5 research outputs found
Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
We consider a system of non-crossing Brownian particles in one dimension.
We find the exact rate function that describes the long-time large deviation
statistics of their occupation fraction in a finite interval in space.
Remarkably, we find that, for any general , the system undergoes
dynamical phase transitions of second order. The transitions are
the boundaries of phases that correspond to different numbers of particles
which are in the vicinity of the interval throughout the dynamics. We achieve
this by mapping the problem to that of finding the ground-state energy for
noninteracting spinless fermions in a square-well potential. The phases
correspond to different numbers of single-body bound states for the quantum
problem. We also study the process conditioned on a given occupation fraction
and the large- limiting behavior.Comment: 11 pages, 4 figure
Large deviations in statistics of the convex hull of passive and active particles: A theoretical study
We investigate analytically the distribution tails of the area A and
perimeter L of a convex hull for different types of planar random walks. For N
noninteracting Brownian motions of duration T we find that the large-L and A
tails behave as and
, while the small- and
tails behave as and
, where is the diffusion
coefficient. We calculated all of the coefficients ()
exactly. Strikingly, we find that and are independent of N, for
and , respectively. We find that the large-L (A) tails are
dominated by a single, most probable realization that attains the desired L
(A). The left tails are dominated by the survival probability of the particles
inside a circle of appropriate size. For active particles and at long times, we
find that large-L and A tails are given by and respectively. We calculate
the large deviation functions exactly and find that they exhibit
multiple singularities. We interpret these as dynamical phase transitions of
first order. We extended several of these results to dimensions . Our
analytic predictions display excellent agreement with existing results that
were obtained from extensive numerical simulations.Comment: 15 pages, 9 figure
Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets
Critical end points and tricritical points are multicritical points that
separate lines of continuous transitions from lines of first order transitions
in the phase diagram of many systems. In models like the spin-1 disordered
Blume-Capel model and the repulsive Blume-Emery-Griffiths model, the
tricritical point splits into a critical end point and a bicritical end point
with an increase in disorder and repulsive coupling strength respectively. In
order to make a distinction between these two multicritical points, we
investigate and contrast the behaviour of the first order phase boundary and
the co-existence diameter around them.Comment: 23 pages, 28 figure
Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields
We study the effect of different symmetric random field distributions:
trimodal and Gaussian on the phase diagram of the infinite range Blume-Capel
model. For the trimodal random field, the model has a very rich phase diagram.
We find three new ordered phases, multicritical points like tricritical point
(TCP), bicritical end point (BEP), critical end point (CEP) along with some
multi-phase coexistence points. We also find re-entrance at low temperatures
for some values of the parameters. On the other hand for the Gaussian
distribution the phase diagram consists of a continuous line of transition
followed by a first order transition line, meeting at a TCP. The TCP vanishes
for higher strength of the random field. In contrast to the trimodal case, in
Gaussian case no new phase emerges.Comment: 25 pages, 19 figures. Version accepted for publication in Journal of
Statistical Physic