Influence functional approach to decoherence during Inflation

We show how the quantum to classical transition of the cosmological fluctuations produced during inflation can be described by means of the influence functional and the master equation. We split the inflaton field into the system-field (long-wavelength modes), and the environment, represented by its own short-wavelength modes. We compute the decoherence times for the system-field modes and compare them with the other time scales of the model.Comment: 6 pages, no figures. Contributed talk to the Second International Workshop DICE2004, Piombino, Ital

A Study of the Impact of the Phividec Industrial Estate

This article is a product of a nine-month training and application program implemented by the micro component of the Economic and Social Impact Analysis/Women in Development (ESIA/WID) and the Food Systems Program of the East-West Center Resource Systems Institute (RSI). Since the industrial estate has yet to be completed, this article presents an impact evaluation of the project based on its accomplishment on the basis of its expected full benefits. This is in the hope of providing a foundation for policy strengthening and alteration.industry sector, infrastructure, survey method, impact analysis

Morse index and multiplicity of min-max minimal hypersurfaces

The Min-max Theory for the area functional, started by Almgren in the early 1960s and greatly improved by Pitts in 1981, was left incomplete because it gave no Morse index estimate for the min-max minimal hypersurface. We advance the theory further and prove the first general Morse index bounds for minimal hypersurfaces produced by it. We also settle the multiplicity problem for the classical case of one-parameter sweepouts.Comment: Cambridge Journal of Mathematics, 4 (4), 463-511, 201

Existence of infinitely many minimal hypersurfaces in positive Ricci curvature

In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the area functional to prove this conjecture in the positive Ricci curvature setting. More precisely, we show that every compact Riemannian manifold with positive Ricci curvature and dimension at most seven contains infinitely many smooth, closed, embedded minimal hypersurfaces. In the last section we mention some open problems related with the geometry of these minimal hypersurfaces.Comment: 34 pages, to appear in Inventiones Mathematica

Correction to the geometric phase by structured environments: the onset of non-Markovian effects

We study the geometric phase of a two-level system under the presence of a structured environment, particularly analysing its correction with the ohmicity parameter $s$ and the onset of non-Markovianity. We firstly examine the system coupled to a set of harmonic oscillators and studied the decoherence factor as function of the environment's ohmicity parameter. Secondly, we propose the two-level system coupled to a non-equilibrium environment, and show that these environments display non-Markovian effects for all values of the ohmicity parameter. The geometric phase of the two-level system is therefore computed under the presence of both types of environment. The correction to the unitary geometric phase is analysed in both, Markovian and non-Markovian regimes. Under Markovian environments, the correction induced on the system's phase is mainly ruled by the coupling constant between the system and the environment, while in the non-Markovian regime, memory effects seem to trigger a significant correction to the unitary geometric phase. The result is significant to the quantum information processing based on the geometric phase in quantum open systemsComment: 7 figures. Accepted for publication in Phys. Rev. A. arXiv admin note: text overlap with arXiv:1303.493