Centre for Cognitive Sciences

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Browsing Centre for Cognitive Sciences by Author "Chaturvedi, Meena"
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    Cluster approaches to random alloys: An appraisal
    ( 1978-12-01) Srivastava, Vipin ; Chaturvedi, Meena ; Joshi, S. K.
    Some of the cluster extensions of the coherent potential approximation (CPA) based on the effective medium theory have been critically studied with respect to the decoupling schemes involved in them. Their computational tractability has been examined and it has been found that the self-consistent calculations in three-dimensional systems are immensely difficult to perform. A self-consistent calculation has been reported for simple cubic lattices with diagonal and off-diagonal disorder using a pair-CPA method. A significant finding of the paper is that it has been shown that non-analyticities are a general feature of extensions of CPA within multiple scattering framework. The non-analyticities were reported several times but a general proof of their existence was not noticed. It was also believed that the so-called molecular-CPA is analytic, this has been shown to be wrong here. The density of states results with off-diagonal randomness have been qualitatively understood to yield some information about the influence of off-diagonal randomness on Anderson localisation of an electron. © 1977 Indian Academy of Sciences.
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    Generalised master equation of random walk in a random medium
    ( 1982-01-01) Srivastava, Vipin ; Chaturvedi, Meena
    A generalised formulation of continuous-time random-walks is introduced to study excitation transport in disordered systems containing permanent traps (the localised states). Its exact equivalence with the generalised master equation is established. The exact generalised transport equation obtained has been shown to reduce under special conditions to other random walk equations known in the literature. © 1982 Springer-Verlag.
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    New scaling results in quantum percolation
    ( 1984-12-01) Srivastava, Vipin ; Chaturvedi, Meena
    Computer simulations are reported for the average number of lattice sites falling under a localized wave function as a function of concentration for a model binary system with "infinite disorder." Novel structures are found near classical and quantum percolation thresholds which are explained using scaling arguments. It is also pointed out that extended states may appear even at infinite disorder in two-dimensional binary systems.
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    Random walk theory for dispersive transport in random media
    ( 1983-01-01) Srivastava, Vipin ; Chaturvedi, Meena
    A continuous-time random-walk theory is developed to study dispersive transport in disordered glassy systems containing conducting states and traps distributed randomly in space. The mechanism giving rise to the dispersive nature of transport and the frequency dependent response of the system to the a.c. field has been discussed. Non existence of minimum metallic conductivity has been argued to be one of the major consequences of the dispersive transport. © 1983.
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    Random‐walk theory for localization
    ( 1983-01-01) Chaturvedi, Meena ; Srivastava, Vipin
    A continuous‐time random‐walk theory has been developed for Anderson localization. On a continuous time scale random walks are performed along extended (i.e., propagating) and localized (i.e., trap) states. Complete information of disorder is contained in a distribution function called “hopping time distribution function” ψnm(t), which gives the probability per unit time for transition from state m to state n in time t. The “stay‐put” probability 𝒫(t = ∞), which is the probability to rediscover an excitation at a site “0” at time t = ∞ if it was there at t = 0, is obtained in terms of ψnm(t). Appropriate forms for ψnm(t) are constructed which are in conformity with the photoconductivity experiments on dispersive transport, and 𝒫(∞) are calculated. The results indicate that the entire spectrum consists of three regimes, namely, those of (i) “diffusion,” (ii) “weak diffusion,” and (iii) “no diffusion,” which, respectively, designate the extension, the power‐law localization, and the exponential localization of states. The results also shed light on the question of “continuous or discontinuous (?)” transition across the mobility edge. Copyright © 1983 John Wiley & Sons, Inc.
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    Studies on Quantum Percolation
    ( 1983-01-01) Chaturvedi, Meena ; Srivastava, Vipin
    Studies on the localisation in binary alloys (commonly termed as ‘quantum percolation’ problem) are reviewed highlighting the special features that this simple model has and which are absent in other models — the most prominent among them being the existence of extended states at infinite disorder. Some new scaling arguments are also reported that enable to predict qualitatively the behaviour of the participation ratio as function of concentration of one of the constituents of the alloy. These are substantiated by numerical simulation results. After summarising all'important approaches and their results, one of the important conclusions drawn is that in two‐dimensional binary alloys not all states are localised at any disorder, contrary to a recent belief. Copyright © 1983 WILEY‐VCH Verlag GmbH & Co. KGaA