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Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
- Source :
- SciPost Physics, Vol 8, Iss 3, p 035 (2020)
- Publication Year :
- 2020
- Publisher :
- SciPost, 2020.
-
Abstract
- We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at $x=0$ either repulsive $A>0$, or attractive $A - \frac{1}{2}$ the large time PDF is the GSE Tracy-Widom distribution. For $A= \frac{1}{2}$, the critical point at which the DP binds to the wall, we obtain the GOE Tracy-Widom distribution. In the critical region, $A+\frac{1}{2} = \epsilon t^{-1/3} \to 0$ with fixed $\epsilon = \mathcal{O}(1)$, we obtain a transition kernel continuously depending on $\epsilon$. Our work extends the results obtained previously for $A=+\infty$, $A=0$ and $A=- \frac{1}{2}$.
Details
- Language :
- English
- ISSN :
- 25424653
- Volume :
- 8
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- SciPost Physics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.959116e49c9748699152377e426c46f6
- Document Type :
- article
- Full Text :
- https://doi.org/10.21468/SciPostPhys.8.3.035