Quantum noise-induced chaotic oscillations

We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.Comment: minor corrections, new references adde

The Hong Kong Declaration and Agriculture: Implications for Bangladesh

This paper reviews the developments in WTO negotiation on agriculture in the light of the Hong Kong Ministerial Declaration. It has critically analysed the decisions and negotiating proposals adopted through the Declaration. The paper has also analysed possible impacts of the adopted decisions and proposals for Bangladesh’s agriculture sector and its economy. Potential impacts are measured in terms of reduction in tariff, domestic support and export subsidy. More importantly, the paper has quantified potential impacts of agricultural trade liberalisation under Doha Round negotiations on prices and welfare gains, production, consumption and trade of agricultural commodities in Bangladesh. Based on the research findings, the paper has suggested some negotiating strategies for Bangladesh to be pursued in the on-going WTO negotiations on agriculture.Agriculture, WTO, Hong Kong Ministerial, Bangladesh

The Hong Kong Declaration and Agriculture - Implications for Bangladesh

This paper reviews the developments in WTO negotiation on agriculture in the light of the Hong Kong Ministerial Declaration. It has critically analysed the decisions and negotiating proposals adopted through the Declaration. The paper has also analysed possible impacts of the adopted decisions and proposals for Bangladeshs agriculture sector and its economy. Potential impacts are measured in terms of reduction in tariff, domestic support and export subsidy. More importantly, the paper has quantified potential impacts of agricultural trade liberalisation under Doha Round negotiations on prices and welfare gains, production, consumption and trade of agricultural commodities in Bangladesh. Based on the research findings, the paper has suggested some negotiating strategies for Bangladesh to be pursued in the on-going WTO negotiations on agriculture.Bangladesh, trade, Hong Kong Declaration, WTO, agriculture

Numerical simulation of transmission coefficient using c-number Langevin equation

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik \textit{et al}, J. Chem. Phys. {\bf 119}, 680 (2003); Banerjee \textit{et al}, Phys. Rev. E {\bf 65}, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the $T^2$ enhancement of the rate at low temperatures and other related features of temporal behaviour of the transmission coefficient over a range of temperature down to absolute zero, noise correlation and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order

Noise correlation-induced splitting of Kramers' escape rate from a metastable state

A correlation between two noise processes driving the thermally activated particles in a symmetric triple well potential, may cause a symmetry breaking and a difference in relative stability of the two side wells with respect to the middle one. This leads to an asymmetric localization of population and splitting of Kramers' rate of escape from the middle well, ensuring a preferential distribution of the products in the course of a parallel reaction

Quantum Kramers' equation for energy diffusion and barrier crossing dynamics in the low friction regime

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers' equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers' equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.Comment: 26 pages, RevTe

Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\it true probability distribution functions} and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermal activated processes and tunneling.Comment: RevTex, 18 pages, 2 figures; Minor corrections; To appear in Phys. Rev.