Reduction of CM elliptic curves and modular function congruences

We study congruences of the form F(j(z)) | U(p) = G(j(z)) mod p, where U(p) is the p-th Hecke operator, j is the basic modular invariant 1/q+744+196884q+... for SL2(Z), and F,G are polynomials with integer coefficients. Using the interplay between singular (a.k.a. CM) j-invariants in characteristic zero and supersingular ones in characteristic p, we obtain such congruences in which F is the minimal polynomial of a CM j-invariant, and give a sufficient condition for G to be a constant polynomial in these congruences.Comment: 11 page

Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

On the basis of the antisymmetrized molecular dynamics (AMD) of wave packets for the quantum system, a novel model (called AMD-V) is constructed by the stochastic incorporation of the diffusion and the deformation of wave packets which is calculated by Vlasov equation without any restriction on the one-body distribution. In other words, the stochastic branching process in molecular dynamics is formulated so that the instantaneous time evolution of the averaged one-body distribution is essentially equivalent to the solution of Vlasov equation. Furthermore, as usual molecular dynamics, AMD-V keeps the many-body correlation and can naturally describe the fluctuation among many channels of the reaction. It is demonstrated that the newly introduced process of AMD-V has drastic effects in heavy ion collisions of 40Ca + 40Ca at 35 MeV/nucleon, especially on the fragmentation mechanism, and AMD-V reproduces the fragmentation data very well. Discussions are given on the interrelation among the frameworks of AMD, AMD-V and other microscopic models developed for the nuclear dynamics.Comment: 26 pages, LaTeX with revtex and epsf, embedded postscript figure

Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei

Antisymmetrized molecular dynamics (AMD) with quantum branching processes is reformulated so that it can be applicable to the collisions of heavy nuclei such as Au + Au multifragmentation reactions. The quantum branching process due to the wave packet diffusion effect is treated as a random term in a Langevin-type equation of motion, whose numerical treatment is much easier than the method of the previous papers. Furthermore a new approximation formula, called the triple-loop approximation, is introduced in order to evaluate the Hamiltonian in the equation of motion with much less computation time than the exact calculation. A calculation is performed for the Au + Au central collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde

High photon number path entanglement in the interference of spontaneously downconverted photon pairs with coherent laser light

We show that the quantum interference between downconverted photon pairs and photons from coherent laser light can produce a maximally path entangled N-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the 2-photon coherence of down-converted light into an almost optimal N-photon coherence.Comment: 5 pages, including 2 figures and 1 table, final version for publication as rapid communication in Phys. Rev.

Nucleon Flow and Fragment Flow in Heavy Ion Reactions

The collective flow of nucleons and that of fragments in the 12C + 12C reaction below 150 MeV/nucleon are calculated with the antisymmetrized version of molecular dynamics combined with the statistical decay calculation. Density dependent Gogny force is used as the effective interaction. The calculated balance energy is about 100 MeV/nucleon, which is close to the observed value. Below the balance energy, the absolute value of the fragment flow is larger than that of nucleon flow, which is also in accordance with data. The dependence of the flow on the stochastic collision cross section and its origin are discussed. All the results are naturally understood by introducing the concept of two components of flow: the flow of dynamically emitted nucleons and the flow of the nuclear matter which contributes to both the flow of fragments and the flow of nucleons due to the statistical decay.Comment: 20 pages, PostScript figures, LaTeX with REVTeX and EPSF, KUNS 121

Using single quantum states as spin filters to study spin polarization in ferromagnets

By measuring electron tunneling between a ferromagnet and individual energy levels in an aluminum quantum dot, we show how spin-resolved quantum states can be used as filters to determine spin-dependent tunneling rates. We also observe magnetic-field-dependent shifts in the magnet's electrochemical potential relative to the dot's energy levels. The shifts vary between samples and are generally smaller than expected from the magnet's spin-polarized density of states. We suggest that they are affected by field-dependent charge redistribution at the magnetic interface.Comment: 4 pages, 1 color figur

First- and Second Order Phase Transitions in the Holstein-Hubbard Model

We investigate metal-insulator transitions in the Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U. We also present results for the quasiparticle weight and the double-occupancy as function of U and g.Comment: 6 pages, 5 figure

Application of Multi-Input Multi-Output Feedback Control for F-16 Ventral Fin Buffet Alleviation Using Piezoelectric Actuators

Control of structural vibrations has been a popular topic. Use of MFC piezoelectric actuators and co-located sensors allows for an active rather than passive control method. The F-16 ventral fin is susceptible to buffet induced vibrations and is a perfect test structure for active vibration control for flight-testing. The research follows the previous ACTIVE FIN project and improves on the design by increasing the number of actuator layers, available actuator power, and using multi-input multi-output (MIMO) control algorithms. The research involved experimental identification of the ventral fin and its principle strain directions, selection of system components, determination of mathematical plant model, and design and test of control algorithms. The research resulted in a control system suitable for flight, a practical controller design process, and comparisons of different control algorithms to include single-input single-output (SISO) positive position feedback (PPF), multivariable PPF, two-input two-output linear quadratic Gaussian (LQG), and two-input fouroutput LQG. Controller effectiveness on target modes, actuator power consumption, and controller robustness were tested in the laboratory. The laboratory results showed that reductions of 7.4 dB, 17.7 dB, 15.7 dB and 3.2 dB in modes one, two, three, and four respectively were achieved using the MIMO LQG controller while maintaining sufficient gain and phase margins

Compatibility of localized wave packets and unrestricted single particle dynamics for cluster formation in nuclear collisions

Antisymmetrized molecular dynamics with quantum branching is generalized so as to allow finite time duration of the unrestricted coherent mean field propagation which is followed by the decoherence into wave packets. In this new model, the wave packet shrinking by the mean field propagation is respected as well as the diffusion, so that it predicts a one-body dynamics similar to that in mean field models. The shrinking effect is expected to change the diffusion property of nucleons in nuclear matter and the global one-body dynamics. The central \xenon+\tin collisions at 50 MeV/nucleon are calculated by the models with and without shrinking, and it is shown that the inclusion of the wave packet shrinking has a large effect on the multifragmentation in a big expanding system with a moderate expansion velocity.Comment: 16 pages, 7 figure