5,024 research outputs found
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
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