Theory of non-stationary activated rate processes : nonexponential relaxation kinetics

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features of non-Markovian Langevin dynamics with a fluctuating barrier. Making use of the Fokker-Planck description we calculate the barrier dynamics in the steady state and non-stationary regimes. The Kramers-Grote-Hynes reactive frequency has been computed in closed form in the steady state to illustrate the strong dependence of the dynamic coupling of the system with the relaxing modes. The influence of nonequilibrium excitation of the bath modes and its relaxation on the kinetics of activation of the system mode is demonstrated. We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong non-exponential relaxation kinetics of the reaction co-ordinate. The feature can be identified as a typical non-Markovian dynamical effect.Comment: Plain Latex, no figure, 31 pages, to appear in J. Chem. Phy

Lie algebraic noncommuting structures from reparametrisation symmetry

We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper \cite{sg}) that for some special choices of the reparametrisation parameter $\epsilon$, one can obtain space-space noncommuting structures which are Lie-algebraic in form even in the case of the relativistic free particle. The connection of these structures with the existing models in the literature is also briefly discussed. Further, there exists some values of $\epsilon$ for which the noncommutativity in the space-space sector can be made to vanish. As a matter of internal consistency of our approach, we also study the angular momentum algebra in details.Comment: 9 pages Latex, some references adde

Permittivity enhancement of aluminum oxide thin films with the addition of silver nanoparticles

doi:10.1063/1.2425010Multilayer reactive electron-beam evaporation of thin aluminum oxide layers with embedded silver nanoparticles (Ag-nps) has been used to create a dielectric thin film with an enhanced permittivity. The results show a frequency dependent increase of the dielectric constant κ. Overall stack κ of the control sample was found to be 7.7-7.4 in the 1 kHz-1 MHz range. This is in comparison with κ = 16.7-13.0 over the same frequency range in the sample with Ag-nps. Capacitance-voltage and conductance-voltage measurements indicate the presence of charge capture resulting from the Ag-nps. The authors attribute this dielectric constant enhancement to dipole and space charge polarization mechanisms.The authors thank M. Othman for ellipsometry measurements. They are also grateful for the funding provided by the National Science Foundation Grant No. ECS0223

Some fixed point theorems in partial metric spaces

Here we prove two fixed point theorems on partial metric space, which was defined by S. Matthews [8] in 1994. In the literature one can find fixed point theorems proved on such spaces by using Picard iteration schemes. Here our main ingredient is Cantor intersection type results.The first author is being supported by University Grants Commission’s (Regional office, Kolkata) Minor Research Project (letter no. F.PSW-032/11-12(ERO), dated 08.08.11) for this work.Publisher's Versio

Microscopic calculation of proton capture reactions in mass 60-80 region and its astrophysical implications

Microscopic optical potentials obtained by folding the DDM3Y interaction with the densities from Relativistic Mean Field approach have been utilized to evaluate S-factors of low-energy $(p,\gamma)$ reactions in mass 60-80 region and to compare with experiments. The Lagrangian density FSU Gold has been employed. Astrophysical rates for important proton capture reactions have been calculated to study the behaviour of rapid proton nucleosynthesis for waiting point nuclei with mass less than A=80