Pancharatnam and Berry Phases in Three-Level Photonic Systems

A theoretical analysis of Pancharatnam and Berry phases is made for biphoton three-level systems, which are produced via frequency degenerate co-linear spontaneous parametric down conversion (SPDC). The general theory of Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical phases are derived for the transformations produced by linear phase-converters. The problem of gauge invariance is treated along all the article

Emerging Markets for GM Foods: An Indian Perspective on Consumer Understanding and Willingness to Pay

This paper addresses the issues of consumer awareness, opinion, acceptance and willingness to pay for GM foods in the Indian market. A random utility approach is used to estimate a logit equation which indicates what factors affect the likelihood of consumption of non-GM and GM foods and whether or not consumers are willing to pay a premium for non-GM/GM foods. Data was generated through questionnaire survey which was administered to 602 respondents in the city of Ahmedabad and 110 respondents on internet. More than 90% of the respondents from the city survey did not know about GM foods. However, after informing them about the pros and cons of GM foods, more than 70% were willing to consume even if GM and non-GM foods were available for the same price. Ceteris paribus as the price difference between non-GM and GM food rose, people were more likely to consume GM foods. Likelihood of GM food consumption seemed to increase as one moved from very poor and not-so-poor income brackets to higher income brackets. Being a female or a joint family member increased the likelihood of choosing non-GM rice and edible oil. On an average, consumers were willing to pay 19.5% and 16.12% premiums for golden rice and GM edible oil, respectively. Overall, it appears that GM foods will be acceptable in the Indian market. However, consumer education societies, government ministries, and food companies may have to create awareness about the GM foods among Indian consumers.

Emerging Markets for GM Foods: A Study of Consumer's Willingness to Pay in India

A random utility approach is used to estimate logit equations which indicate what factors affect the likelihood of consumption of non-GM and GM foods, and, whether or not consumers are willing to pay a premium for non-GM/GM foods. Ceteris paribus as the price difference between non-GM and GM food rose, people were more likely to consume GM foods. Likelihood of GM food consumption was higher in the middle income brackets. Consumers were willing to pay an expected premium of 19.5% and 16.12% for golden rice and GM edible oil respectively. In case of chicken, consumers seemed to pay a very negligible premium for non-GM fed chicken. Overall, it appears that GM foods may be acceptable in the Indian market. However, basic awareness about the GM foods may have to be created among the consumers through government ministries, consumer interest groups, and biotech food-crop companies.GM Foods, Golden Rice, Bt cottonseed oil, GM fed chicken, Willingness to Pay, Random utility approach, Logit, India., Demand and Price Analysis, Food Consumption/Nutrition/Food Safety, Q13, D12,

Quantization and Corrections of Adiabatic Particle Transport in a Periodic Ratchet Potential

We study the transport of an overdamped particle adiabatically driven by an asymmetric potential which is periodic in both space and time. We develop an adiabatic perturbation theory after transforming the Fokker-Planck equation into a time-dependent hermitian problem, and reveal an analogy with quantum adiabatic particle transport. An analytical expression is obtained for the ensemble average of the particle velocity in terms of the Berry phase of the Bloch states. Its time average is shown to be quantized as a Chern number in the deterministic or tight-binding limit, with exponentially small corrections. In the opposite limit, where the thermal energy dominates the ratchet potential, a formula for the average velocity is also obtained, showing a second order dependence on the potential.Comment: 8 page

Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3?

Explicit Riemannian metrics with Euclidean signature and anti-self dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogenous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coordinates and parameters it can be the metric on a compact manifold. Then, by the theorem of Hitchin, it could be a class of metrics on $K3$, or on surfaces whose universal covering is $K3$.Comment: Misprints in eqs.(9-11) corrected. Submitted to Classical and Quantum Gravit

Spinor formulation of topologically massive gravity

In the framework of real 2-component spinors in three dimensional space-time we present a description of topologically massive gravity (TMG) in terms of differential forms with triad scalar coefficients. This is essentially a real version of the Newman-Penrose formalism in general relativity. A triad formulation of TMG was considered earlier by Hall, Morgan and Perjes, however, due to an unfortunate choice of signature some of the spinors underlying the Hall-Morgan-Perjes formalism are real, while others are pure imaginary. We obtain the basic geometrical identities as well as the TMG field equations including a cosmological constant for the appropriate signature. As an application of this formalism we discuss the Bianchi Type $VIII - IX$ exact solutions of TMG and point out that they are parallelizable manifolds. We also consider various re-identifications of these homogeneous spaces that result in black hole solutions of TMG.Comment: An expanded version of paper published in Classical and Quantum Gravity 12 (1995) 291

Resonant Coherent Phonon Spectroscopy of Single-Walled Carbon Nanotubes

Using femtosecond pump-probe spectroscopy with pulse shaping techniques, one can generate and detect coherent phonons in chirality-specific semiconducting single-walled carbon nanotubes. The signals are resonantly enhanced when the pump photon energy coincides with an interband exciton resonance, and analysis of such data provides a wealth of information on the chirality-dependence of light absorption, phonon generation, and phonon-induced band structure modulations. To explain our experimental results, we have developed a microscopic theory for the generation and detection of coherent phonons in single-walled carbon nanotubes using a tight-binding model for the electronic states and a valence force field model for the phonons. We find that the coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We compared our theoretical results with experimental results on mod 2 nanotubes and found that our model provides satisfactory overall trends in the relative strengths of the coherent phonon signal both within and between different mod 2 families. We also find that the coherent phonon intensities are considerably weaker in mod 1 nanotubes in comparison with mod~2 nanotubes, which is also in excellent agreement with experiment.Comment: 21 pages, 22 figure

A factorization of a super-conformal map

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.Comment: 21 page

Gravitational Chern-Simons Lagrangians and black hole entropy

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, we define a general procedure, valid in any odd dimensions both for purely gravitational CS terms and for mixed gauge-gravitational ones. The final formula is very similar to Wald's original formula valid for covariant actions, with a significant modification. Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.Comment: 39 page