Universität zu Köln

Meerson, Baruch ORCID: 0000-0002-6709-8140 and Schmidt, Johannes (2017). Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions. J. Stat. Mech.-Theory Exp.. BRISTOL: IOP PUBLISHING LTD. ISSN 1742-5468

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Abstract

For stationary interface growth, governed by the Kardar-ParisiZhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al (2016 arXiv: 1611.06690) used the totally asymmetric simple exclusion process (TASEP) to study the height fluctuations in systems of the KPZ universality class for Brownian interfaces with arbitrary diffusion constant. They showed that there is a one-parameter family of long-time distributions, parameterized by the di. usion constant of the initial random height profile. They also computed these distributions numerically by using Monte Carlo (MC) simulations. Here we address this problem analytically and focus on the distribution tails at short times. We determine the (stretched exponential) tails of the height distribution by applying the optimal fluctuation method (OFM) to the KPZ equation. We argue that, by analogy with other initial conditions, the 'slow' tail holds at arbitrary times and therefore provides a proper asymptotic to the family of longtime distributions studied in Chhita et al (2016 arXiv: 1611.06690). We verify this hypothesis by performing large-scale MC simulations of a TASEP with a parallelupdate rule. The 'fast' tail, predicted by the OFM, is also expected to hold at arbitrary times, at sufficiently large heights.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Meerson, Baruch UNSPECIFIED orcid.org/0000-0002-6709-8140 UNSPECIFIED Schmidt, Johannes UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-214993
DOI:	10.1088/1742-5468/aa8c12
Journal or Publication Title:	J. Stat. Mech.-Theory Exp.
Date:	2017
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1742-5468
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NOISY BURGERS-EQUATION; CURRENT FLUCTUATIONS; DIRECTED POLYMERS; GROWTH; UNIVERSALITY; INVARIANCE; MODELS Multiple languages Mechanics; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21499