arXiv subjects

Sanjib Sabhapandit

Publications and source records attributed to Sanjib Sabhapandit.

78 records · Page 5Linked to original sources

arXiv2007

Statistical properties of single-file diffusion front

Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are investigated. Exact as well as asymptotic results are provided for the probability density function of (a) the front-position, (b) the maximum of the front-positions, and (c) the first-passage time to a given position. The asymptotic laws for the front-position and the maximum front-position are found to be governed by the Fisher-Tippett-Gumbel extreme value statistics. The asymptotic properties of the first-passage time is dominated by a stretched-exponential tail in the distribution. The farness of the front with the rest of the system is investigated by considering (i) the gap from the front to the closest particle, and (ii) the density profile with respect to the front-position, and analytical results are provided for late time behaviors.

cond-mat.stat-mech↗

arXiv2006

Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size $t$. We compute the disorder average distributions of the local time, the inverse local time, the occupation time and the inverse occupation time, and show that in many cases disorder modifies the behavior drastically.

cond-mat.stat-mech↗

arXiv2005

Absence of jump discontinuity in the magnetization in quasi-one-dimensional random-field Ising models

We consider the zero-temperature random-field Ising model in the presence of an external field, on ladders and in one dimension with finite range interactions, for unbounded continuous distributions of random fields, and show that there is no jump discontinuity in the magnetizations for any quasi-one dimensional model. We show that the evolution of the system at an external field can be described by a stochastic matrix and the magnetization can be obtained using the eigenvector of the matrix corresponding to the eigenvalue one, which is continuous and differentiable function of the external field.

cond-mat.stat-mech↗

arXiv2002

Hysteresis and Avalanches in the Random Field Ising Model

In this thesis, we discuss nonequilibrium ferromagnetic random field Ising model (RFIM) with zero temperature Glauber single spin flip dynamics. We briefly review the hysteresis in ferromagnets and Barkhausen effect. We discuss some earlier results on the zero temperature RFIM. We also discuss some of the equilibrium properties of RFIM. We setup the generating function for the avalanche distribution for arbitrary distribution of the quenched random field on a Bethe lattice. We explicitly calculate the probability distribution of avalanches, for the for Bethe lattices with coordination numbers $z=2$ and 3, for the special case of a rectangular distribution of the random field. We analyse the self-consistent equations to determine the form of the avalanche distribution for some general unimodal continuous distributions of the random field. We derive the self-consistent equations for the magnetization on minor hysteresis loops on a Bethe lattice, when the external field is varying cyclically with decreasing magnitudes. We also discuss some properties of stable configurations, when the external field is varying. We study the 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 find nontrivial dependence of the coercive field on the coordination number of the lattice.

cond-mat.stat-mech↗

arXiv2002

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 $L^*$ increases as $exp(exp (J/Δ))$ in 2d, and as $exp(exp(exp(J/Δ)))$ in 3d, for disorder strength $Δ$ much less than the exchange coupling J. For system size $1 << L < L^*$, the coercive field $h_{coer}$ varies as $2J - Δ\ln \ln L$ for the square lattice, and as $2J - Δ\ln \ln \ln L$ on the cubic lattice. Its limiting value is 0 for L tending to infinity, both for square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and $h_{coer}$ tends to J.

cond-mat.stat-mech↗

arXiv2001

Distribution of Avalanche Sizes in the Hysteretic Response of Random Field Ising Model on a Bethe Lattice at Zero Temperature

We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of avalanche sizes s, as the external field increases from large negative to positive values. We solve these equations explicitly for a rectangular distribution of the random fields for a linear chain and the Bethe lattice of coordination number z=3, and show that in these cases, Prob(s) decreases exponentially with s for large s for all h on the hysteresis loop. We found that for z >3 and for small disorder, the magnetization shows a first order discontinuity for several continuous and unimodel distributions of random fields. The avalanche distribution Prob(s) varies as s^{-3/2} for large s near the discontinuity.

cond-mat.stat-mech↗