541 research outputs found
On compatibility between isogenies and polarisations of abelian varieties
We discuss the notion of polarised isogenies of abelian varieties, that is,
isogenies which are compatible with given principal polarisations. This is
motivated by problems of unlikely intersections in Shimura varieties. Our aim
is to show that certain questions about polarised isogenies can be reduced to
questions about unpolarised isogenies or vice versa.
Our main theorem concerns abelian varieties B which are isogenous to a fixed
abelian variety A. It establishes the existence of a polarised isogeny A to B
whose degree is polynomially bounded in n, if there exist both an unpolarised
isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As
a further result, we prove that given any two principally polarised abelian
varieties related by an unpolarised isogeny, there exists a polarised isogeny
between their fourth powers.
The proofs of both theorems involve calculations in the endomorphism algebras
of the abelian varieties, using the Albert classification of these endomorphism
algebras and the classification of Hermitian forms over division algebras
Optical Study of GaAs quantum dots embedded into AlGaAs nanowires
We report on the photoluminescence characterization of GaAs quantum dots
embedded into AlGaAs nano-wires. Time integrated and time resolved
photoluminescence measurements from both an array and a single quantum
dot/nano-wire are reported. The influence of the diameter sizes distribution is
evidenced in the optical spectroscopy data together with the presence of
various crystalline phases in the AlGaAs nanowires.Comment: 5 page, 5 figure
Superrigid subgroups and syndetic hulls in solvable Lie groups
This is an expository paper. It is not difficult to see that every group
homomorphism from the additive group Z of integers to the additive group R of
real numbers extends to a homomorphism from R to R. We discuss other examples
of discrete subgroups D of connected Lie groups G, such that the homomorphisms
defined on D can ("virtually") be extended to homomorphisms defined on all of
G. For the case where G is solvable, we give a simple proof that D has this
property if it is Zariski dense. The key ingredient is a result on the
existence of syndetic hulls.Comment: 17 pages. This is the final version that will appear in the volume
"Rigidity in Dynamics and Geometry," edited by M. Burger and A. Iozzi
(Springer, 2002
Competing anisotropy in the (TmxPr1-x)2Fe17 system
The magnetization curves of magnetically aligned finely powdered samples of the (TmxPr1-x)2Fe17 compounds have been measured at 4 K. The easy magnetization axis is oriented in the basal plane or along the hexagonal axis for the compounds with x = 0-0.3 and 0.7-1, respectively. This is because of the absence of magnetic ordering in the Tm and Pr subsystems in these ranges, respectively, and because of competing anisotropy of the subsystems. For the compositions with x = 0.4-0.6, both rare-earth subsystems are magnetically ordered and the easy magnetization axis is oriented between the basal plane and the hexagonal axis. The critical fields of FOMPs decrease quickly as the Pr or Tm content decreases in the ranges 0-0.3 and 0.7-1, respectively. The magnetization anisotropy also diminishes as the Tm content becomes smaller than x = 0.7. No influence of the intrinsic microdeformations on the magnetization of the compounds was detected. © 2018 The Authors, published by EDP Sciences
Arbitrarily large families of spaces of the same volume
In any connected non-compact semi-simple Lie group without factors locally
isomorphic to SL_2(R), there can be only finitely many lattices (up to
isomorphism) of a given covolume. We show that there exist arbitrarily large
families of pairwise non-isomorphic arithmetic lattices of the same covolume.
We construct these lattices with the help of Bruhat-Tits theory, using Prasad's
volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde
Self-consistent calculations of quadrupole moments of the first 2+ states in Sn and Pb isotopes
A method of calculating static moments of excited states and transitions
between excited states is formulated for non-magic nuclei within the Green
function formalism. For these characteristics, it leads to a noticeable
difference from the standard QRPA approach. Quadrupole moments of the first 2+
states in Sn and Pb isotopes are calculated using the self-consistent TFFS
based on the Energy Density Functional by Fayans et al. with the set of
parameters DF3-a fixed previously. A reasonable agreement with available
experimental data is obtained.Comment: 5 pages, 6 figure
Temperature-dependent magnetospectroscopy of HgTe quantum wells
We report on magnetospectroscopy of HgTe quantum wells in magnetic fields up
to 45 T in temperature range from 4.2 K up to 185 K. We observe intra- and
inter-band transitions from zero-mode Landau levels, which split from the
bottom conduction and upper valence subbands, and merge under the applied
magnetic field. To describe experimental results, realistic
temperature-dependent calculations of Landau levels have been performed. We
show that although our samples are topological insulators at low temperatures
only, the signature of such phase persists in optical transitions at high
temperatures and high magnetic fields. Our results demonstrate that
temperature-dependent magnetospectroscopy is a powerful tool to discriminate
trivial and topological insulator phases in HgTe quantum wells
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