Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that, even without electric potential, the spectrum has positive measure if the magnetic field is a perturbation of a constant one.Comment: 17 page

Influence of anisotropic next-nearest-neighbor hopping on diagonal charge-striped phases

We consider the model of strongly-correlated system of electrons described by an extended Falicov-Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbor hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbor hopping anisotropy reduces the $\pi/2$-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbor hopping: the stripes are oriented in the direction of the weaker next-nearest-neighbor hopping.Comment: 9 pages, 3 figures, 1 tabl

LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices

We theoretically analyze Fermi-Bose mixtures consisting of light fermions and heavy bosons that are loaded into optical lattices (ignoring the trapping potential). To describe such mixtures, we consider the Fermi-Bose version of the Falicov-Kimball model on a periodic lattice. This model can be exactly mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature for all parameter space as long as the mixture is thermodynamically stable. We employ dynamical mean-field theory to investigate the evolution of the Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral moment sum rules for the retarded Green's function and self-energy, and use them to benchmark the accuracy of our numerical calculations, as well as to reduce the computational cost by exactly including the tails of infinite summations or products. We show how the occupancy of the bosons, single-particle many-body density of states for the fermions, momentum distribution, and the average kinetic energy evolve with temperature. We end by briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball model in ultracold atomic systems.Comment: 10 pages with 4 figure

Xenon ion propulsion for orbit transfer

For more than 30 years, NASA has conducted an ion propulsion program which has resulted in several experimental space flight demonstrations and the development of many supporting technologies. Technologies appropriate for geosynchronous stationkeeping, earth-orbit transfer missions, and interplanetary missions are defined and evaluated. The status of critical ion propulsion system elements is reviewed. Electron bombardment ion thrusters for primary propulsion have evolved to operate on xenon in the 5 to 10 kW power range. Thruster efficiencies of 0.7 and specific impulse values of 4000 s were documented. The baseline thruster currently under development by NASA LeRC includes ring-cusp magnetic field plasma containment and dished two-grid ion optics. Based on past experience and demonstrated simplifications, power processors for these thrusters should have approximately 500 parts, a mass of 40 kg, and an efficiency near 0.94. Thrust vector control, via individual thruster gimbals, is a mature technology. High pressure, gaseous xenon propellant storage and control schemes, using flight qualified hardware, result in propellant tankage fractions between 0.1 and 0.2. In-space and ground integration testing has demonstrated that ion propulsion systems can be successfully integrated with their host spacecraft. Ion propulsion system technologies are mature and can significantly enhance and/or enable a variety of missions in the nation's space propulsion program

On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.Comment: 29 pages, 9 figures submitted to Journal of Statistical Physics (2003