Results for “kink creation and annihilation”

DOE OSTI2021

Novel deformation function creating or destroying any number of even kink solutions

Here, we present a one-parameter family of deformation functions f(Φ) which have novel properties. Firstly, the deformation function is its own inverse. We show that a class of potentials remains invariant under this deformation. Further, when applied to a certain class of kink bearing potentials, one obtains potentials which are not bounded from below. Besides, we show that there is a wide class of potentials having power law kink tails which are connected by this deformation but the corresponding kink tails of the two potentials have different asymptotic behavior. Finally, we show that when this deformation function is applied to an appropriate one-parameter family of potentials having two kink solutions, it creates new potentials with an arbitrary even number (2n) of kink solutions. Conversely, by starting from this potential with 2n kink solutions the deformation function annihilates 2n-2 kinks and we get back the potential which we started with having only two kink solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Generic two-phase coexistence in a type-2 Schloegl model for autocatalysis on a square lattice: Analysis via heterogeneous master equations

Schloegl's second model (also known as the quadratic contact process) on a square lattice involves spontaneous annihilation of particles at lattice sites at rate p, and their autocatalytic creation at unoccupied sites with n ≥ 2 occupied neighbors at rate k n . Here, kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition with generic two-phase coexistence: the p value for equistability of coexisting populated and vacuum states, p eq (S), depends on the orientation or slope, S, of a planar interface separating those phases. The vacuum state displaces the populated state for p > eq (S), and the opposite applies for p < p eq (S) for 0 < S < ∞. The special “combinatorial” rate choice k n = n(n–1)/12 facilitates an appealing simplification of the exact master equations for the evolution of spatially heterogeneous states in the model, which aids analytic investigation of these equations via hierarchical truncation approximations. Truncation produces coupled sets of lattice differential equations which can describe orientation-dependent interface propagation and equistability. The pair approximation predicts that p eq (max) = p eq (S = 1) = 0.09645 and p eq (min) = p eq (S → ∞) = 0.08827, values deviating less than 15% from KMC predictions. In the pair approximation, a perfect vertical interface is stationary for all p < p eq (S = ∞) = 0.08907, a value exceeding p eq (S → ∞). One can regard an interface for large S → ∞ as a vertical interface decorated with isolated kinks. For p < p eq (S = ∞), the kink can move in either direction along this otherwise stationary interface depending upon p, but for p = p eq (min) the kink is also stationary.

97 MATHEMATICS AND COMPUTING↗