arXiv subjects

Parongama Sen

Publications and source records attributed to Parongama Sen.

At least 73 records · Page 4Linked to original sources

arXiv2012

Quantum random walk : effect of quenching

We study the effect of quenching on a discrete quantum random walk by removing a detector placed at a position $x_D$ abruptly at time $t_R$ from its path. The results show that this may lead to an enhancement of the occurrence probability at $x_D$ provided the time of removal $t_R < t_{R}^{lim}$ where $t_{R}^{lim}$ scales as $x_D{^2}$. The ratio of the occurrence probabilities for a quenched walker ($t_R \neq 0$) and free walker ($t_R =0$) shows that it scales as $1/t_R$ at large values of $t_R$ independent of $x_D$. On the other hand if $t_R$ is fixed this ratio varies as $x_{D}^{2}$ for small $x_D$. The results are compared to the classical case. We also calculate the correlations as functions of both time and position.

quant-ph↗

arXiv2012

Non-conservative kinetic exchange model of opinion dynamics with randomness and bounded confidence

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values $\in [-1,1]$. The characteristics of the unrestricted model, which has one parameter $λ$ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrised by $δ$. Three distinct regions are identified in the phase diagram in the $δ-λ$ plane and the evidences of a first order phase transition for $δ\geq 0.3$ are presented. A neutral state with all opinions equal to zero occurs for $λ\leq λ_{c_1} \simeq 2/3$, independent of $δ$, while for $λ_{c_1} \leq λ\leq λ_{c_2}(δ)$, an ordered region is seen to exist where opinions of only one sign prevail. At $λ_{c_2}(δ)$, a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values ($\pm 1$) as $λ$ is increased. For confidence level $δ< 0.3$, the ordered phase exists for a narrow range of $λ$ only. The line $δ= 0$ is apparently a line of discontinuity and this limit is discussed in some detail.

physics.soc-ph↗

arXiv2012

Effect of the nature of randomness on quenching dynamics of Ising model on complex networks

Randomness is known to affect the dynamical behaviour of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero temperature quench of Ising model on two types of random networks. In both the networks, which are embedded in a one dimensional space, the first neighbour connections exist and the average degree is four per node. In the random model A, the second neighbour connections are rewired with a probability $p$ while in the random model B, additional connections between neighbours at Euclidean distance $l ~ (l >1)$ are introduced with a probability $P(l) \propto l^{-α}$. We find that for both models, the dynamics leads to freezing such that the system gets locked in a disordered state. The point at which the disorder of the nonequilibrium steady state is maximum is located. Behaviour of dynamical quantities like residual energy, order parameter and persistence are discussed and compared. Overall, the behaviour of physical quantities are similar although subtle differences are observed due to the difference in the nature of randomness.

cond-mat.stat-mech↗

arXiv2012

Disorder induced phase transition in kinetic models of opinion dynamics

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter $p$ denoting the fraction of negative interactions, are considered. Results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=p_c below which a consensus is reached. Although the order-disorder transition is analogous to a ferromagnetic-paramagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system.

physics.soc-ph↗

arXiv2011

Antipersistent dynamics in kinetic models of wealth exchange

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. The concept of a walk in an abstract gain-loss space for the agents had been introduced in an earlier work. For models in which agents do not save, or save with uniform saving propensity, this walk has diffusive behavior. In case the saving propensity $λ$ is distributed randomly ($0 \leq λ< 1$), the resultant walk showed a ballistic nature (except at a particular value of $λ^* \approx 0.47$). Here we consider several other features of the walk with random $λ$. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency towards making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.

physics.soc-ph↗

arXiv2011

Opinion dynamics model with domain size dependent dynamics: novel features and new universality class

A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening dynamics of the equivalent Ising model shows power law behavior and has been found to belong to a new universality class with the dynamic exponent $z=1.0 \pm 0.01$ and persistence exponent $θ\simeq 0.235$ in one dimension. The critical behavior has been found to be robust for a large variety of annealed disorder that has been studied. Further, by mapping Model I to a system of random walkers in one dimension with a tendency to walk towards their nearest neighbour with probability $ε$, we find that for any $ε> 0.5$, the Model I dynamical behaviour is prevalent at long times.

physics.soc-ph↗

arXiv2011

Novel ballistic to diffusive crossover in the dynamics of a one dimensional Ising model with variable range of interaction

The idea that the dynamics of a spin is determined by the size of its neighbouring domains was recently introduced (S. Biswas and P. Sen, Phys. Rev. E {\bf 80}, 027101 (2009)) in a Ising spin model (henceforth, referred to as model I). A parameter $p$ is now defined to modify the dynamics such that a spin can sense domain sizes up to $R = pL/2$ in a one dimensional system of size $L$. For the cutoff factor $p$ \to 0$, the dynamics is Ising like and the domains grow with time $t$ diffusively as $ t^{1/z}$ with $z=2$, while for $p=1$, the original model I showed ballistic dynamics with $z \simeq 1$. For intermediate values of $p$, the domain growth, magnetisation and persistence show model I like behaviour up to a macroscopic crossover time $ t_1 \sim pL/2$. Beyond $t_1$, characteristic power law variations of the dynamic quantities are no longer observed. The total time to reach equilibrium is found to be $t = apL + b(1-p)^3L^2$, from which we conclude that the later time behaviour is diffusive. We also consider the case when a random but quenched value of $p$ is used for each spin for which ballistic behaviour is once again obtained.

cond-mat.stat-mech↗

arXiv2010

Phase transitions in a two parameter model of opinion dynamics with random kinetic exchanges

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported [M. Lallouache et al, Phys. Rev. E, {\bf 82} 056112 (2010)]. We generalise the model to incorporate two parameters, $λ$, to represent conviction and $μ$, to represent the influencing ability of individuals. A phase boundary given by $λ=1-μ/2$ is obtained separating the symmetric and symmetry broken phases: the effect of the influencing term enhances the possibility of reaching a consensus in the society. The time scale diverges near the phase boundary in a power law manner. The order parameter and the condensate also show power law growth close to the phase boundary albeit with different exponents. Theexponents in general change along the phase boundary indicating a non-universality. The relaxation times, however, become constant with increasing system size near the phase boundary indicating the absence of any diverging length scale. Consistently, the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated.

physics.soc-ph↗

arXiv2010

Agent dynamics in kinetic models of wealth exchange

We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, we observe ballistic diffusion in the model with distributed savings. There is an associated skewness in the gain-loss distribution which explains the steady state behavior in such models. We find that in general an agent gains while interacting with an agent with a larger saving propensity.

physics.soc-ph↗

arXiv2010

Complex Networks: effect of subtle changes in nature of randomness

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values.

cond-mat.stat-mech↗

arXiv2010

Funnelling related phase transitions in networks

cond-mat.dis-nn↗

arXiv2010

Noise driven dynamic phase transition in a a one dimensional Ising-like model

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $β$ such that $β=0$ corresponds to the Ising model and $β\to \infty$ to the original model I. The equilibrium behaviour for any value of $β$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $β\neq 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $β= 0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}(β, L) = (β/L)^αf(β)$, where $α$ remains constant for all $β\neq 0$ supporting the existence of the dynamic phase transition at $β=0$. The scaling function $f(β)$ shows a crossover behaviour with $f(β) = \rm{constant} $ for $β<<1$ and $f(β) \propto β^{-α}$ for $β>>1$.

cond-mat.stat-mech↗

arXiv2010

Quantum Persistence: A Random Walk Scenario

In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence is defined as the time during which a given site remains unvisited by the walker. We also investigated the behavior of related quantities, e.g., the first-passage time and the succession probability (newly defined), etc. The study reveals power law scaling behavior of these quantities with new exponents. Comparable features of the classical and the quantum walks are discussed.

cond-mat.stat-mech↗

arXiv2009

A new model of binary opinion dynamics: coarsening and effect of disorder

We propose a model of binary opinion in which the opinion of the individuals change according to the state of their neighbouring domains. If the neighbouring domains have opposite opinions, then the opinion of the domain with the larger size is followed. Starting from a random configuration, the system evolves to a homogeneous state. The dynamical evolution show novel scaling behaviour with the persistence exponent $θ\simeq 0.235$ and dynamic exponent $z \simeq1.02 \pm 0.02$. Introducing disorder through a parameter called rigidity coefficient $ρ$ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at $ρ= 0^{+}$ is obtained. Close to $ρ=0$, the equilibrium values of the dynamic variables show power law scaling behaviour with $ρ$. We also discuss the effect of having both quenched and annealed disorder in the system.

cond-mat.stat-mech↗

arXiv2009

Persistence of unvisited sites in presence of a quantum random walker

A study of persistence dynamics is made for the first time in a quantum system by considering the dynamics of a quantum random walk. For a discrete walk on a line starting at $x=0$ at time $t=0$, the persistence probability $P(x,t)$ that a site at $x$ has not been visited till time $t$ has been calculated. $P(x,t)$ behaves as $(t/|x|-1)^{-α}$ with $α\sim 0.3$ while the global fraction ${\cal{P}}(t) = \sum_xP(x,t)/2t$ of sites remaining unvisited at time $t$ attains a constant value. $F(x,t)$, the probability that the site at $x$ is visited for the first time at $t$ behaves as $(t/|x|-1)^{-β}/|x|$ where $β= 1+ α$ for $t/|x|>> 1$,and ${\cal{F}}(t) =\sum_xF(x,t)/2t \sim 1/t$. A few other properties related to the persistence and first passage times are studied and some fundamental differences between the classical and the quantum cases are observed.

cond-mat.stat-mech↗

arXiv2009

Funnelling effect in networks

Funnelling effect, in the context of searching on networks, precisely indicates that the search takes place through a few specific nodes. We define the funnelling capacity $f$ of a node as the fraction of successful dynamic paths through it with a fixed target. The distribution $D(f)$ of the fraction of nodes with funnelling capacity $f$ shows a power law behaviour in random networks (with power law or stretched exponential degree distribution) for a considerable range of values of the parameters defining the networks. Specifically we study in detail $D_1=D(f=1)$, which is the quantity signifying the presence of nodes through which all the dynamical paths pass through. In scale free networks with degree distribution $P(k) \propto k^{-γ}$, $D_1$ increases linearly with $γ$ initially and then attains a constant value. It shows a power law behaviour, $D_1 \propto N^{-ρ}$, with the number of nodes $N$ where $ρ$ is weakly dependent on $γ$ for $γ> 2.2$. The latter variation is also independent of the number of searches. On stretched exponential networks with $P(k) \propto \exp{(-k^δ)}$, $ρ$ is strongly dependent on $δ$. The funnelling distribution for a model social network, where the question of funnelling is most relevant, is also investigated.

physics.soc-ph↗

arXiv2008

Zero temperature dynamics in two dimensional ANNNI model

We investigate the dynamics of a two dimensional axial next nearest neighbour Ising (ANNNI) model following a quench to zero temperature. The Hamiltonian is given by $H = -J_0\sum_{i,j=1}^L S_{i,j}S_{i+1,j} - J_1\sum_{i,j=1} [S_{i,j} S_{i,j+1} -κS_{i,j} S_{i,j+2}]$. For $κ<1$, the system does not reach the equilibrium ground state but slowly evolves to a metastable state. For $κ> 1$, the system shows a behaviour similar to the two dimensional ferromagnetic Ising model in the sense that it freezes to a striped state with a finite probability. The persistence probability shows algebraic decay here with an exponent $θ= 0.235 \pm 0.001$ while the dynamical exponent of growth $z=2.08\pm 0.01$. For $κ=1$, the system belongs to a completely different dynamical class; it always evolves to the true ground state with the persistence and dynamical exponent having unique values. Much of the dynamical phenomena can be understood by studying the dynamics and distribution of the number of domains walls. We also compare the dynamical behaviour to that of a Ising model in which both the nearest and next nearest neighbour interactions are ferromagnetic.

cond-mat.stat-mech↗

arXiv2008

Realistic searches on stretched exponential networks

We consider navigation or search schemes on networks which have a degree distribution of the form $P(k) \propto \exp(-k^γ)$. In addition, the linking probability is taken to be dependent on social distances and is governed by a parameter $λ$. The searches are realistic in the sense that not all search chains can be completed. An estimate of $μ=ρ/s_d$, where $ρ$ is the success rate and $s_d$ the dynamic path length, shows that for a network of $N$ nodes, $μ\propto N^{-δ}$ in general. Dynamic small world effect, i.e., $δ\simeq 0$ is shown to exist in a restricted region of the $λ-γ$ plane.

physics.soc-ph↗