144,121 research outputs found
Crossover from the pair contact process with diffusion to directed percolation
Crossover behaviors from the pair contact process with diffusion (PCPD) and
the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one
dimension by introducing a single particle annihilation/branching dynamics. The
crossover exponents are estimated numerically as for the PCPD and for the DPCPD.
Nontriviality of the PCPD crossover exponent strongly supports non-DP nature of
the PCPD critical scaling, which is further evidenced by the anomalous critical
amplitude scaling near the PCPD point. In addition, we find that the DPCPD
crossover is consistent with the mean field prediction of the tricritical DP
class as expected
Crossover from the parity-conserving pair contact process with diffusion to other universality classes
The pair contact process with diffusion (PCPD) with modulo 2 conservation
(\pcpdt) [, ] is studied in one dimension, focused on the
crossover to other well established universality classes: the directed Ising
(DI) and the directed percolation (DP). First, we show that the \pcpdt shares
the critical behaviors with the PCPD, both with and without directional bias.
Second, the crossover from the \pcpdt to the DI is studied by including a
parity-conserving single-particle process (). We find the crossover
exponent , which is argued to be identical to that of the
PCPD-to-DP crossover by adding . This suggests that the PCPD
universality class has a well defined fixed point distinct from the DP. Third,
we study the crossover from a hybrid-type reaction-diffusion process belonging
to the DP [, ] to the DI by adding . We find
for the DP-to-DI crossover. The inequality of and
further supports the non-DP nature of the PCPD scaling. Finally, we
introduce a symmetry-breaking field in the dual spin language to study the
crossover from the \pcpdt to the DP. We find , which is
associated with a new independent route from the PCPD to the DP.Comment: 8 pages, 8 figure
Remark on the effective potential of the gravitational perturbation in the black hole background projected on the brane
The polar perturbation is examined when the spacetime is expressed by a 4d
metric induced from higher-dimensional Schwarzschild geometry. Since the
spacetime background is not a vacuum solution of 4d Einstein equation, the
various general principles are used to understand the behavior of the
energy-momentum tensor under the perturbation. It is found that although the
general principles fix many components, they cannot fix two components of the
energy-momentum tensor. Choosing two components suitably, we derive the
effective potential which has a correct 4d limit.Comment: 12 pages, no figure, CQG accepte
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