Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $\lambda$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,\lambda,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $\zeta = \hbar^{\alpha}\lambda^{\beta}D^{\gamma}$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.Comment: Submitte

Stabilizing an Attractive Bose-Einstein Condensate by Driving a Surface Collective Mode

Bose-Einstein condensates of $^7$Li have been limited in number due to attractive interatomic interactions. Beyond this number, the condensate undergoes collective collapse. We study theoretically the effect of driving low-lying collective modes of the condensate by a weak asymmetric sinusoidally time-dependent field. We find that driving the radial breathing mode further destabilizes the condensate, while excitation of the quadrupolar surface mode causes the condensate to become more stable by imparting quasi-angular momentum to it. We show that a significantly larger number of atoms may occupy the condensate, which can then be sustained almost indefinitely. All effects are predicted to be clearly visible in experiments and efforts are under way for their experimental realization.Comment: 4 ReVTeX pages + 2 postscript figure

Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions

Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and classical time-evolving distribution functions are exposed by both analytical and numerical means. The quantum-classical correspondence of low-order statistical moments is also studied. The results shed considerable light on quantum-classical correspondence.Comment: 16 pages, 5 figures, to appear in Physical Review

Entropy and Wigner Functions

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functionsComment: 18 page

Bhat (Black Soybean): A traditional legume with high nutritional and nutraceutical properties from NW Himalayan region of India

307-319Bhat (black soybean) under the genus Glycine, is cultivated for food, fodder and medicinal uses by rural communities in Asia particularly, in China, Japan, Korea, Indonesia and India. In the Himalayan region of India, this legume is not only an integral part of a climate resilient farming system but also finds place in ethnodietary recipes and fondly consumed as a pulse. Black soybean ensures both food and nutritional security in hills where nutritional deficiencies are in abundance among rural, tribal and backward population engaged in subsistence farming in marginal rainfed terrains. Cultivation of black soybean is less capital intensive. Its ability to survive under harsh conditions particularly, in the event of failure of rain, makes it a better choice than other competitive crops grown during rainy season. Despite its enormous potentials, the legume has not gained the popularity in India and presently, area under this valuable legume is confined to North Himalayan hill region and scattered pockets of central India. Its high nutritive value, remedial and health promoting effects due to presence of various bioactive compounds make this legume an excellent functional food. Present review summarises the potential role of black soybean for human nutrition and health benefits