2,680 research outputs found
On semiring complexity of Schur polynomials
Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial {s_\lambda(x_1,\dots,x_k)} labeled by a partition {\lambda=(\lambda_1\ge\lambda_2\ge\cdots)} is bounded by {O(\log(\lambda_1))} provided the number of variables is fixed
Andreev scattering in nanoscopic junctions at high magnetic fields
We report on the measurement of multiple Andreev resonances at atomic size
point contacts between two superconducting nanostructures of Pb under magnetic
fields higher than the bulk critical field, where superconductivity is
restricted to a mesoscopic region near the contact. The small number of
conduction channels in this type of contacts permits a quantitative comparison
with theory through the whole field range. We discuss in detail the physical
properties of our structure, in which the normal bulk electrodes induce a
proximity effect into the mesoscopic superconducting part.Comment: 4 page
Phonons in magnon superfluid and symmetry breaking field
Recent experiments [1],[2] which measured the spectrum of the Goldstone
collective mode of coherently precessing state in 3He-B are discussed using the
presentation of the coherent spin precession in terms of the Bose-Einstein
condensation of magnons. The mass in the spectrum of the Goldstone boson --
phonon in the superfluid magnon liquid -- is induced by the symmetry breaking
field, which is played by the RF magnetic fieldComment: 2 pages, JETP Letters style, no figures, version accepted in JETP
Letter
Optical spectra of quantum dots: effects of non-adiabaticity
It is shown that in many cases an adequate description of optical spectra of
semiconductor quantum dots requires a treatment beyond the commonly used
adiabatic approximation. We have developed a theory of phonon-assisted optical
transitions in semiconductor quantum dots, which takes into account
non-adiabaticity of the exciton-phonon system. Effects of non-adiabaticity lead
to a mixing of different exciton and phonon states that provides a key to the
understanding of surprisingly high intensities of phonon satellites observed in
photoluminescence spectra of quantum dots. A breakdown of the adiabatic
approximation gives an explanation also for discrepancies between the serial
law, observed in multi-phonon optical spectra of some quantum dots, and the
Franck-Condon progression, prescribed by the adiabatic approach.Comment: 4 pages, 3 figures, E-mail addresses: [email protected],
[email protected], [email protected], [email protected],
[email protected]
Polynomial kernelization for removing induced claws and diamonds
A graph is called (claw,diamond)-free if it contains neither a claw (a
) nor a diamond (a with an edge removed) as an induced subgraph.
Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of
triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex
is in at most two maximal cliques and every edge is in exactly one maximal
clique.
In this paper we consider the parameterized complexity of the
(claw,diamond)-free Edge Deletion problem, where given a graph and a
parameter , the question is whether one can remove at most edges from
to obtain a (claw,diamond)-free graph. Our main result is that this problem
admits a polynomial kernel. We complement this finding by proving that, even on
instances with maximum degree , the problem is NP-complete and cannot be
solved in time unless the Exponential Time
Hypothesis fai
Electron locking in semiconductor superlattices
We describe a novel state of electrons and phonons arising in semiconductor
superlattices (SSL) due to strong electron-phonon interactions. These states
are characterized by a localization of phonons and a self-trapping or locking
of electrons in one or several quantum wells due to an additional,
deformational potential arising around these locking wells in SSL. The effect
is enhanced in a longitudinal magnetic field.
Using the tight-binding and adiabatic approximations the whole energy
spectrum of the self-trapped states is found and accurate, analytic expressions
are included for strong electron-phonon coupling. Finally, we discuss possible
experiments which may detect these predicted self-trapped states.Comment: 8 pages, 2 figures. Please note that the published article has the
title 'Electron locking in layered structures by a longitudinal magnetic
field
Signatures of pairing mechanisms and order parameters in ferromagnetic superconductors
Two predictions are made for properties of the ferromagnetic superconductors
discovered recently. The first one is that spin-triplet, p-wave pairing in such
materials will give the magnons a mass inversely proportional to the square of
the magnetization. The second one is based on a specific mechanism for p-wave
pairing, and predicts that the observed broad anomaly in the specific heat of
URhGe will be resolved into a split transition with increasing sample quality.
These predictions will help discriminate between different possible mechanisms
for ferromagnetic superconductivity.Comment: 4 pp., 1 ps fi
Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element
When W is a finite reflection group, the noncrossing partition lattice NCP_W
of type W is a rich combinatorial object, extending the notion of noncrossing
partitions of an n-gon. A formula (for which the only known proofs are
case-by-case) expresses the number of multichains of a given length in NCP_W as
a generalised Fuss-Catalan number, depending on the invariant degrees of W. We
describe how to understand some specifications of this formula in a case-free
way, using an interpretation of the chains of NCP_W as fibers of a
Lyashko-Looijenga covering (LL), constructed from the geometry of the
discriminant hypersurface of W. We study algebraically the map LL, describing
the factorisations of its discriminant and its Jacobian. As byproducts, we
generalise a formula stated by K. Saito for real reflection groups, and we
deduce new enumeration formulas for certain factorisations of a Coxeter element
of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation.
Version 3 : corrected typos, added illustrated example. To appear in Journal
of Algebraic Combinatoric
Short-Distance Structure of Nuclei
One of Jefferson Lab's original missions was to further our understanding of
the short-distance structure of nuclei. In particular, to understand what
happens when two or more nucleons within a nucleus have strongly overlapping
wave-functions; a phenomena commonly referred to as short-range correlations.
Herein, we review the results of the (e,e'), (e,e'p) and (e,e'pN) reactions
that have been used at Jefferson Lab to probe this short-distance structure as
well as provide an outlook for future experiments.Comment: 16 pages, 8 figures, for publication in Journal of Physics
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