Produção Nacional
Revisado por pares
Crossover to the Stochastic Burgers Equation for the WASEP with a Slow Bond
2016; Springer Science+Business Media; Volume: 346; Issue: 3 Linguagem: Inglês
10.1007/s00220-016-2607-x
ISSN1432-0916
AutoresTertuliano Franco, Patrícia Gonçalves, Marielle Simon,
Tópico(s)Theoretical and Computational Physics
ResumoWe consider the weakly asymmetric simple exclusion process in the presence of a slow bond and starting from the invariant state, namely the Bernoulli product measure of parameter $${\rho \in (0,1)}$$ . The rate of passage of particles to the right (resp. left) is $${\frac{1}{2} + \frac{a}{2n^{\gamma}}}$$ (resp. $${\frac{1}{2} - \frac{a}{2n^{\gamma}}}$$ ) except at the bond of vertices $${\{-1,0\}}$$ where the rate to the right (resp. left) is given by $${\frac{\alpha}{2n^\beta} + \frac{a}{2n^{\gamma}}}$$ (resp. $${\frac{\alpha}{2n^\beta}-\frac{a}{2n^{\gamma}}}$$ ). Above, $${\alpha > 0}$$ , $${\gamma \geq \beta \geq 0}$$ , $${a\geq 0}$$ . For $${\beta < 1}$$ , we show that the limit density fluctuation field is an Ornstein–Uhlenbeck process defined on the Schwartz space if $${\gamma > \frac{1}{2}}$$ , while for $${\gamma = \frac{1}{2}}$$ it is an energy solution of the stochastic Burgers equation. For $${\gamma \geq \beta =1}$$ , it is an Ornstein–Uhlenbeck process associated to the heat equation with Robin's boundary conditions. For $${\gamma \geq \beta > 1}$$ , the limit density fluctuation field is an Ornstein–Uhlenbeck process associated to the heat equation with Neumann's boundary conditions.
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