Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions

We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of solution of the harmonic oscillator problem.Comment: 9 pages, 3 figure

Dynamical polarizability of graphene beyond the Dirac cone approximation

We compute the dynamical polarizability of graphene beyond the usual Dirac cone approximation, integrating over the full Brillouin zone. We find deviations at $\hbar\omega=2t$ ($t$ the hopping parameter) which amount to a logarithmic singularity due to the van Hove singularity and derive an approximate analytical expression. Also at low energies, we find deviations from the results obtained from the Dirac cone approximation which manifest themselves in a peak spitting at arbitrary direction of the incoming wave vector \q. Consequences for the plasmon spectrum are discussed.Comment: 8 pages, 6 figure

No directed fractal percolation in zero area

We show that fractal (or "Mandelbrot") percolation in two dimensions produces a set containing no directed paths, when the set produced has zero area. This improves a similar result by the first author in the case of constant retention probabilities to the case of retention probabilities approaching 1

Charge and Spin Transport in the One-dimensional Hubbard Model

In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $\eta$-spin triplet excitations carry charge but no spin, and both spin-singlet and charge $\eta$-spin-singlet excitations carry neither spin nor charge currents.Comment: 24 pages, 14 figure

Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N=7 and verify that they are minimal up to N=5. We finally propose an expression which gives the size of the minimal optimal measurements for arbitrary $N$.Comment: 9 pages, Late

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

Speakable in Quantum Mechanics

At the 1927 Como conference Bohr spoke the now famous words "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." However, if the Copenhagen interpretation really holds on to this motto, why then is there this feeling of conflict when comparing it with realist interpretations? Surely what one can say about nature should in a certain sense be interpretation independent. In this paper I take Bohr's motto seriously and develop a quantum logic that avoids assuming any form of realism as much as possible. To illustrate the non-triviality of this motto a similar result is first derived for classical mechanics. It turns out that the logic for classical mechanics is a special case of the derived quantum logic. Finally, some hints are provided in how these logics are to be used in practical situations and I discuss how some realist interpretations relate to these logics

An obstruction based approach to the Kochen-Specker theorem

In [1] it was shown that the Kochen Specker theorem can be written in terms of the non-existence of global elements of a certain varying set over the partially ordered set of boolean subalgebras of projection operators on some Hilbert space. In this paper, we show how obstructions to the construction of such global elements arise, and how this provides a new way of looking at proofs of the theorem.Comment: 14 pages, 6 figure