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

Gaussian resolutions for equilibrium density matrices

A Gaussian resolution method for the computation of equilibrium density matrices rho(T) for a general multidimensional quantum problem is presented. The variational principle applied to the ``imaginary time'' Schroedinger equation provides the equations of motion for Gaussians in a resolution of rho(T) described by their width matrix, center and scale factor, all treated as dynamical variables. The method is computationally very inexpensive, has favorable scaling with the system size and is surprisingly accurate in a wide temperature range, even for cases involving quantum tunneling. Incorporation of symmetry constraints, such as reflection or particle statistics, is also discussed.Comment: 4 page

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

Forage Production in Peach Based Hortipastoral System in Indian Himalaya

The North West Himalayan region (NWHR) exhibits a great diversity in geology, physiography, climate, socio-ecology and land use pattern and supports vast livestock population. The annual average rainfall varies from 80 mm in Ladakh to over 2000 mm in some parts of Himachal Pradesh and Uttarakhand. Livestock rearing is an integral part of hill agriculture. The huge animal population (190 lakh) and poor fodder availability (30 to 40 % of the requirement) has widen the gap between demand and supply of forage crops in the region. The area under permanent pasture and grasslands in NWHR is said to be of 15.8 lakh ha and a major portion of it is located in Himachal Pradesh (HP). Considerable area is under grazing lands and but on the whole their productivity (quantity and quality-wise) is rather poor and is continuously deteriorating. The availability of green grasses during winter season is practically nil due to severe winter and burning of forest (Bisht and Yadav, 2014). Thus, livestock is facing acute nutritional stress due to shortage of nutritional fodder and high cost of concentrates. The commonly preferred horticultural based agro-forestry systems are agri-horticulture, silvi-horticulture and silvipastoral in the NWHR. Various studies showed that peach (Prunus persica L.) which belong to family Rosaceae can be intercropped with crops and grasses in Himalayan region. Turmeric performed better than ginger in the peach garden (Arora and Mohan, 1986). The perennial vegetation have been the primary source to rejuvenate productivity of land through recycling of nutrients and make soil physico-chemical properties favorable for plant growth. Farming system approach integrating all the components viz., soil-plant-fodder-animal management is necessary for the economic well being of the inhabitants. Hence, it is suggested to develop hortipastoral systems/models by introducing pasture and foliage component under fruit trees so as to provide nutritious green forage and foliage (Pathak and Roy, 1994) to animals for getting higher production from unit of land in rainfed areas. Hortipastoral system, where in the inter spaces between fruit trees species are utilized for cultivation of grasses and grass legume mixtures. Winter grasses i.e., Perennial rye, Tall fescue, Grassland manava and Hima are grown in Sikkim, J&K, HP, Nilgiri hills and Kumaon and Garhwal hills of Uttaranchal. Under irrigated conditions it can also be grown successfully in subtropical region as winter forage. These grasses are extremely resistant to cold and frost, a good crop can be raised between 1800 to 2500 m altitudes, but in mid hills its cultivation is feasible under irrigated condition. Hortipastoral is a fodder production system to meet the acute shortage of fodder, to improve the soil and to increase the farmer’s income. This will combine horticultural trees, grasses and use of wasteland for fodder production. Therefore, the production techniques for ensuring green fodder supply during winter months, and total fodder supply for the larger period of the year by adoption of hortipastoral system with improved grass species needs to be exploited