67,344 research outputs found
On the discrete spectrum of quantum layers
Consider a quantum particle trapped between a curved layer of constant width
built over a complete, non-compact, smooth surface embedded in
. We assume that the surface is asymptotically flat in the sense
that the second fundamental form vanishes at infinity, and that the surface is
not totally geodesic. This geometric setting is known as a quantum layer. We
consider the quantum particle to be governed by the Dirichlet Laplacian as
Hamiltonian. Our work concerns the existence of bound states with energy
beneath the essential spectrum, which implies the existence of discrete
spectrum. We first prove that if the Gauss curvature is integrable, and the
surface is weakly -parabolic, then the discrete spectrum is non-empty.
This result implies that if the total Gauss curvature is non-positive, then the
discrete spectrum is non-empty. We next prove that if the Gauss curvature is
non-negative, then the discrete spectrum is non-empty. Finally, we prove that
if the surface is parabolic, then the discrete spectrum is non-empty if the
layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from
previous version is proven here (Theorem 1.5), additional references include
The formation of ion acoustic shocks
Recent experiments performed in the double plasma (DP) device have verified the existence of electrostatic ion acoustic laminar shocks. The influence of the piston on the shock structure is investigated by modeling the DP device and by numerically solving the temporal and spatial evolution of the shock. In order to isolate piston effects, as opposed to kinetic theory effects such as reflected ions and trapped electrons, the DP plasma is modeled as a cold ion fluid with isothermal Boltzmann electrons. It is shown that laminar shock transitions with structure agreeing with DP shock experiments can be excited
Charge ordering in doped manganese oxides: lattice dynamics and magnetic structure
Based on the Hamiltonian of small polarons with the strong nearest neighbor
repulsion, we have investigated the charge ordering phenomena observed in
half-doped manganites R_{1/2}A_{1/2}MnO_3. We have explored possible
consequences of the charge ordering phase in the half-doped manganites. First,
we have studied the renormalization of the sound velocity around ,
considering the acoustic phonons coupled to the electrons participating in the
charge ordering. Second, we have found a new antiferromagnetic phase induced by
the charge ordering, and discussed its role in connection with the specific
CE-type antiferromagnetic structure observed in half-doped manganites.Comment: 5 pages, 2 Postscript figures. To appear in Phys. Rev. B - Rapid
Comm. (01Jun97
Is Cosmology Solved?
We have fossil evidence from the thermal background radiation that our
universe expanded from a considerably hotter denser state. We have a well
defined and testable description of the expansion, the relativistic
Friedmann-Lemaitre model. Its observational successes are impressive but I
think hardly enough for a convincing scientific case. The lists of
observational constraints and free hypotheses within the model have similar
lengths. The scorecard on the search for concordant measures of the mass
density parameter and the cosmological constant shows that the high density
Einstein-de Sitter model is challenged, but that we cannot choose between low
density models with and without a cosmological constant. That is, the
relativistic model is not strongly overconstrained, the usual test of a mature
theory. Work in progress will greatly improve the situation and may at last
yield a compelling test. If so, and the relativistic model survives, it will
close one line of research in cosmology: we will know the outlines of what
happened as our universe expanded and cooled from high density. It will not end
research: some of us will occupy ourselves with the details of how galaxies and
other large-scale structures came to be the way they are, others with the issue
of what our universe was doing before it was expanding. The former is being
driven by rapid observational advances. The latter is being driven mainly by
theory, but there are hints of observational guidance.Comment: 13 pages, 3 figures. To be published in PASP as part of the
proceedings of the Smithsonian debate, Is Cosmology Solved
A cosmic gamma-ray burst on May 14, 1975
A cosmic gamma-ray burst is reported that occurred at 29309.11 s UTC, May 14, 1975. The burst was detected at an atmospheric depth of 4 g/sq cm residual atmosphere with the University of California double scatter gamma-ray telescope launched on a balloon from Palestine, Texas at 1150 UTC, May 13, 1975. The burst was observed both in the single scatter mode by the top liquid scintillator tank in anti-coincidence with the surrounding plastic scintillator and in the double scatter mode from which energy and directional information are obtained. The burst is 24 standard deviations above the background for single scatter events. The total gamma-ray flux in the burst, incident on the atmosphere with photon energy greater than 0.5 MeV, is 0.59 + or - 0.15 photons/sq cm. The initial rise time to 90% of maximum is 0.015 + or - 0.005 s and the duration is 0.11 s. Time structure down to the 5 ms resolution of the telescope is seen. The mean flux over this time period is 5.0 + or - 1.3 photons/sq cm/s and the maximum flux is 8.5 + or - 2.1 photons/sq cm/s
Strongly interacting bosons in a disordered optical lattice
Disorder, prevalent in nature, is intimately involved in such spectacular
effects as the fractional quantum Hall effect and vortex pinning in type-II
superconductors. Understanding the role of disorder is therefore of fundamental
interest to materials research and condensed matter physics. Universal
behavior, such as Anderson localization, in disordered non-interacting systems
is well understood. But, the effects of disorder combined with strong
interactions remains an outstanding challenge to theory. Here, we
experimentally probe a paradigm for disordered, strongly-correlated bosonic
systems-the disordered Bose-Hubbard (DBH) model-using a Bose-Einstein
condensate (BEC) of ultra-cold atoms trapped in a completely characterized
disordered optical lattice. We determine that disorder suppresses condensate
fraction for superfluid (SF) or coexisting SF and Mott insulator (MI) phases by
independently varying the disorder strength and the ratio of tunneling to
interaction energy. In the future, these results can constrain theories of the
DBH model and be extended to study disorder for strongly-correlated fermionic
particles.Comment: 15 pages, 4 figures updated to correct errors in referencing previous
wor
Comment on ``Stripes and the t-J Model''
This is a comment being submitted to Physical Review Letters on a recent
letter by Hellberg and Manousakis on stripes in the t-J model.Comment: One reference correcte
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