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

κ\kappa-Minkowski and Snyder algebra from reparametrisation symmetry

Following our earlier work \cite{sunandan1, sunandan2}, we derive noncommuting phase-space structures which are combinations of both the $\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation symmetry of the recently proposed Lagrangian for a point particle \cite{subir} satisfying the exact Doubly Special Relativity dispersion relation in the Magueijo-Smolin framework.Comment: Accepted in Euro Physics Letter

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

Model Insensitive and Calibration Independent Method for Determination of the Downstream Neutral Hydrogen Density Through Ly-alpha Glow Observations

Our knowledge of the various heliospheric phenomena (location of the solar wind termination shock, heliopause configuration and very local interstellar medium parameters) is limited by uncertainties in the available heliospheric plasma models and by calibration uncertainties in the observing instruments. There is, thus, a strong motivation to develop model insensitive and calibration independent methods to reduce the uncertainties in the relevant heliospheric parameters. We have developed such a method to constrain the downstream neutral hydrogen density inside the heliospheric tail. In our approach we have taken advantage of the relative insensitivity of the downstream neutral hydrogen density profile to the specific plasma model adopted. We have also used the fact that the presence of an asymmetric neutral hydrogen cavity surrounding the sun, characteristic of all neutral densities models, results in a higher multiple scattering contribution to the observed glow in the downstream region than in the upstream region. This allows us to approximate the actual density profile with one which is spatially uniform for the purpose of calculating the downstream backscattered glow. Using different spatially constant density profiles, radiative transfer calculations are performed, and the radial dependence of the predicted glow is compared with the observed I/R dependence of Pioneer 10 UV data. Such a comparison bounds the large distance heliospheric neutral hydrogen density in the downstream direction to a value between 0.05 and 0.1/cc

Deformation Projected RMF Calculation for Cr and Fe nuclei in Hybrid Derivative Coupling Model

The ground state properties of even mass Cr and Fe isotopes are studied using the generalized hybrid derivative coupling model. The energy surface of each isotope is plotted as a function of the mass quadrupole moment. The neutron numbers N=20 and N=40 are seen to remain magic numbers but N= 28 and 50 are predicted to be non-magic. The neutron number N=70 turns out to be a magic number according to the present calculation. In all the isotopes studied the calculated binding energy values are less than those obtained from experiment while the deformation is in better agreement.Comment: To appear in Int. Jour. Mod. Phys.

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