Steady state of the KPZ equation on an interval and Liouville quantum mechanics

被引：13
作者：
Barraquand, Guillaume [1 ]
Le Doussal, Pierre [1 ]
机构：
[1] Univ Paris, Lab Phys, Ecole Normale Super, ENS,CNRS,Univ PSL,Sorbonne Univ, 24 Rue Lhomond, F-75231 Paris, France
来源：
EPL | 2022年 / 137卷 / 06期
关键词：
BROWNIAN-MOTION; RENORMALIZATION; DIFFUSION; POLYMERS; PARTICLE; MODEL;
D O I：
10.1209/0295-5075/ac25a9
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval [0, L] with general Neumann-type boundary conditions and any interval size. This is achieved using the recent results of Corwin and Knizel (arXiv:2103.12253) together with Liouville quantum mechanics. Our formula allows to easily determine the stationary measure in various limits: KPZ fixed point on an interval, half-line KPZ equation, KPZ fixed point on a half-line, as well as the Edwards-Wilkinson equation on an interval. Copyright (C) 2022 EPLA
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页数：7
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