arXiv subjects

Anjan Kumar Chandra

Publications and source records attributed to Anjan Kumar Chandra.

22 records · Page 2Linked to original sources

arXiv2006

Floating Phase in 1D Transverse ANNNI Model

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $κ$ and field strength $Γ$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $κ=0.5$ and $Γ=0$ as the unperturbed state and treat an increase of the field from 0 to $Γ$ coupled with an increase of $κ$ from 0.5 to $0.5+rΓ$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $κ=0.5$, $Γ=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.

cond-mat.stat-mech↗

arXiv2006

Jamming of directed traffic on a square lattice

Phase transition from a free-flow phase to a jammed phase is an important feature of traffic networks. We study this transition in the case of a simple square lattice network for different values of data posting rate $(ρ)$ by introducing a parameter $p$ which selects a neighbour for onward data transfer depending on queued traffic. For every $ρ$ there is a critical value of $p$ above which the system become jammed. The $ρ-p$ phase diagram shows some interesting features. We also show that the average load diverges logarithmically as $p$ approaches $p_c$ and the queue length distribution exhibits exponential and algebraic nature in different regions of the phase diagram.

cond-mat.stat-mech↗

arXiv2006

A Small World Network of Prime Numbers

According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers : $n = p + q$. We construct a network where each node is a prime number and corresponding to every even number $n$, we put a link between the component primes $p$ and $q$. In most cases, an even number can be broken up in many ways, and then we chose {\em one} decomposition with a probability $|p - q|^α$. Through computation of average shortest distance and clustering coefficient, we conclude that for $α> -1.8$ the network is of small world type and for $α< -1.8$ it is of regular type. We also present a theoretical justification for such behaviour.

math.NT↗

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↗