A Formalization of Polytime Functions

We present a deep embedding of Bellantoni and Cook's syntactic characterization of polytime functions. We prove formally that it is correct and complete with respect to the original characterization by Cobham that required a bound to be proved manually. Compared to the paper proof by Bellantoni and Cook, we have been careful in making our proof fully contructive so that we obtain more precise bounding polynomials and more efficient translations between the two characterizations. Another difference is that we consider functions on bitstrings instead of functions on positive integers. This latter change is motivated by the application of our formalization in the context of formal security proofs in cryptography. Based on our core formalization, we have started developing a library of polytime functions that can be reused to build more complex ones.Comment: 13 page

Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions

When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behaviours at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.Comment: 4 pages, 3 figures; v2: added scaling theory; v3: published versio

Outflows in Infrared-Luminous Starbursts at z < 0.5. II. Analysis and Discussion

We have performed an absorption-line survey of outflowing gas in 78 starburst-dominated, infrared-luminous galaxies. This is the largest study of superwinds at z < 3. Superwinds are found in almost all infrared-luminous galaxies, and changes in detection rate with SFR--winds are found twice as often in ultraluminous infrared galaxies (ULIRGs) as in less-luminous galaxies--reflect different wind geometries. The maximum velocities we measure are 600 km/s, though most of the outflowing gas has lower velocities (100-200 km/s). (One galaxy has velocities exceeding 1000 km/s.) Velocities in LINERs are higher than in HII galaxies, and outflowing ionized gas often has higher velocities than the neutral gas. Wind properties (velocity, mass, momentum, and energy) scale with galaxy properties (SFR, luminosity, and galaxy mass), consistent with ram-pressure driving of the wind. Wind properties increase strongly with increasing galactic mass, contrary to expectation. These correlations flatten at high SFR (> 10-100 M_sun/yr), luminosities, and masses. This saturation is due to a lack of gas remaining in the wind's path, a common neutral gas terminal velocity, and/or a decrease in the efficiency of thermalization of the supernovae energy. It means that mass entrainment efficiency, rather than remaining constant, declines in galaxies with SFR > 10 M_sun/yr and M_K < -24. Half of our sample consists of ULIRGs, which host as much as half of the star formation in the universe at z > 1. The powerful, ubiquitous winds we observe in these galaxies imply that superwinds in massive galaxies at redshifts above unity play an important role in the evolution of galaxies and the intergalactic medium.Comment: 68 pages, 20 figures in AASTeX preprint style; to appear in September issue of ApJS; Figure 17 replaced with correct versio