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

Bell's inequality with Dirac particles

We study Bell's inequality using the Bell states constructed from four component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo vector which is relativistic invariant operator. By using Lorentz transformation, in both Bell states and spin operator, we obtain an observer independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.Comment: 7 pages. arXiv admin note: text overlap with arXiv:quant-ph/0308156 by other author

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

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

Nonlocal effects in Fock space

If a physical system contains a single particle, and if two distant detectors test the presence of linear superpositions of one-particle and vacuum states, a violation of classical locality can occur. It is due to the creation of a two-particle component by the detecting process itself.Comment: final version in PRL 74 (1995) 4571; 76 (1996) 2205 (erratum

A Schmidt number for density matrices

We introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local quantum operations and classical communication. We show that $k$-positive maps witness Schmidt number, in the same way that positive maps witness entanglement. We show that the family of states which is made from mixing the completely mixed state and a maximally entangled state have increasing Schmidt number depending on the amount of maximally entangled state that is mixed in. We show that Schmidt number {\it does not necessarily increase} when taking tensor copies of a density matrix $\rho$; we give an example of a density matrix for which the Schmidt numbers of $\rho$ and $\rho \otimes \rho$ are both 2.Comment: 5 pages RevTex, 1 typo in Proof Lemma 1 correcte

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