arXiv subjects

Pratap Kumar Das

Publications and source records attributed to Pratap Kumar Das.

5 recordsLinked to original sources

arXiv2006

Modelling temporal and spatial features of collaboration network

The collaboration network is an example of a social network which has both non-trivial temporal and spatial dependence. Based on the observations of collaborations in Physical Review Letters, a model of collaboration network is proposed which correctly reproduces the time evolution of the link length distributions, clustering coefficients, degree distributions and assortative property of real data to a large extent.

physics.soc-ph↗

arXiv2006

Time evolution of link length distribution in PRL collaboration network

An important aspect of a Euclidean network is its link length distribution, studied in a few real networks so far. We compute the distribution of the link lengths between collaborators whose papers appear in the PhysicalReview Letters (PRL) in several years within a range of four decades. The distribution is non-monotonic; there is a peak at nearest neighbour distances followed by a sharp fall and a subsequent rise at larger distances. The behaviour of the statistical properties of the distribution with time indicates that collaborations might become distance independent in about thirty to forty years.

physics.soc-ph↗

arXiv2005

Zero temperature dynamics of Ising model on a densely connected small world network

The zero temperature quenching dynamics of the ferromagnetic Ising model on a densely connected small world network is studied where long range bonds are added randomly with a finite probability $p$. We find that in contrast to the sparsely connected networks and random graph, there is no freezing and an initial random configuration of the spins reaches the equilibrium configuration within a very few Monte Carlo time steps in the thermodynamic limit for any $p \ne 0$. The residual energy and the number of spins flipped at any time shows an exponential relaxation to equilibrium. The persistence probability is also studied and it shows a saturation within a few time steps, the saturation value being 0.5 in the thermodynamic limit. These results are explained in the light of the topological properties of the network which is highly clustered and has a novel small world behaviour.

cond-mat.stat-mech↗

arXiv2005

Dynamical frustration in ANNNI model and annealing

Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI) model fails to bring it to its ground state for a certain range of values of the frustration parameter $κ$, the ratio of the next nearest neighbour antiferromagnetic interaction strength to the nearest neighbour one. We apply several annealing methods, both classical and quantum, and observe that the behaviour of the residual energy and the order parameter depends on the value of $κ$ strongly. Classical or thermal annealing is found to be adequate for small values of $κ$. However, neither classical nor quantum annealing is effective at values of $κ$ close to the fully frustrated point $κ=0.5$, where the residual energy shows a very slow algebraic decay with the number of MCS.

cond-mat.stat-mech↗

arXiv2004

Probability distribution of persistent spins in a Ising chain

We study the probability distribution $Q(n,t)$ of $n(t)$, the fraction of spins unflipped till time $t$, in a Ising chain with ferromagnetic interactions. The distribution shows a peak at $n=n_{max}$ and in general is non-Gaussian and asymmetric in nature. However for $n>n_{max}$ it shows a Gaussian decay. A data collapse can be obtained when $Q(n,t)/L^α$ versus $(n-n_{max})L^β$ is plotted with $α\sim 0.45$ and $β\sim 0.6$. Interestingly, $n_{max}(t)$ shows a different behaviour compared to $ = P(t)$, the persistence probability which follows the well-known behaviour $P(t)\sim t^{-θ}$. A quantitative estimate of the asymmetry and non-Gaussian nature of $Q(n,t)$ is made by calculating its skewness and kurtosis.

cond-mat.stat-mech↗