Nonequilibrium dynamics of a growing interface

Fogedby, Hans C.

doi:10.1088/0953-8984/14/7/313

Cited by 10 publications

(22 citation statements)

References 34 publications

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“…The possibility to interpret KPZ as a gas of solitons was put forward by Fogedby [57] starting with the WKB solution of the Fokker-Planck equation in the weak noise limit, with in particular the prediction of the dispersion relation |k| 3/2 as a function of momentum k, corresponding in our notations to κ 3 a (ν) ∼ |a| 3/2 for large a, see also [58] for recent related work.…”

Section: Kdv Solitonsmentioning

confidence: 99%

Riemann surfaces for KPZ with periodic boundaries

Prolhac

2020

SciPost Phys.

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The Riemann surface for polylogarithms of half-integer index, which has the topology of an infinite dimensional hypercube, is studied in relation to onedimensional KPZ universality in finite volume. Known exact results for fluctuations of the KPZ height with periodic boundaries are expressed in terms of meromorphic functions on this Riemann surface, summed over all the sheets of a covering map to an infinite cylinder. Connections to stationary large deviations, particle-hole excitations and KdV solitons are discussed.

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Section: Kdv Solitonsmentioning

confidence: 99%

Riemann surfaces for KPZ with periodic boundaries

Prolhac

2020

SciPost Phys.

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“…The function s → log e sh(x,t) is the cumulant generating function of the height. At late times, (17) implies that the cumulant generating function is equal to te(s) + log θ(s; h 0 ) up to exponentially small corrections. The Legendre transform g of e is the large deviation function of the height in the stationary state, i.e., the probability density of the height behaves as P(h(x, t) = tu) ∼ e −tg(u) for large t.…”

Section: First Cumulants Of the Heightmentioning

confidence: 99%

Brownian Bridges for Late Time Asymptotics of KPZ Fluctuations in Finite Volume

Mallick

Prolhac

2018

J Stat Phys

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Height fluctuations are studied in the one-dimensional totally asymmetric simple exclusion process with periodic boundaries, with a focus on how late time relaxation towards the non-equilibrium steady state depends on the initial condition. Using a reformulation of the matrix product representation for the dominant eigenstate, the statistics of the height at large scales is expressed, for arbitrary initial conditions, in terms of extremal values of independent standard Brownian bridges. Comparison with earlier exact Bethe ansatz asymptotics leads to explicit conjectures for some conditional probabilities of non-intersecting Brownian bridges with exponentially distributed distances between the endpoints.

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“…Another issue is the clear experimental observation of the KPZ universality and the role of quenched noise in the asymptotic KPZ scaling [5,8,16]. For one dimensional KPZ growth, by applying a weak noise canonical phase-space method, it has been shown recently that the KPZ dynamic exponent is associated with the soliton dispersion law [17]. However, at saturation all KPZ correlations are exactly the same as would result from the linear EW equation [5,17,18].…”

Section: Introductionmentioning

confidence: 99%

“…For one dimensional KPZ growth, by applying a weak noise canonical phase-space method, it has been shown recently that the KPZ dynamic exponent is associated with the soliton dispersion law [17]. However, at saturation all KPZ correlations are exactly the same as would result from the linear EW equation [5,17,18]. The fact that the EW equation is sort of "embedded" in the KPZ equation may give rise to ambiguous values of scaling exponents for growth mechanisms (or models) that interpolate between the weak and the strong nonlinear coupling regimes.…”

Section: Introductionmentioning

confidence: 99%

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

2004

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We simulate competitive two-component growth on a one dimensional substrate of L sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a nonuniversal parameter, but its presence is universal. We introduce a method to measure the length of this initial non-scaling phase. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.

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Nonequilibrium dynamics of a growing interface

Cited by 10 publications

References 34 publications

Riemann surfaces for KPZ with periodic boundaries

Riemann surfaces for KPZ with periodic boundaries

Brownian Bridges for Late Time Asymptotics of KPZ Fluctuations in Finite Volume

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

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