5,610 research outputs found
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 -spin
triplet excitations carry charge but no spin, and both spin-singlet and charge
-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 ( 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
-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 ; we give an
example of a density matrix for which the Schmidt numbers of and 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
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