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

A new class of composition operators

A new class of composition operators Pϕ:H2(T)→H2(T), with ϕ:T→D¯ is introduced. Sufficient conditions on ϕ for Pϕ to be bounded and Hilbert-Schmidt are obtained. Properties of Pϕ with ϕ(eit)=aeit+be−it for different values of the parameters a and b have been investigated. This paper concludes with a discussion on the compactness of Pϕ

Quasi-static remanence as a generic-feature of spin-canting in Dzyaloshinskii-Moriya Interaction driven canted-antiferromagnets

We consistently observe a unique pattern in remanence in a number of canted-antiferromagnets (AFM) and piezomagnets. A part of the remanence is $\textit{quasi-static}$ in nature and vanishes above a critical magnetic field. Present work is devoted to exploring this $\textit{quasi-static}$ remanence ($\mu$) in a series of isostructural canted-AFMs and piezomagnets that possess progressively increasing N\'eel temperature ($T{_N}$). Comprehensive investigation of remanence as a function of $\textit{magnetic-field}$ and $\textit{time}$ in CoCO$_{3}$, NiCO$_{3}$ and MnCO$_{3}$ reveals that the magnitude of $\mu$ increases with decreasing $T{_N}$, but the stability with time is higher in the samples with higher $T{_N}$. Further to this, all three carbonates exhibit a universal scaling in $\mu$, which relates to the concurrent phenomenon of piezomagnetism. Overall, these data not only establish that the observation of $\textit{quasi-static}$ remanence with $\textit{counter-intuitive}$ magnetic-field dependence can serve as a foot-print for spin-canted systems, but also confirms that simple remanence measurements, using SQUID magnetometry, can provide insights about the extent of spin canting - a non trivial parameter to determine. In addition, these data suggest that the functional form of $\mu$ with $\textit{magnetic-field}$ and $\textit{time}$ may hold key to isolate Dzyaloshinskii Moriya Interaction driven spin-canted systems from Single Ion Anisotropy driven ones. We also demonstrate the existence of $\mu$ by tracking specific peaks in neutron diffraction data, acquired in remnant state in CoCO$_{3}$

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

Performance of summer sunflower (Helianthus annuus L.) hybrids under different nutrient management practices in coastal Odisha

The field experiment was conducted at Department of Agronomy, College of Agriculture, OUAT, Bhubaneswar during summer 2014 to find out appropriate hybrids and nutrient management practices for summer sunflower. Application of recommended dose of Fertiliser(RDF) i.e. 60-80- 60 kg N, P2O5-K2O ha -1 + ZnSO4 @ 25 kg ha -1 recorded the maximum capitulum diameter (15.60cm), seed yield (2.17 t ha -1 ), stover yield (4.88 t ha -1 ) and oil yield (0.91 t ha -1 ), while application of RDF + Boron@ 1 kg ha-1 recorded the highest number of total seed (970) and filled seed per capitulum (890) with the lowest unfilled seed (80) and sterility percentage (9.0%). The hybrid ‘Super-48’ recorded the highest seed and oil yield of 2.17 and 0.91 t ha -1 , respectively, at recommended dose of fertiliser + ZnSO4 @ 25 kg ha -1 . Experiment was conducted in evaluating the new hybrids in addition to evaluate the response of variety to different nutrient management practices

Chaos in Time Dependent Variational Approximations to Quantum Dynamics

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos correcte