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Deepak Dhar

Publications and source records attributed to Deepak Dhar.

9 recordsLinked to original sources
PubMed2006

Preserving quantum states using inverting pulses: a super-Zeno effect.

We construct an algorithm for suppressing the transitions of a quantum mechanical system, initially prepared in a subspace P of the full Hilbert space of the system, to outside this subspace by subjecting it to a sequence of unequally spaced short-duration pulses. Each pulse multiplies the amplitude of the vectors in the subspace by -1. The number of pulses required by the algorithm to limit the leakage probability to epsilon in time increases as T exp[square root log(T(2)/epsilon)], compared to T(2)epsilon(-1) in the standard quantum Zeno effect.

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PubMed2006

Probability distribution of residence times of grains in models of rice piles.

We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different rice pile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size L, the probabilities that the residence time at a site or the total residence time is greater than t, both decay as 1/t(ln t)x for L(omega) << t << exp(L(gamma)) where gamma is an exponent > or = 1, and values of x and omega in the two cases are different. In the Oslo rice pile model we find that the probability of the residence time T(i) at a site i being greater than or equal to t is a nonmonotonic function of L for a fixed t and does not obey simple scaling. For model in d dimensions, we show that the probability of minimum slope configuration in the steady state, for large L, varies as exp(-kappaL(d+2)) where kappa is a constant, and hence gamma=d+2.

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PubMed2005

Branched polymers on the Given-Mandelbrot family of fractals.

We study the average number A (n) per site of the number of different configurations of a branched polymer of n bonds on the Given-Mandelbrot family of fractals using exact real-space renormalization. Different members of the family are characterized by an integer parameter b , 2 < or = b < or = infinity . The fractal dimension varies from log(2) 3 to 2 as b is varied from 2 to infinity. We find that for all b > or = 3 , A (n) varies as lambda(n) exp (b n(psi)) where lambda and b are some constants, and 0 < psi < 1 . We determine the exponent psi, and the size exponent nu (average diameter of polymer varies as n(nu) ), exactly for all b , 3 < or = b < o r= infinity . This generalizes the earlier results of Knezevic and Vannimenus for b = 3 [Phys. Rev B 35, 4988 (1987)].

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PubMed2005

Convex lattice polygons of fixed area with perimeter-dependent weights.

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a critical exponent which does not change with t. Using heuristic arguments, we find that theta(conv) is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected nonuniversality of theta(conv) is traced to existence of sharp corners in the asymptotic shape of these polygons.

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PubMed2002

Generic sandpile models have directed percolation exponents.

We study sandpile models with stochastic toppling rules and having sticky grains so that with a nonzero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a small probability of particle loss at each toppling. Generically for the models with a preferred direction, the avalanche exponents are those of critical directed percolation clusters. For undirected models, avalanche exponents are those of directed percolation clusters in one higher dimension.

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PubMed2002

Adsorption and collapse transitions in a linear polymer chain near an attractive wall.

We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically from series expansion up to 19 sites of a self-attracting self-avoiding walk in three dimensions. In two dimensions, we calculate phase boundaries analytically in some cases for a partially directed model. Both the numerical and analytical results corroborate the proposed qualitative phase diagram.

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PubMed2002

Hysteresis in the random-field Ising model and bootstrap percolation.

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging L small star, filled increases as exp[exp(J/Delta)] in 2D, and as exp(exp[exp(J/Delta)]) in 3D, for disorder strength Delta much less than the exchange coupling J. For system size 1< infinity for both square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and h(coer) tends to J.

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PubMed2002

Probability distribution of the sizes of the largest erased loops in loop-erased random walks.

We have studied the probability distribution of the perimeter and the area of the kth largest erased loop in loop-erased random walks in two dimensions for k=1 to 3. For a random walk of N steps, for large N, the average value of the kth largest perimeter and area scales as N(5/8) and N, respectively. The behavior of the scaled distribution functions is determined for very large and very small arguments. We have used exact enumeration for N< or =20 to determine the probability that no loop of size greater than l is erased. We show that correlations between loops have to be taken into account to describe the average size of the kth largest erased loops. We propose a one-dimensional Levy walk model that takes care of these correlations. The simulations of this simpler model compare very well with the simulations of the original problem.

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