Alladi Ramakrishnan Hall

Dynamical Phenomena in Reaction Diffusion and Spin Systems

Reshmi Roy

Calcutta University

In the first part, dynamical features of tagged particles will be discussed in
one dimensional A + A → ∅ system on a periodic lattice, where the particles
A have a bias ǫ (−0.5 ≤ ǫ ≤ 0.5) to hop one step in the direction of their
nearest neighboring particle and they annihilate on contact. We found that for
ǫ > 0 when asynchronous dynamics is used to update the system, probability
distribution Π(x, t) of the particles shows a double peak structure with a dip at
x = 0 and it assumes a double delta form at very late time regime. For any ǫ > 0,
there is a diverging time scale t
∗
, below which the particle motions are highly

correlated, and beyond t
∗
, the particles move as independent biased walkers.
When we use parallel updating rule, Π(x, t) shows a non-Gaussian single peaked.
For the deterministic point ǫ = 0.5, we found that an isolated pair of particles,
termed as dimers, can survive indefinitely in the system which is exclusive for
parallel dynamics. When ǫ is made negative, Π(x, t) becomes Gaussian as found
in ǫ = 0. A comparative analysis for the relevant quantities using asynchronous
and parallel dynamics shows that there are significant differences for ǫ > 0 while
the results are qualitatively similar for ǫ < 0.
In the next part, non equilibrium dynamics will be discussed in Ising like

models where we have investigated the dynamical fixed points of the zero tem-
perature Glauber dynamics. The stability analysis of the fixed points in the

mean field calculation shows the existence of an exponent that depends on the
coordination number z in the Ising model. For the generalised voter model, a
phase diagram is also obtained based on this study.