Driven Pair Contact Process with Diffusion

Abstract

The pair contact process with diffusion (PCPD) has been recently investigated extensively, but its critical behavior is not yet clearly established. By introducing biased diffusion, we show that the external driving is relevant and the driven PCPD exhibits a mean-field-type critical behavior even in one dimension. In systems which can be described by a single-species bosonic field theory, the Galilean invariance guarantees that the driving is irrelevant. The well-established directed percolation (DP) and parity conserving (PC) classes are such examples. This leads us to conclude that the PCPD universality class should be distinct from the DP or PC class. Moreover, it implies that the PCPD is generically a multi-species model and a field theory of two species is suitable for proper description.PACS numbers: 64.60. Ht,05.70.Ln,89.75.Da The steady state of an equilibrium system is characterized by its Hamiltonian and Gibbs measure. There is no systematic generalization to the stationary state of nonequilibrium systems so far. Since nonequilibrium systems encompass all kinds of many body systems without a constraint of detailed balance, it may be hopeless to find a universal formalism applied to general nonequilibrium systems. At this point, model studies or case-by-case studies are rather useful to accumulate our knowledge on nonequilibrium systems.Our experience on equilibrium systems illustrates the scale-free fluctuation or power law behavior at the critical point where the continuous phase change occurs. The scale-free nature is worth while to be studied not only because of its theoretical attraction, but also because of ubiquity in nature -the clustering of galaxies [1], 1/f noise [2], percolation structure [3], to name only a few. This scale-free nature is also expected at criticality under nonequilibrium circumstances. As a prototype of nonequilibrium critical phenomena, absorbing phase transitions (APTs) have been studied extensively [4]. APT is a transition from an active phase to an absorbing phase in nonequilibrium steady states. The absorbing states are defined as the configurations where the system cannot escape by the prescribed dynamic rules. As in equilibrium systems, this transition is possible only at the thermodynamic limit because the finite systems eventually fall into the absorbing states.In epidemiology, for example, the virus extinct state is an absorbing state. Actually, the disease spreading is modeled and dubbed the contact process (CP) by Harris [5]. CP shows a phase transition from the virus infested state (active state), to the quiescent state (absorbing state). This transition is known to belong to the directed percolation (DP) universality class. Actually, many types of models belong to the DP class and it is conjectured that a phase transition occurred in a system with a single absorbing state should share the critical behavior with the DP [6,7].As in equilibrium critical phenomena, a symmetry or conservation may play an important role in determining the universality class. Accor...

Implications of a new particle from the HyperCP data on Σ+→pμ+μ−

“…Three events for the decay mode Σ + → pµ + µ − with an invariant mass of 214.3 ± 0.5 MeV for the muon-antimuon pair have been recently observed by the HyperCP collaboration [1]. The branching ratio is obtained to be 8.6 +6.…”

“…The branching ratio is obtained to be 8.6 +6. 6 −5.4 (stat) ± 5.5(syst) × 10 −8 [1]. The central value is considerably larger than the short-distance contribution in the standard model [2].…”

“…Instead, we will assume the existence of the new particles and study the implications from the HyperCP data. To be consistent with observations, we follow HyperCP and assume that the hypothetical particles have small widths, are short-lived (they decay inside the detector), and do not interact strongly [1].…”

Yangian description for decays and possible explanation of X in the decay KL0→π0π0X

“…It is reported [1,4] that the mass of this unknown pseudo-scalar particle is about 214.3M eV , and X immediately decays to two photons.…”

“…Recently, HyperCP collaboration has reported [1] the first evidence for the decay Σ + → pµ + µ − with branching ratio at the level of 10 −8 from data taken by the HyperCP (E871) experiment at Fermilab. Narrow range of dimuon masses in three observed events in that experiment suggested a new particle X with mass of 214.3 MeV.…”