16,326 research outputs found
An alternative approach to efficient simulation of micro/nanoscale phonon transport
Starting from the recently proposed energy-based deviational formulation for
solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys.
Rev. B 84, 2011], which provides significant computational speedup compared to
standard Monte Carlo methods for small deviations from equilibrium, we show
that additional computational benefits are possible in the limit that the
governing equation can be linearized. The proposed method exploits the
observation that under linearized conditions (small temperature differences)
the trajectories of individual deviational particles can be decoupled and thus
simulated independently; this leads to a particularly simple and efficient
algorithm for simulating steady and transient problems in arbitrary
three-dimensional geometries, without introducing any additional approximation.Comment: 4 pages, 2 figure
Spin-mechanics with levitating ferromagnetic particles
We propose and demonstrate first steps towards schemes where the librational
mode of levitating ferromagnets is strongly coupled to the electronic spin of
Nitrogen-Vacancy (NV) centers in diamond. Experimentally, we levitate
ferromagnets in a Paul trap and employ magnetic fields to attain oscillation
frequencies in the hundreds of kHz range with Q factors close to . These
librational frequencies largely exceed the decoherence rate of NV centers in
typical CVD grown diamonds offering prospects for sideband resolved operation.
We also prepare and levitate composite diamond-ferromagnet particles and
demonstrate both coherent spin control of the NV centers and read-out of the
particle libration using the NV spin. Our results will find applications in
ultra-sensitive gyroscopy and bring levitating objects a step closer to
spin-mechanical experiments at the quantum level.Comment: Lengthened to 11 pages. To appear in PR
Pathwise super-replication via Vovk's outer measure
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback
option. In: Finance Stoch. (1998)] the connection between model-independent
pricing and the Skorokhod embedding problem has been a driving force in robust
finance. We establish a general pricing-hedging duality for financial
derivatives which are susceptible to the Skorokhod approach.
Using Vovk's approach to mathematical finance we derive a model-independent
super-replication theorem in continuous time, given information on finitely
many marginals. Our result covers a broad range of exotic derivatives,
including lookback options, discretely monitored Asian options, and options on
realized variance.Comment: 18 page
An Exotic Theory of Massless Spin-Two Fields in Three Dimensions
It is a general belief that the only possible way to consistently deform the
Pauli-Fierz action, changing also the gauge algebra, is general relativity.
Here we show that a different type of deformation exists in three dimensions if
one allows for PT non-invariant terms. The new gauge algebra is different from
that of diffeomorphisms. Furthermore, this deformation can be generalized to
the case of a collection of massless spin-two fields. In this case it describes
a consistent interaction among them.Comment: 21+1 pages. Minor corrections and reference adde
Dynamo quenching due to shear flow
We provide a theory of dynamo (α effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the α effect is reduced by the shear even in the absence of magnetic field. The α effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun
Experimental Implementation of a Concatenated Quantum Error-Correcting Code
Concatenated coding provides a general strategy to achieve the desired level
of noise protection in quantum information storage and transmission. We report
the implementation of a concatenated quantum error-correcting code able to
correct against phase errors with a strong correlated component. The experiment
was performed using liquid-state nuclear magnetic resonance techniques on a
four spin subsystem of labeled crotonic acid. Our results show that
concatenation between active and passive quantum error-correcting codes offers
a practical tool to handle realistic noise contributed by both independent and
correlated errors.Comment: 4 pages, 2 encapsulated eps figures. REVTeX4 styl
Tensor hypercontraction: A universal technique for the resolution of matrix elements of local, finite-range -body potentials in many-body quantum problems
Configuration-space matrix elements of N-body potentials arise naturally and
ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For
the common specialization of local, finite-range potentials, we develop the
eXact Tensor HyperContraction (X-THC) method, which provides a quantized
renormalization of the coordinate-space form of the N-body potential, allowing
for a highly separable tensor factorization of the configuration-space matrix
elements. This representation allows for substantial computational savings in
chemical, atomic, and nuclear physics simulations, particularly with respect to
difficult "exchange-like" contractions.Comment: Third version of the manuscript after referee's comments. In press in
PRL. Main text: 4 pages, 2 figures, 1 table; Supplemental material (also
included): 14 pages, 2 figures, 2 table
Schur elements for the Ariki-Koike algebra and applications
We study the Schur elements associated to the simple modules of the
Ariki-Koike algebra. We first give a cancellation-free formula for them so that
their factors can be easily read and programmed. We then study direct
applications of this result. We also complete the determination of the
canonical basic sets for cyclotomic Hecke algebras of type in
characteristic 0.Comment: The paper contains the results of arXiv:1101.146
Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions
We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite
dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka
and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of
coideal subalgebras. We reduce the study to KD(n) by proving that the others
are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We
derive many examples of lattices of intermediate subfactors of the inclusions
of depth 2 associated to those Kac algebras, as well as the corresponding
principal graphs, which is the original motivation.
Along the way, we extend some general results on the Galois correspondence
for depth 2 inclusions, and develop some tools and algorithms for the study of
twisted group algebras and their lattices of coideal subalgebras. This research
was driven by heavy computer exploration, whose tools and methodology we
further describe.Comment: v1: 84 pages, 13 figures, submitted. v2: 94 pages, 15 figures, added
connections with Masuoka's families KA and KB, description of K3 in KD(n),
lattices for KD(8) and KD(15). v3: 93 pages, 15 figures, proven lattice for
KD(6), misc improvements, accepted for publication in Journal of Algebra and
Its Application
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