A study of disordered systems with gain: Stochastic Amplification

A study of statistics of transmission and reflection from a random medium with stochastic amplification as opposed to coherent amplification is presented. It is found that the transmission coefficient $t$, for sample length $L$ less than the critical length $L_c$ grows exponentially with $L$. In the limit $L \to \infty$ transmission decays exponentially as \avg{lnt} = -L/\xi where $\xi$ is the localization length. In this limit reflection coefficient $r$ saturates to a fixed value which shows a monotonic increase as a function of strength of amplification $\alpha$. The stationary distribution of super-reflection coefficient agrees well with the analytical results obtained within the random phase approximation (RPA). Our model also exhibits the well known duality between absorption and amplification. We emphasize the major differences between coherent amplification and stochastic amplification where-ever appropriate.Comment: 7 pages RevTex, two column format, 9 eps figures included mpeg simulations at http://www.iopb.res.in/~joshi/mpg.htm

Dephasing of Aharonov-Bohm oscillations in a mesoscopic ring with a magnetic impurity

We present a detailed analysis of the Aharonov-Bohm interference oscillations manifested through transmission of an electron in a mesoscopic ring with a magnetic impurity atom inserted in one of its arms. The electron interacts with the impurity through the exchange interaction leading to exchange spin-flip scattering. Transmission in the spin-flipped and spin-unflipped channels are explicitly calculated. We show that the spin-flipper acts as a dephasor in spite of absence of any inelastic scattering. The spin-conductance (related to spin-polarized transmission coefficient) is asymmetric in the flux reversal as opposed to the two probe conductance which is symmetric under flux reversal.Comment: 4 pages RevTex, 6 figures, brief repor

Modelling of Stochastic Absorption in a Random Medium

We report a detailed and systematic study of wave propagation through a stochastic absorbing random medium. Stochastic absorption is modeled by introducing an attenuation constant per unit length $\alpha$ in the free propagation region of the one-dimensional disordered chain of delta function scatterers. The average value of the logarithm of transmission coefficient decreases linearly with the length of the sample. The localization length is given by $\xi ~ = ~ \xi_w \xi_\alpha / (\xi_w + \xi_\alpha)$, where $\xi_w$ and $\xi_\alpha$ are the localization lengths in the presence of only disorder and of only absorption respectively. Absorption does not introduce any additional reflection in the limit of large $\alpha$, i.e., reflection shows a monotonic decrease with $\alpha$ and tends to zero in the limit of $\alpha\to\infty$, in contrast to the behavior observed in case of coherent absorption. The stationary distribution of reflection coefficient agrees well with the analytical results obtained within random phase approximation (RPA) in a larger parameter space. We also emphasize the major differences between the results of stochastic and coherent absorption.Comment: 7 pages RevTex, 9 eps figures included, modified version of cond-mat/9909327, to appear in PRB, mpeg simulations at http://www.iopb.res.in/~joshi/mpg.htm

Quantum Stochastic Absorption

We report a detailed and systematic study of wave propagation through a stochastic absorbing random medium. Stochastic absorption is modeled by introducing an attenuation constant per unit length $\alpha$ in the free propagation region of the one-dimensional disordered chain of delta function scatterers. The average value of the logarithm of transmission coefficient decreases linearly with the length of the sample. The localization length is given by $\xi ~ = ~ \xi_w \xi_\alpha / (\xi_w + \xi_\alpha)$, where $\xi_w$ and $\xi_\alpha$ are the localization lengths in the presence of only disorder and of only absorption respectively. Absorption does not introduce any additional reflection in the limit of large $\alpha$, i.e., reflection shows a monotonic decrease with $\alpha$ and tends to zero in the limit of $\alpha\to\infty$, in contrast to the behavior observed in case of coherent absorption. The stationary distribution of reflection coefficient agrees well with the analytical results obtained within random phase approximation (RPA) in a larger parameter space. We also emphasize the major differences between the results of stochastic and coherent absorption.Comment: RevTex, 6 pages,2 column format, 9 .eps figures include

Loss of interference in an Aharonov-Bohm ring

We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.Comment: 4 pages, latex/revtex, 4 eps figures. Proceedings of CMDAYS2K, held at Guru Ghasidas University, Bilaspur, Chattisgarh, India, Aug 29-31, 2

Multi-frequency scatter broadening evolution of pulsars - I

We present multi-wavelength scatter broadening observations of 47 pulsars, made with the Giant Metre-wave Radio Telescope (GMRT), Ooty Radio Telescope (ORT) and Long Wavelength Array (LWA). The GMRT observations have been made in the phased array mode at 148, 234, and 610 MHz and the ORT observations at 327 MHz. The LWA data sets have been obtained from the LWA pulsar data archive. The broadening of each pulsar as a function of observing frequency provides the frequency scaling index, $\alpha$. The estimations of $\alpha$ have been obtained for 39 pulsars, which include entirely new estimates for 31 pulsars. This study increases the total sample of pulsars available with $\alpha$ estimates by $\sim$50\%. The overall distribution of $\alpha$ with the dispersion measure (DM) of pulsar shows interesting variations, which are consistent with the earlier studies. However, for a given value of DM a range of $\alpha$ values are observed, indicating the characteristic turbulence along each line of sight. For each pulsar, the estimated level of turbulence, $C^{2}_{n_e}$, has also been compared with $\alpha$ and DM. Additionally, we compare the distribution of $\alpha$ with the theoretically predicated model to infer the general characteristics of the ionized interstellar medium (ISM). Nearly 65\% of the pulsars show a flatter index (i.e., $\alpha < 4.4$) than that is expected from the Kolmogorov turbulence model. Moreover, the group of pulsars having flatter index is typically associated with an enhanced value of $C^{2}_{n_e}$ than those with steeper index.Comment: 13 pages, 4 figures, 3 tables. Accepted for publication in Ap