Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain

Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent z = 1 , none of the known variants of conformal invariance can act as its dynamical symmetry. In d = 1 spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.

• Publication year

  2016

• Venue

  Symmetry

• Publication date

  2016-11-04

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.3390/sym9010002arXiv 1611.02975
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Local scale-invariance of the 2 + 1 dimensional Kardar – Parisi – Zhang model

  2017cited by this paper
• Universality of (2+1)-dimensional restricted solid-on-solid models.

  2016cited by this paper
• From dynamical scaling to local scale-invariance: a tutorial

  2016cited by this paper
• Minimal realization of ℓ-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

  2016cited by this paper
• Non-local meta-conformal invariance in diffusion-limited erosion

  2016influential reference
• Meta-conformal invariance and the boundedness of two-point correlation functions

  2016cited by this paper
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry

  2016cited by this paper
• Local scale-invariance of the 2  +  1 dimensional Kardar–Parisi–Zhang model

  2016cited by this paper
• Conformal Invariance in Driven Diffusive Systems at High Currents.

  2016cited by this paper
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry

  2016cited by this paper
• Universality of 2+1 dimensional RSOS models

  2016cited by this paper
• Analysis of etching at a solid-solid interface.

  2016cited by this paper
• Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

  2015cited by this paper
• From Conformal Invariance towards Dynamical Symmetries of the Collisionless Boltzmann Equation

  2015cited by this paper
• Conformal invariance in the long-range Ising model

  2015cited by this paper
• Geometric inequalities for fractional Laplace operators and applications

  2015cited by this paper
• On the existence of an upper critical dimension for systems within the KPZ universality class

  2015cited by this paper
• Growth exponents of the etching model in high dimensions

  2015cited by this paper
• Ricci-flat spacetimes with l-conformal Galilei symmetry

  2015cited by this paper
• Macroscopic fluctuation theory

  2014cited by this paper
• Conformal Newton–Hooke symmetry of Pais–Uhlenbeck oscillator

  2014cited by this paper
• Critical Dynamics: Near-equilibrium critical dynamics

  2014cited by this paper
• Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

  2014cited by this paper
• Universal correlators and distributions as experimental signatures of (2 + 1)-dimensional Kardar-Parisi-Zhang growth

  2014cited by this paper
• On Microscopic Derivation of a Fractional Stochastic Burgers Equation

  2014cited by this paper
• Ageing of the 2+1 dimensional Kardar-Parisi-Zhang model

  2013cited by this paper
• Dynamical realizations of l-conformal Newton–Hooke group

  2013cited by this paper
• Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains

  2013cited by this paper
• Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory

  2012cited by this paper
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1, and 3+1 dimensions.

  2012influential reference
• Hitchhiker's guide to the fractional Sobolev spaces

  2011cited by this paper
• Phenomenology of aging in the Kardar-Parisi-Zhang equation.

  2011cited by this paper
• Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux

  2010cited by this paper
• Ageing and dynamical scaling far from equilibrium

  2010cited by this paper
• GCA in 2 d

  2010cited by this paper
• On logarithmic extensions of local scale-invariance

  2010cited by this paper
• GCA in 2d

  2009cited by this paper
• The exotic conformal Galilei algebra and nonlinear partial differential equations

  2009cited by this paper
• Non-relativistic conformal symmetries and Newton–Cartan structures

  2009cited by this paper
• Affine extension of Galilean conformal algebra in 2+1 dimensions

  2009cited by this paper
• Non-relativistic conformal symmetries in fluid mechanics

  2009cited by this paper
• Lie Theory and Its Applications in Physics

  2007cited by this paper
• Fractional Laplacian in bounded domains.

  2007cited by this paper
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

  2007cited by this paper
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

  2006cited by this paper
• Crossover of interface growth dynamics during corrosion and passivation

  2006cited by this paper
• THE POINCARÉ ALGEBRA IN THE CONTEXT OF AGEING SYSTEMS: LIE STRUCTURE, REPRESENTATIONS, APPELL SYSTEMS AND COHERENT STATES

  2006cited by this paper
• Symmetry-based determination of space-time functions in nonequilibrium growth processes.

  2006cited by this paper
• Dynamics of a mean spherical model with competing interactions

  2005cited by this paper
• Local scale-invariance and ageing in noisy systems

  2004influential reference
• Surface growth models with a random-walk-like nonlocality.

  2003cited by this paper
• Schr"odinger invariance and space-time symmetries

  2003cited by this paper
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

  2002cited by this paper
• Symmetry

  2000cited by this paper
• Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory.

  1999cited by this paper
• Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensor-densities on S1

  1998cited by this paper
• Origins of scale invariance in growth processes

  1997cited by this paper
• Nonrelativistic conformal groups

  1997influential reference
• Nonrelativistic conformal groups. II. Further developments and physical applications

  1997cited by this paper
• Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

  1996cited by this paper
• Mode-coupling and renormalization group results for the noisy Burgers equation.

  1996cited by this paper
• Fractal Concepts in Surface Growth

  1996cited by this paper
• Short-Time-Scaling Behavior of Growing Interfaces

  1996influential reference
• Local Scale Invariance and Strongly Anisotropic Equilibrium Critical Systems

  1996cited by this paper
• Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

  1995cited by this paper
• SCALE INVARIANCE, INTERFACES AND NON-EQUILIBRIUM DYNAMICS

  1995cited by this paper
• Statistical physics of growth processes

  1995cited by this paper
• Bounds on the decay of the autocorrelation in phase ordering dynamics.

  1994cited by this paper
• Schrödinger invariance and strongly anisotropic critical systems

  1993cited by this paper
• Proof of scale invariant solutions in the Kardar−Parisi−Zhang and Kuramoto-Sivashinsky equations in 1+1 dimensions: analytical and numerical results

  1993cited by this paper
• Conformal Field Theory.

  1992cited by this paper
• Kinetic roughening of Laplacian fronts.

  1991influential reference
• Dynamic scaling of growing interfaces.

  1986cited by this paper
• Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model

  1985cited by this paper
• The surface statistics of a granular aggregate

  1982cited by this paper
• Conformal extensions of the Galilei group and their relation to the Schrödinger group

  1978cited by this paper
• The maximal kinematical invariance group of the free Schrodinger equation.

  1972cited by this paper
• Conformal symmetry of critical fluctuations

  1970influential reference
• Generalized Functions, Volume 1: Properties and Operations

  1967cited by this paper
• On Unitary ray representations of continuous groups

  1954cited by this paper
• ON FRACTIONAL INTEGRALS AND DERIVATIVES

  1940cited by this paper
• Les groupes de transformations continus, infinis, simples

  year unknowncited by this paper

• Schrödinger Symmetry: A Historical Review

  2024cites this paper
• Improved Correlation Coefficients of Quadripartitioned Single-Valued Neutrosophic Sets and Interval-Quadripartitioned Neutrosophic Sets

  2020cites this paper
• Construction of meta-conformal algebras in d spatial dimensions

  2019cites this paper
• Correlation Coefficient of Neutrosophic Sets and Its Applications in Decision-Making

  2018cites this paper
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

  2018cites this paper
• CNC router selection for SMEs in woodwork manufacturing using hesitant fuzzy AHP method

  2018cites this paper
• Infinite- Dimensional Metaconformal Symmetries: 1 D Diffusion-Limited Erosion and Ballistic Transport in $$(1+2)$$ Dimensions

  2017cites this paper
• Meta-conformal algebras in $d$ spatial dimensions

  2017cites this paper
• Dynamical universality classes of simple growth and lattice gas models

  2017cites this paper
• Local scale-invariance of the 2  +  1 dimensional Kardar–Parisi–Zhang model

  2016cites this paper