5,451 research outputs found
Geometric and combinatorial realizations of crystal graphs
For irreducible integrable highest weight modules of the finite and affine
Lie algebras of type A and D, we define an isomorphism between the geometric
realization of the crystal graphs in terms of irreducible components of
Nakajima quiver varieties and the combinatorial realizations in terms of Young
tableaux and Young walls. For affine type A, we extend the Young wall
construction to arbitrary level, describing a combinatorial realization of the
crystals in terms of new objects which we call Young pyramids.Comment: 34 pages, 17 figures; v2: minor typos corrected; v3: corrections to
section 8; v4: minor typos correcte
Energy gaps and roton structure above the nu=1/2 Laughlin state of a rotating dilute Bose-Einstein condensate
Exact diagonalization study of a rotating dilute Bose-Einstein condensate
reveals that as the first vortex enters the system the degeneracy of the
low-energy yrast spectrum is lifted and a large energy gap emerges. As more
vortices enter with faster rotation, the energy gap decreases towards zero, but
eventually the spectrum exhibits a rotonlike structure above the nu=1/2
Laughlin state without having a phonon branch despite the short-range nature of
the interaction.Comment: 4 pages, 4 figures, 1 tabl
High-Symmetry Polarization Domains in Low-Symmetry Ferroelectrics
We present experimental evidence for hexagonal domain faceting in the
ferroelectric polymer PVDF-TrFE films having the lower orthorhombic
crystallographic symmetry. This effect can arise from purely electrostatic
depolarizing forces. We show that in contrast to magnetic bubble shape domains
where such type of deformation instability has a predominantly elliptical
character, the emergence of more symmetrical circular harmonics is favored in
ferroelectrics with high dielectric constant
Weight Vectors of the Basic A_1^(1)-Module and the Littlewood-Richardson Rule
The basic representation of \A is studied. The weight vectors are
represented in terms of Schur functions. A suitable base of any weight space is
given. Littlewood-Richardson rule appears in the linear relations among weight
vectors.Comment: February 1995, 7pages, Using AMS-Te
Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves
We define complexes of vector bundles on products of moduli spaces of framed
rank r torsion-free sheaves on the complex projective plane. The top
non-vanishing Chern classes of the cohomology of these complexes yield actions
of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology
of the moduli spaces. In this way we obtain a geometric realization of the
boson-fermion correspondence and related vertex operators.Comment: 36 pages; v2: Definition of geometric Heisenberg operators modified;
v3: Minor typos correcte
Vacuum entanglement governs the bosonic character of magnons
It is well known that magnons, elementary excitations in a magnetic material,
behave as bosons when their density is low. We study how the bosonic character
of magnons is governed by the amount of a multipartite entanglement in the
vacuum state on which magnons are excited. We show that if the multipartite
entanglement is strong, magnons cease to be bosons. We also consider some
examples, such as ground states of the Heisenberg ferromagnet and the
transverse Ising model, the condensation of magnons, the one-way quantum
computer, and Kitaev's toric code. Our result provides insights into the
quantum statistics of elementary excitations in these models, and into the
reason why a non-local transformation, such as the Jordan-Wigner
transformation, is necessary for some many-body systems.Comment: 4 pages, no figur
Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature
ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and the converse holds under mild assumptions. A natural question is for what singular rings these invariants are closest to one. For Hilbert–Kunz multiplicity this question was first considered by the last two authors and attracted significant attention. In this paper, we study this question, i.e., an upper bound, for F-signature and revisit lower bounds on Hilbert–Kunz multiplicity.La Caixa Junior Leader Postdoctoral Fellowship: LCF/BQ/PI21/1183003
Dynamical Properties in the Bilayer Quantum Hall Ferromagnet
The spectral functions of the pseudospin correlation functions in the bilayer
quantum Hall system at \nu=1 are investigated numerically, where the pseudospin
describes the layer degrees of freedom. In the pseudospin-ferromagnetic phase,
the lowest-energy excitation branch is closely connected with the ground state
through the fluctuations of pseudospin S_y and S_z, and it plays a significant
role on the tunneling properties in this system. For the system with very small
tunneling amplitude and layer separation smaller than the critical one, the
system-size dependence of calculated spectral function A_{y z} suggests the
superfluidity on the tunneling current in the absence of impurities.Comment: 4 pages, 1 Postscript figur
A crystal theoretic method for finding rigged configurations from paths
The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one
correspondences between the set of highest paths and the set of rigged
configurations. In this paper, we give a crystal theoretic reformulation of the
KKR map from the paths to rigged configurations, using the combinatorial R and
energy functions. This formalism provides tool for analysis of the periodic
box-ball systems.Comment: 24 pages, version for publicatio
Analyzing powers in inclusive pion production at high energy and the nucleon spin structure
Analyzing powers in inclusive pion production in high energy transversely
polarized proton-proton collisions are studied theoretically in the framework
of the quark recombination model. Calculations by assuming the SU(6)
spin-flavor symmetry for the nucleon structure disagree with the experiments.
We solve this difficulty by taking into account the %We overcome this
difficulty by taking into account the realistic spin distribution functions of
the nucleon, which differs from the SU(6) expectation at large , %but
coincides with a perturbative QCD constraint on the ratio of the unpolarized
valence distributions, as . We also discuss the kaon spin
asymmetry and find in the polarized proton-proton
collisions at large .Comment: 13 pages, 4 figures, late
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