Centre for Cognitive Sciences

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  • Item
    Phonons in disordered Si-Ge alloys
    ( 1973-01-01) Srivastava, Vipin ; Joshi, S. K.
    The coherent-potential approximation for phonons in disordered binary alloys has been used to interpret the observed Raman spectra of the substitutionally disordered Si-Ge alloys. The spectral density function is calculated for the q→=0 optical phonons. © 1973 The American Physical Society.
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    Cluster effects in disordered alloys
    ( 1973-12-01) Srivastava, V. ; Joshi, S. K.
    Cluster effects are dealt with self-consistently in disordered alloys within the multiple scattering framework. Pairs are handled explicitly. The results are also shown to be compatible with the findings of the diagrammatic analysis and the mean field approach.
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    Short range order in disordered alloys
    ( 1977-01-01) Srivastava, V. ; Kumar, D. ; Joshi, S. K.
    Effect of short range order on the electronic density of states and localization in disordered alloys has been studied. Self-consistent pair-calculations have been performed on disordered binary alloys possessing cubic structure and short range order has been introduced in the averaging procedure. Promising agreement has been found with the qualitative arguments given by Lifshitz. © 1977.
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    NEW NUMERICAL RESULTS FOR ANDERSON LOCALISATION.
    ( 1977-01-01) Weaire, D. ; Srivastava, V.
    Calculations of the average inverse participation ratio by the method of Weaire and Williams have produced a number of new results. These include a revision of the critical value of diagonal disorder in three dimensions, and the first numerical results for localisation in the presence of off-diagonal disorder, and for localisation in lattices of dimension d greater than 3.
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    Numerical results for Anderson localisation in the presence of off-diagonal disorder
    ( 1977-01-01) Weaire, D. ; Srivastava, V.
    Numerical calculations of the inverse participation ratio have been performed for the diamond cubic lattice with nearest neighbour interactions, and both diagonal and off-diagonal disorder. We confirm the prediction of Economou and Antoniou that off-diagonal disorder cannot, per se, produce an Anderson transition, although it reduces the amount of diagonal disorder necessary for the transition. In the presence of off-diagonal disorder alone we do not detect any substantial localisation even in the wings of the band. © 1977.
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    On a recent theory for localisation in random lattices
    ( 1977-01-01) Srivastava, Vipin ; Kumar, Deepak ; Joshi, S. K.
    An attempt has been reported which avoids an approximation used in a method proposed by Licciardello and Economou to study the problem of localisation in random lattices. Contrary to expectation, our improved approximation leads to physically unreasonable results for percolation concentration. © 1977.
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    The Anderson localisation problem II. Some detailed numerical results
    ( 1977-12-01) Weaire, D. ; Srivastava, V.
    For pt.I see ibid., vol.10, p.1239 (1977). The method of Weaire and Williams is applied to the problem of Anderson localisation in two and three dimensions with careful attention to the time extrapolations involved and analysis of the dependence of results on the size of the samples used. In two dimensions, the conclusions are fully in accordance with previous numerical results. In three dimensions a much lower value of critical disorder is obtained than that tentatively advanced by Thouless (1974), resolving an apparent discrepancy between analytic theory and numerical calculations in this case.
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    Anderson localization in a model binary alloy
    ( 1978-01-01) Srivastava, Vipin ; Weaire, D.
    The equation-of-motion method is applied to a random binary alloy represented by a simple tight-binding Hamiltonian in the split-band limit. The results suggest that Anderson localization occurs well above the percolation threshold, which was not predicted by previous analytic studies. © 1978 The American Physical Society.
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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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    Diffusion on the Cayley tree
    ( 1979-01-01) Srivastava, Vipin ; Mookerjee, Abhijit ; Joshi, S. K.
    A method is proposed for calculating the average probability for an electron being localized at a site in a disordered Cayley-tree lattice with arbitrary connectivity. The numerical results reported for weak disorder exhibit some novel features in the behavior of localization length. © 1979 The American Physical Society.
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    Continuous time random walk along inequivalent states
    ( 1981-12-01) Chaturvedi, M. ; Srivastava, V.
    A generalisation of the continuous time random walk (CTRW) approach for a system consisting of inequivalent states is presented. The new CTRW equation is found to bear the same structure as that of the CTRW equation for equivalent states, but the parameters have modified forms and meanings. In the earlier approaches the hopping time distribution function was taken to be same for all states, whereas in our generalisation this function is different for different states. Because of the nature of the distribution function, the authors have introduced the probability that the carrier can remain unmoved on a state due to the particular nature of that state. They have generalised the CTRW approach in the situations: (a) where the hopping time distribution is a function of both space and time; and (b) in which the space and time parts of the hopping time distribution function are uncorrelated, i.e. the decoupled case. In the latter situation, the time part of the function is not rigorously space independent in the sense that it depends upon the nature of the state on which the carrier is situated at an instant.
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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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    Localisation and marginal dimensionality
    ( 1982-12-01) Srivastava, V. ; Chaturvedi, M.
    The renormalised perturbation series (RPS) of self-energy is transformed into a simple continued fraction through a rearrangement procedure that incorporates into the denominators of the continued fraction all the contributions from closed polygonal paths. Convergence of RPS implies the convergence of the continued fraction. This results is used to prove that apart from one dimension no other marginal dimension exists for Anderson localisation in the sense of absence of either extended states or localised states.
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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
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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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    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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    New exponent in self-avoiding walks
    ( 1984-06-01) srivastava, Vipin
    A new exponent is reported in the problem of non-intersecting self-avoiding random walks. It is connected with the asymptotic behaviour of the growth of number of such walks. The value of the exponent is found to be nearly 0.90 for all two dimensional and nearly 0.96 for all three dimensional, lattices studied here. It approaches the value 1.0 assymptotically as the dimensionality approaches infinity. © 1984 Springer-Verlag.
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    IS d equals 2 A MARGINAL DIMENSION FOR LOCALIZATION?
    ( 1984-12-01) Srivastava, Vipin
    The renormalized perturbation series (RPS) for self energy is transformed into a simple continued fraction using a rearrangement procedure that dumps into the denominators of the continued fraction all the contributions from closed polygonal paths. Convergence of RPS implies the convergence of the continued fraction. This is used to prove that d equals 2 is not the lower marginal dimension for localization.
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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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    Superconducting Tc enhancement in weakly disordered Ge-covered tin films
    ( 1985-01-01) Parashar, R. S. ; Srivastava, Vipin
    We report on the variation of the superconducting transition temperature with the electrical resistance ratio in weakly disordered Ge-covered tin films deposited at room temperature. The normal-state sheet resistance RN- varied between 0.2