Non-commutative Bloch theory

For differential operators which are invariant under the action of an abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a non-commutative Bloch theory for elliptic operators on Hilbert C*-modules. It relates properties of C*-algebras to spectral properties of module operators such as band structure, weak genericity of cantor spectra, and absence of discrete spectrum. It applies e.g. to differential operators invariant under a projective group action, such as Schroedinger, Dirac and Pauli operators with periodic magnetic field, as well as to discrete models, such as the almost Matthieu equation and the quantum pendulum.Comment: 37 pages, 2 figure

Low power arcjet thruster pulse ignition

An investigation of the pulse ignition characteristics of a 1 kW class arcjet using an inductive energy storage pulse generator with a pulse width modulated power converter identified several thruster and pulse generator parameters that influence breakdown voltage including pulse generator rate of voltage rise. This work was conducted with an arcjet tested on hydrogen-nitrogen gas mixtures to simulate fully decomposed hydrazine. Over all ranges of thruster and pulser parameters investigated, the mean breakdown voltages varied from 1.4 to 2.7 kV. Ignition tests at elevated thruster temperatures under certain conditions revealed occasional breakdowns to thruster voltages higher than the power converter output voltage. These post breakdown discharges sometimes failed to transition to the lower voltage arc discharge mode and the thruster would not ignite. Under the same conditions, a transition to the arc mode would occur for a subsequent pulse and the thruster would ignite. An automated 11 600 cycle starting and transition to steady state test demonstrated ignition on the first pulse and required application of a second pulse only two times to initiate breakdown

Proof of phase separation in the binary-alloy problem: the one-dimensional spinless Falicov-Kimball model

The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively equal to $\frac{p}{q}$, $\frac{p_i}{q}$, with $p$ relatively prime to $q$ and $\frac{p_i}{q}$ close enough to $\frac{1}{2}$, we find that in the ground state the ion configuration has period $q$. The situation is analogous to the Peierls instability where the usual arguments predict a period-$q$ state that produces a gap at the Fermi level and is insulating. However for $\frac{p_i}{q}$ far enough from $\frac{1}{2}$, this phase becomes unstable against phase separation. The ground state is a mixture of a period-$q$ ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these new results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from $\frac{1}{2}$.Comment: 22 pages, typeset in ReVTeX and one encapsulated postscript file embedded in the text with eps

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

Results from a Second RXTE Observation of the Coma Cluster

The RXTE satellite observed the Coma cluster for 177 ksec during November and December 2000, a second observation motivated by the intriguing results from the first 87 ksec observation in 1996. Analysis of the new dataset confirms that thermal emission from isothermal gas does not provide a good fit to the spectral distribution of the emission from the inner 1 degree radial region. While the observed spectrum may be fit by emission from gas with a substantial temperature gradient, it is more likely that the emission includes also a secondary non-thermal component. If so, non-thermal emission comprises ~8% of the total 4--20 keV flux. Interpreting this emission as due to Compton scattering of relativistic electrons (which produce the known extended radio emission) by the cosmic microwave background radiation, we determine that the mean, volume-averaged magnetic field in the central region of Coma is B = 0.1-0.3 microgauss.Comment: 10 pages, 1 figure; APJ, in pres

Nursing Home Quality as a Public Good

There has been much debate among economists about whether nursing home quality is a public good across Medicaid and private-pay patients within a common facility. However, there has been only limited empirical work addressing this issue. Using a unique individual level panel of residents of nursing homes from seven states, we exploit both within-facility and within-patient variation in payer source and quality to examine this issue. We also test the robustness of these results across states with different Medicaid and private-pay rate differentials. Across our various identification strategies, the results generally support the idea that quality is a public good within nursing homes. That is, within a common nursing home, there is very little evidence to suggest that Medicaid-funded residents receive consistently lower quality care relative to their private-paying counterparts.