34,503 research outputs found
Thermodynamics of localized magnetic moments in a Dirac conductor
We show that the magnetic susceptibility of a dilute ensemble of magnetic
impurities in a conductor with a relativistic electronic spectrum is
non-analytic in the inverse tempertature at . We derive a general
theory of this effect and construct the high-temperature expansion for the
disorder averaged susceptibility to any order, convergent at all tempertaures
down to a possible ordering transition. When applied to Ising impurities on a
surface of a topological insulator, the proposed general theory agrees with
Monte Carlo simulations, and it allows us to find the critical temperature of
the ferromagnetic phase transition.Comment: 5 pages, 1 figure, 2 tables, RevTe
Identities for hyperelliptic P-functions of genus one, two and three in covariant form
We give a covariant treatment of the quadratic differential identities
satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of
genera 1, 2 and 3
Deriving bases for Abelian functions
We present a new method to explicitly define Abelian functions associated
with algebraic curves, for the purpose of finding bases for the relevant vector
spaces of such functions. We demonstrate the procedure with the functions
associated with a trigonal curve of genus four. The main motivation for the
construction of such bases is that it allows systematic methods for the
derivation of the addition formulae and differential equations satisfied by the
functions. We present a new 3-term 2-variable addition formulae and a complete
set of differential equations to generalise the classic Weierstrass identities
for the case of the trigonal curve of genus four.Comment: 35page
An ultra-bright atom laser
We present a novel, ultra-bright atom-laser and ultra-cold thermal atom beam.
Using rf-radiation we strongly couple the magnetic hyperfine levels of 87Rb
atoms in a magnetically trapped Bose-Einstein condensate. At low rf-frequencies
gravity opens a small hole in the trapping potenital and a well collimated,
extremely bright atom laser emerges from just below the condensate. As opposed
to traditional atom lasers based on weak coupling, this technique allows us to
outcouple atoms at an arbitrarily large rate. We demonstrate an increase in
flux per atom in the BEC by a factor of sixteen compared to the brightest
quasi-continuous atom laser. Furthermore, we produce by two orders of magnitude
the coldest thermal atom beam to date (200 nK).Comment: 20 pages, 9 figures, supplementary material online at
http://www.bec.g
A purely reflective large wide-field telescope
Two versions of a fast, purely reflective Paul-Baker type telescope are
discussed, each with an 8.4-m aperture, 3 deg diameter flat field and f/1.25
focal ratio.
The first version is based on a common, even asphere type of surface with
zero conic constant. The primary and tertiary mirrors are 6th order aspheres,
while the secondary mirror is an 8th order asphere (referred to here for
brevity, as the 6/8/6 configuration). The D_80 diameter of a star image varies
from 0''.18 on the optical axis up to 0''.27 at the edge of the field (9.3-13.5
mcm).
The second version of the telescope is based on a polysag surface type which
uses a polynomial expansion in the sag z, r^2 = 2R_0z - (1+b)z^2 + a_3 z^3 +
a_4 z^4 + ... + a_N z^N, instead of the common form of an aspheric surface.
This approach results in somewhat better images, with D_80 ranging from 0''.16
to 0''.23, using a lower-order 3/4/3 combination of powers for the mirror
surfaces. An additional example with 3.5-m aperture, 3.5 deg diameter flat
field, and f/1.25 focal ratio featuring near-diffraction-limited image quality
is also presented.Comment: 14 pages, 6 figures; new examples adde
Early- and late-migrating cranial neural crest cell populations have equivalent developmental potential in vivo
We present the first in vivo study of the long-term fate and potential of early-migrating and late-migrating mesencephalic neural crest cell populations, by performing isochronic and heterochronic quail-to-chick grafts. Both early- and late-migrating populations form melanocytes, neurons, glia, cartilage and bone in isochronic, isotopic chimeras, showing that neither population is lineage-restricted. The early-migrating population distributes both dorsally and ventrally during normal development, while the late-migrating population is confined dorsally and forms much less cartilage and bone. When the late-migrating population is substituted heterochronically for the early-migrating population, it contributes extensively to ventral derivatives such as jaw cartilage and bone. Conversely, when the early-migrating population is substituted heterochronically for the late-migrating population, it no longer contributes to the jaw skeleton and only forms dorsal derivatives. When the late-migrating population is grafted into a late-stage host whose neural crest had previously been ablated, it migrates ventrally into the jaws. Thus, the dorsal fate restriction of the late-migrating mesencephalic neural crest cell population in normal development is due to the presence of earlier-migrating neural crest cells, rather than to any change in the environment or to any intrinsic difference in migratory ability or potential between early- and late-migrating cell populations. These results highlight the plasticity of the neural crest and show that its fate is determined primarily by the environment
Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV)
and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given
curve whose genus is three. This study was based upon the fact
that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F.
Baker essentially derived KdV hierarchy and KP equation by using bilinear
differential operator , identities of Pfaffians, symmetric
functions, hyperelliptic -function and -functions; . The connection between his theory and the modern
soliton theory was also discussed.Comment: AMS-Tex, 12 page
Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type
We discuss a family of multi-term addition formulae for Weierstrass functions
on specialized curves of genus one and two with many automorphisms. In the
genus one case we find new addition formulae for the equianharmonic and
lemniscate cases, and in genus two we find some new addition formulae for a
number of curves, including the Burnside curve.Comment: 19 pages. We have extended the Introduction, corrected some typos and
tidied up some proofs, and inserted extra material on genus 3 curve
Ground state energy of the modified Nambu-Goto string
We calculate, using zeta function regularization method, semiclassical energy
of the Nambu-Goto string supplemented with the boundary, Gauss-Bonnet term in
the action and discuss the tachyonic ground state problem.Comment: 10 pages, LaTeX, 2 figure
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