3,206 research outputs found
Semiclassical approximation with zero velocity trajectories
We present a new semiclassical method that yields an approximation to the
quantum mechanical wavefunction at a fixed, predetermined position. In the
approach, a hierarchy of ODEs are solved along a trajectory with zero velocity.
The new approximation is local, both literally and from a quantum mechanical
point of view, in the sense that neighboring trajectories do not communicate
with each other. The approach is readily extended to imaginary time propagation
and is particularly useful for the calculation of quantities where only local
information is required. We present two applications: the calculation of
tunneling probabilities and the calculation of low energy eigenvalues. In both
applications we obtain excellent agrement with the exact quantum mechanics,
with a single trajectory propagation.Comment: 16 pages, 7 figure
A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes
We design a novel provably stable discontinuous Galerkin spectral element
(DGSEM) approximation to solve systems of conservation laws on moving domains.
To incorporate the motion of the domain, we use an arbitrary
Lagrangian-Eulerian formulation to map the governing equations to a fixed
reference domain. The approximation is made stable by a discretization of a
skew-symmetric formulation of the problem. We prove that the discrete
approximation is stable, conservative and, for constant coefficient problems,
maintains the free-stream preservation property. We also provide details on how
to add the new skew-symmetric ALE approximation to an existing discontinuous
Galerkin spectral element code. Lastly, we provide numerical support of the
theoretical results
Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
We derive a multi-band formulation of the orbital magnetization in a normal
periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern
number, vanishes). Following the approach used recently to develop the
single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta,
Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier
representation and find that the magnetization is comprised of two
contributions, an obvious one associated with the internal circulation of
bulk-like Wannier functions in the interior and an unexpected one arising from
net currents carried by Wannier functions near the surface. Unlike the
single-band case, where each of these contributions is separately
gauge-invariant, in the multi-band formulation only the \emph{sum} of both
terms is gauge-invariant. Our final expression for the orbital magnetization
can be rewritten as a bulk property in terms of Bloch functions, making it
simple to implement in modern code packages. The reciprocal-space expression is
evaluated for 2d model systems and the results are verified by comparing to the
magnetization computed for finite samples cut from the bulk. Finally, while our
formal proof is limited to normal insulators, we also present a heuristic
extension to Chern insulators (having nonzero Chern invariant) and to metals.
The validity of this extension is again tested by comparing to the
magnetization of finite samples cut from the bulk for 2d model systems. We find
excellent agreement, thus providing strong empirical evidence in favor of the
validity of the heuristic formula.Comment: 14 pages, 8 figures. Fixed a typo in appendix
Sobre o problema da verdade e da compreensão em ciência
Tradução de Amélia Império Hamburger (1985) (Aprovada pelo autor)
Experimental Demonstration of Greenberger-Horne-Zeilinger Correlations Using Nuclear Magnetic Resonance
The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum
correlations that cannot be explained by classical local hidden variables. This
paper reports on the experimental realization of GHZ correlations using nuclear
magnetic resonance (NMR). The NMR experiment differs from the originally
proposed GHZ experiment in several ways: it is performed on mixed states rather
than pure states; and instead of being widely separated, the spins on which it
is performed are all located in the same molecule. As a result, the NMR version
of the GHZ experiment cannot entirely rule out classical local hidden
variables. It nonetheless provides an unambiguous demonstration of the
"paradoxical" GHZ correlations, and shows that any classical hidden variables
must communicate by non-standard and previously undetected forces. The NMR
demonstration of GHZ correlations shows the power of NMR quantum information
processing techniques for demonstrating fundamental effects in quantum
mechanics.Comment: Latex2.09, 8 pages, 1 eps figur
A Categorical Approach to Groupoid Frobenius Algebras
In this paper, we show that \C{G}-Frobenius algebras (for \C{G} a finite
groupoid) correspond to a particular class of Frobenius objects in the
representation category of D(k[\C{G}]), where D(k[\C{G}]) is the Drinfeld
double of the quantum groupoid k[\C{G}].Comment: final version; to appear in Applied Categorical Structure
Neutral Higgs-pair production at Linear Colliders within the general 2HDM: quantum effects and triple Higgs boson self-interactions
The pairwise production of neutral Higgs bosons is analyzed in the context of
the future linear colliders, such as the ILC and CLIC, within the general
Two-Higgs-Doublet Model (2HDM). The corresponding cross-sections are computed
at the one-loop level in full compliance with the current phenomenological
bounds and the stringent theoretical constraints inherent to the consistency of
the model. We uncover regions across the 2HDM parameter space, mainly for low
tan\beta near 1 and moderate values of the relevant lambda_5 parameter, wherein
the radiative corrections to the Higgs-pair production cross sections can
comfortably reach 50% This behavior can be traced back to the enhancement
capabilities of the trilinear Higgs self-interactions -- a trademark feature of
the 2HDM, with no counterpart in the Minimal Supersymmetric Standard Model.
Interestingly enough, the quantum effects are positive for energies around 500
GeV, thereby producing a significant enhancement in the expected number of
events precisely around the fiducial startup energy of the ILC. The Higgs-pair
production rates can be substantial, typically amounting to a few thousand
events per 500 inverse femtobarn of integrated luminosity. In contrast, the
corrections are negative in the highest energy range (1 TeV). We also compare
the exclusive pairwise production of Higgs bosons with the inclusive gauge
boson fusion channels leading to 2H+X finals states, and also with the
exclusive triple Higgs boson production. We find that these multiparticle final
states can be highly complementary in the overall Higgs bosons search strategy.Comment: 42 pages, 23 figures, 10 tables. Accepted in Phys. Rev. D (the
published version is shorter
The EPR paradox, Bell's inequality, and the question of locality
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox
exemplifies much of the strange behavior of quantum mechanics, but argument
persists about what assumptions underlie the paradox. To clarify what the
debate is about, we employ a simple and well-known thought experiment involving
two correlated photons to help us focus on the logical assumptions needed to
construct the EPR and Bell arguments. The view presented in this paper is that
the minimal assumptions behind Bell's inequality are locality and
counterfactual definiteness, but not scientific realism, determinism, or hidden
variables, as is often suggested. We further examine the resulting constraints
on physical theory with an illustration from the many-worlds interpretation of
quantum mechanics -- an interpretation that we argue is deterministic, local,
and realist, but that nonetheless violates the Bell inequality.Comment: 28 pages; change of title, minor wording changes, move to TeX forma
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