منابع مشابه
Generalizations of the Kpz Equation
We generalize the KPZ equation to an O(3) N = 2j + 1 component model. In the limit N → ∞ we show that the mode coupling equations become exact. Solving these approximately we find that the dynamic exponent z increases from 3/2 for d = 1 to 2 at the dimension d ≈ 3.6. For d = 1 it can be shown analytically that z = 3/2 for all j. The case j = 2 for d = 2 is investigated by numerical integration ...
متن کاملWeakly asymmetric bridges and the KPZ equation
We consider a discrete bridge from (0, 0) to (2N, 0) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order N with α > 0. We provide a classification of the static and dynamic behaviour of this model according to the value of the parameter α. Our main results concern the hydrodynamic limit and the fluctuations of the bridge. For α < 1,...
متن کاملKPZ Equation and Surface Growth Model
We consider the ultra-discrete Burgers equation. All variables of the equation are discrete. We classify the equation into five regions in the parameter space. We discuss behavior of solutions. Using this equation we construct the deterministic surface growth models respectively. Furthermore we introduce noise into the ultra-discrete Burgers equation. We present the automata models of the KPZ e...
متن کاملOn the Perturbation Expansion of the KPZ- Equation
Thanks to a fluctuation dissipation theorem and the mapping to exactly solvable models, much is known for space-dimension d = 1 [1, 2, 3]. In contrast, the case of d ≥ 2 can only be attacked by approximative methods or field-theoretic perturbative expansions. Using the latter, the fixed point structure of the renormalization group flow for d = 2 + ε has been obtained [1, 4, 5]. Two domains can ...
متن کاملFluctuation Exponent of the Kpz/stochastic Burgers Equation
(1.4) hε(t, x) = ε 1/2h(ε−zt, ε−1x). We will be considering these models in equilibrium, in which case h(t, x)−h(t, 0) is a two-sided Brownian motion with variance ν−1σ2 for each t. There are many physical arguments for (1.3), none of which are good starting points for rigorous analysis, and which are really only convincing in the sense that they are very well backed up by numerical work. Perha...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2018
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-018-3089-9