418 research outputs found
Modular polynomials via isogeny volcanoes
We present a new algorithm to compute the classical modular polynomial Phi_n
in the rings Z[X,Y] and (Z/mZ)[X,Y], for a prime n and any positive integer m.
Our approach uses the graph of n-isogenies to efficiently compute Phi_n mod p
for many primes p of a suitable form, and then applies the Chinese Remainder
Theorem (CRT). Under the Generalized Riemann Hypothesis (GRH), we achieve an
expected running time of O(n^3 (log n)^3 log log n), and compute Phi_n mod m
using O(n^2 (log n)^2 + n^2 log m) space. We have used the new algorithm to
compute Phi_n with n over 5000, and Phi_n mod m with n over 20000. We also
consider several modular functions g for which Phi_n^g is smaller than Phi_n,
allowing us to handle n over 60000.Comment: corrected a typo in equation (14), 31 page
Layer- and bulk roton excitations of 4He in porous media
We examine the energetics of bulk and layer-roton excitations of 4He in
various porous medial such as aerogel, Geltech, or Vycor, in order to find out
what conclusions can be drawn from experiments on the energetics about the
physisorption mechanism. The energy of the layer-roton minimum depends
sensitively on the substrate strength, thus providing a mechanism for a direct
measurement of this quantity. On the other hand, bulk-like roton excitations
are largely independent of the interaction between the medium and the helium
atoms, but the dependence of their energy on the degree of filling reflects the
internal structure of the matrix and can reveal features of 4He at negative
pressures. While bulk-like rotons are very similar to their true bulk
counterparts, the layer modes are not in close relation to two-dimensional
rotons and should be regarded as a third, completely independent kind of
excitation
Low temperature phase diagram of condensed para-Hydrogen in two dimensions
Extensive Path Integral Monte Carlo simulations of condensed para-Hydrogen in
two dimensions at low temperature have been carried out. In the zero
temperature limit, the system is a crystal at equilibrium, with a triangular
lattice structure. No metastable liquid phase is observed, as the system
remains a solid down to the spinodal density, and breaks down into solid
clusters at lower densities. The equilibrium crystal is found to melt at a
temperature close to 7 K
Molecular hydrogen isotopes adsorbed on krypton-preplated graphite: Quantum Monte Carlo simulations
Adsorption of ortho-deuterium and para-hydrogen films on a graphite
substrate, pre-plated with a single atomic layer of krypton, is studied
theoretically by means of quantum Monte Carlo simulations at low temperature.
Our model explicitly includes substrate corrugation. Energetic and structural
properties of these adsorbed films are computed for a range of hydrogen
coverages. Thermodynamically stable adsorbed films are solid, with no clear
evidence of any liquid-like phase. Quantum exchanges of ortho-deuterium and
para-hydrogen are essentially absent in this system, down to zero temperature;
consequently, this system displays no superfluidity in this limit. Our
simulations provide evidence of a stable domain wall fluid at low temperature,
consistently with recent experimental observations.Comment: 7 pages, 7 figure
Melting of a p-H2 monolayer on a lithium substrate
Adsorption of para-hydrogen films on Alkali metals substrates at low
temperature is studied theoretically by means of Path Integral Monte Carlo
simulations. Realistic potentials are utilized to model the interaction between
two para-hydrogen molecules, as well as between a para-hydrogenmolecule and the
substrate, assumed smooth. Results show that adsorption of para-hydrogen on a
Lithium substrate, the most attractive among the Alkali, occurs through
completion of successive solid adlayers. Each layer has a two-dimensional
density approximatley equal 0.070 inverse square Angstroms. A solid
para-hydrogen monolayer displays a higher degree of confinement, in the
direction perpendicular to the substrate, than a monolayer Helium film, and has
a melting temperature of about 6.5 K. The other Alkali substrates are not
attractive enough to be wetted by molecular hydrogen at low temperature. No
evidence of a possible superfluid phase of para-hydrogen is seen in these
systems.Comment: Scales on the y-axis in Figs. 4,5 and 7 are off by a factor 2 in
published version; corrected her
Excitations in confined helium
We design models for helium in matrices like aerogel, Vycor or Geltech from a
manifestly microscopic point of view. For that purpose, we calculate the
dynamic structure function of 4He on Si substrates and between two Si walls as
a function of energy, momentum transfer, and the scattering angle. The
angle--averaged results are in good agreement with the neutron scattering data;
the remaining differences can be attributed to the simplified model used here
for the complex pore structure of the materials. A focus of the present work is
the detailed identification of coexisting layer modes and bulk--like
excitations, and, in the case of thick films, ripplon excitations. Involving
essentially two--dimensional motion of atoms, the layer modes are sensitive to
the scattering angle.Comment: Phys. Rev. B (2003, in press
Nonconventional magnetic phenomena in neodymium thin film
Neodymium is a remarkable active component in numerous magnetic alloys that
are used in various applications. However, the application of bare neodymium
thin film is limited due to the lack of information about its electrical and
magnetic properties. We report synergistic study of Nd thin film using
experimental and theoretical techniques of polarized neutron reflectometry,
magnetoresistance measurement and density functional theory. Unlike bulk Nd,
thin film specimen is a very poor electrical conductor. Also, as grown thin
film on silicon substrate does not exhibit any magnetism in zero field.
However, moderate inplane field application of = 1.2 T tends to induce weak
magnetism in the system at low temperature of 18 K, which coincides
with an unusual cross-over behavior in magnetoresistance. The study provides
important insight in the physical characteristics of Nd thin film that are
atypical for a magnetic system.Comment: 5 pages, 4 figure
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