. 785219) and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. In addition, N.M.R.P. acknowledges COMPETE2020, PORTUGAL2020, FEDER, and the FCT through Projects No. PTDC/FIS-NAN/3668/2013, No. POCI-01-0145-FEDER-028114, No. POCI-01-0145FEDER-029265, No. PTDC/NAN-OPT/29265/2017, and No. POCI-01-0145-FEDER-02888. The authors acknowledge P. A. Goncalves and R. Ribeiro for a critical reading of the manuscript

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

A review of the decoherent histories approach to the arrival time problem in quantum theory

We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expressed in terms of a POVM in this case. We turn finally to the question of decoherence of the corresponding histories, and we show that this can be achieved for simple states in the case of a free particle, and for general states for a particle coupled to an environment.Comment: 10 pages. To appear in DICE 2010 conference proceeding

Optimal copying of entangled two-qubit states

We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect to two separable copies. These optimal copying processes hint at the intricate relationship between fundamental laws of quantum theory and entanglement.Comment: 13 pages, 7 figure

Ionisation rate and Stark shift of a one-dimensional model of the Hydrogen molecular ion

In this paper we study the ionization rate and the Stark shift of a one-dimensional model of the H$_{2}^{+}$ ion. The finding of these two quantities is reduced to the solutions of a complex eigenvalue problem. We solve this problem both numerically and analytically. In the latter case we consider the regime of small external electrostatic fields and small internuclear distances. We find an excellent agreement between the ionization rate computed with the two approaches, even when the approximate result is pushed beyond its expected validity. The ionization rate is very sensitive to small changes of the external electrostatic field, spanning many orders of magnitude for small changes of the intensity of the external field. The dependence of the ionization on the internuclear distance is also studied, as this has a direct connection with experimental methods in molecular physics. It is shown that for large distances the ionization rate saturates, which is a direct consequence of the behavior of the energy eigenvalue with the internuclear distance. The Stark shift is computed and from it we extract the static polarizability of H$_{2}^{+}$ and compare our results with those found by other authors using more sophisticated methods.Comment: 14 page