Set mapping reflection

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that L(P(omega_1)) satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that combinatorial principle Square(kappa) fails for all regular kappa > omega_1.Comment: 11 page

Spectral theorem for the Lindblad equation for quadratic open fermionic systems

The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly constructed for all eigenvalues. For eigenvalue zero we describe an algebraic procedure for constructing (possibly higher dimensional) spaces of (degenerate) non-equilibrium steady states.Comment: 19 pages, no figure

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

Modeling the Local Warm/Hot Bubble

In this paper we review the modeling of the Local Bubble (LB) with special emphasis on the progress we have made since the last major conference "The Local Bubble and Beyond (I)" held in Garching in 1997. Since then new insight was gained into the possible origin of the LB, with a moving group crossing its volume during the last 10 - 15 Myr being most likely responsible for creating a local cavity filled with hot recombining gas. Numerical high resolution 3D simulations of a supernova driven inhomogeneous interstellar medium show that we can reproduce both the extension of the LB and the OVI column density in absorption measured with FUSE for a LB age of 13.5 - 14.5 Myr. We further demonstrate that the LB evolves like an ordinary superbubble expanding into a density stratified medium by comparing analytical 2D Kompaneets solutions to NaI contours, representing the extension of the local cavity. These results suggest that LB blow-out into the Milky Way halo has occurred roughly 5 Myr ago.Comment: 8 pages, 3 figures, to appear in the proceedings of "The Local Bubble and Beyond II", Philadelphia, USA, April 21-24, 200

Asymptotic Entanglement and Lindblad Dynamics: a Perturbative Approach

We consider an open bipartite quantum system with dissipative Lindblad type dynamics. In order to study the entanglement of the stationary states, we develop a perturbative approach and apply it to the physically significant case when a purely dissipative perturbation is added to the unperturbed generator which by itself would produce reversible unitary dynamics.Comment: 15 page