2,147 research outputs found
Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d
For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P
of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of
arithmetic genus n), and exhibit all (E,P) attaining this minimum. The minimal
h^(P) was known to equal 1/30 for n=1 (Oguiso-Shioda) and 11/420 for n=2
(Nishiyama), but the formulas for the general (E,P) were not known, nor was the
fact that these are also the minima for an elliptic curve of discriminant
degree 12n over a function field of any genus. For n=3 both the minimal height
(23/840) and the explicit curves are new. These (E,P) also have the property
that that mP is an integral point (a point of naive height zero) for each
m=1,2,...,M, where M=6,8,9 for n=1,2,3; this, too, is maximal in each of the
three cases.Comment: 15 pages; some lines in the TeX source are commented out with "%" to
meet the 15-page limit for ANTS proceeding
Unitary representations of nilpotent super Lie groups
We show that irreducible unitary representations of nilpotent super Lie
groups can be obtained by induction from a distinguished class of sub super Lie
groups. These sub super Lie groups are natural analogues of polarizing
subgroups that appear in classical Kirillov theory. We obtain a concrete
geometric parametrization of irreducible unitary representations by nonnegative
definite coadjoint orbits. As an application, we prove an analytic
generalization of the Stone-von Neumann theorem for Heisenberg-Clifford super
Lie groups
Phase diagram and hidden order for generalized spin ladders
We investigate the phase diagram of antiferromagnetic spin ladders with
additional exchange interactions on diagonal bonds by variational and numerical
methods. These generalized spin ladders interpolate smoothly between the
chain with competing nn and nnn interactions, the chain with
alternating exchange and the antiferromagnetic chain. The Majumdar-Ghosh
ground states are formulated as matrix product states and are shown to exhibit
the same type of hidden order as the af chain. Generalized matrix product
states are used for a variational calculation of the ground state energy and
the spin and string correlation functions. Numerical (Lanczos) calculations of
the energies of the ground state and of the low-lying excited states are
performed, and compare reasonably with the variational approach. Our results
support the hypothesis that the dimer and Majumdar-Ghosh points are in the same
phase as the af chain.Comment: 23 pages, REVTEX, 7 figure
Field induced long-range-ordering in an S=1 quasi-one-dimensional Heisenberg antiferromagnet
We have measured the heat capacity and magnetization of the spin one
one-dimensional Heisenberg antiferromagnet NDMAP and constructed a magnetic
field versus temperature phase diagram. We found a field induced long-range
magnetic ordering. We have been successful in explaining the phase diagram
theoretically.Comment: 6 pages, 18 figure
Electronic structure of the muonium center as a shallow donor in ZnO
The electronic structure and the location of muonium centers (Mu) in
single-crystalline ZnO were determined for the first time. Two species of Mu
centers with extremely small hyperfine parameters have been observed below 40
K. Both Mu centers have an axial-symmetric hyperfine structure along with a
[0001] axis, indicating that they are located at the AB_{O,//} and BC_{//}
sites. It is inferred from their small ionization energy (~6 meV and 50 meV)
and hyperfine parameters (~10^{-4} times the vacuum value) that these centers
behave as shallow donors, strongly suggesting that hydrogen is one of the
primary origins of n type conductivity in as-grown ZnO.Comment: 4 pages, 4 figures, submitted to PR
Hidden Orders and RVB Formation of the Four-Leg Heisenberg Ladder Model
The ground state of the four-chain Heisenberg ladder model is numerically
investigated. Hidden-order correlations suitable for the system are introduced
and calculated with an emphasis on the spatially isotropic point, where a
corresponding material exists. The existence of a long-range hidden correlation
indicates formation of a short-range RVB state in the case of the
antiferromagnetic inter-chain coupling. A transition between the phase of the
ferromagnetic inter-chain coupling and that of the antiferromagnetic one is
discussed.Comment: 9 pages, 16 Postscript figure
Elementary excitations in the gapped phase of a frustrated S=1/2 spin ladder: from spinons to the Haldane triplet
We use the variational matrix-product ansatz to study elementary excitations
in the S=1/2 ladder with additional diagonal coupling, equivalent to a single
S=1/2 chain with alternating exchange and next-nearest neighbor interaction. In
absence of alternation the elementary excitation consists of two free S=1/2
particles ("spinons") which are solitons in the dimer order. When the
nearest-neighbor exchange alternates, the "spinons" are confined into one S=1
excitation being a soliton in the generalized string order. Variational results
are found to be in a qualitative agreement with the exact diagonalization data
for 24 spins. We argue that such an approach gives a reasonably good
description in a wide range of the model parameters.Comment: RevTeX, 13 pages, 11 embedded figures, uses psfig and multico
Randomness-driven quantum phase transition in bond-alternating Haldane chain
The effect of bond randomness on the spin-gapped ground state of the spin-1
bond-alternating antiferromagnetic Heisenberg chain is discussed. By using the
loop cluster quantum Monte Carlo method, we investigate the stability of
topological order in terms of the recently proposed twist order parameter [M.
Nakamura and S. Todo: Phys. Rev. Lett. 89 (2002) 077204]. It is observed that
the dimer phases as well as the Haldane phase of the spin-1 Heisenberg chain
are robust against a weak randomness, though the valence-bond-solid-like
topological order in the latter phase is destroyed by introducing a disorder
stronger than the critical value.Comment: 4 pages, 5 figures; minor changes; accepted for publication in J.
Phys. Soc. Jp
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