Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1306.5643 · Journal of Statistical Physics

Coupled Kardar-Parisi-Zhang Equations in One Dimension

Patrik L. Ferrari, Tomohiro Sasamoto, Herbert Spohn

Published Sep 18, 2013• 54 citations
arXivHTMLPDF
DOI
10.1007/s10955-013-0842-5

Related papers

Efimov effect at the Kardar-Parisi-Zhang roughening transition

Yu Nakayama, Yusuke Nishida

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.

arXiv:2010.15161•Physical review. E•Jan 19, 2021•7 citations

Instability in one-dimensional systems

Bikiran Prasad Barua, S.K. Sinha

Physics Letters A•Oct 1, 1979•0 citations

Kardar-Parisi-Zhang universality in a two-component driven diffusive model

Pritha Dolai, Aditi Simha, Abhik Basu

We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We thus establish that the model belongs to the 1D KPZ universality class.

•Dec 22, 2020•0 citations

Exact Results for One-Dimensional Systems

WORLD SCIENTIFIC eBooks•May 1, 1989•0 citations

Kardar-Parisi-Zhang universality in two-component driven diffusive models: Symmetry and renormalization group perspectives

Pritha Dolai, Aditi Simha, Abhik Basu

We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations. We thus establish that these models belong to the 1D KPZ universality class.

arXiv:2012.12210•Physical review. E•Jun 7, 2024•1 citation

Toward a statistical theory of one-dimensional systems.

S. M. Bortsaǐkin, Yu. V. Mikhaǐlova

•Jan 1, 1972•0 citations
Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.
We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations. We thus establish that these models belong to the 1D KPZ universality class.