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

Spherical Dust Collapse in Higher Dimensions

We consider here the question if it is possible to recover cosmic censorship when a transition is made to higher dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear that in a generic higher dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes, on the nature of the initial data from which the collapse develops, is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.Comment: Revtex4, Title changed, To appear in Physical Review

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.Comment: 19 pages, To be published in the Raychaudhuri Volume, eds. Naresh Dadhich, Pankaj Joshi and Probir Ro

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

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

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