Short-time large deviations of the spatially averaged height of a Kardar-Parisi-Zhang interface on a ring

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2FCZ______%3A_____%2F23%3AN0000060" target="_blank" >RIV/CZ______:_____/23:N0000060 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1742-5468/ad0a94" target="_blank" >https://iopscience.iop.org/article/10.1088/1742-5468/ad0a94</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1742-5468/ad0a94" target="_blank" >10.1088/1742-5468/ad0a94</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Short-time large deviations of the spatially averaged height of a Kardar-Parisi-Zhang interface on a ring

Popis výsledku v původním jazyce

Using the optimal fluctuation method, we evaluate the short-time probability distribution P((H) over bar, L, t = T) of the spatially averaged height (H) over bar (1/L)(0)integral(L)h(x, t = T)dx of a one-dimensional interface h(x, t) governed by the Kardar-Parisi-Zhang equation partial derivative(t)h =nu partial derivative(2)(x)h+lambda/2 (partial derivative(x)h)(2) + root D xi (x, t) on a ring of length L. The process starts from a flat interface, h(x, t = 0) = 0. Both at lambda(H) over bar < 0 and at sufficiently small positive. lambda<(H)over bar> the optimal (that is, the least-action) path h(x, t) of the interface, conditioned on (H) over bar, is uniform in space, and the distribution P((H) over bar, L, T) is Gaussian. However, at sufficiently large. lambda(H) over bar < 0 the spatially uniform solution becomes sub-optimal and gives way to non-uniform optimal paths. We study these, and the resulting non-Gaussian distribution P(<(H)over bar>, L, T), analytically and numerically. The loss of optimality of the uniform solution occurs via a dynamical phase transition of either first or second order, depending on the rescaled system size l = L/root nu T, at a critical value (H) over bar = (H) over bar (c)(l). At large but finite l the transition is of first order. Remarkably, it becomes an 'accidental' second-order transition in the limit of l ->infinity, where a large-deviation behavior - ln P((H) over bar H, L, T) similar or equal to (L/T) f((H) over bar) (in the units lambda = nu = D = 1) is observed. At small l the transition is of second order, while at l = O(1) transitions of both types occur.

Název v anglickém jazyce

Short-time large deviations of the spatially averaged height of a Kardar-Parisi-Zhang interface on a ring

Popis výsledku anglicky

Using the optimal fluctuation method, we evaluate the short-time probability distribution P((H) over bar, L, t = T) of the spatially averaged height (H) over bar (1/L)(0)integral(L)h(x, t = T)dx of a one-dimensional interface h(x, t) governed by the Kardar-Parisi-Zhang equation partial derivative(t)h =nu partial derivative(2)(x)h+lambda/2 (partial derivative(x)h)(2) + root D xi (x, t) on a ring of length L. The process starts from a flat interface, h(x, t = 0) = 0. Both at lambda(H) over bar < 0 and at sufficiently small positive. lambda<(H)over bar> the optimal (that is, the least-action) path h(x, t) of the interface, conditioned on (H) over bar, is uniform in space, and the distribution P((H) over bar, L, T) is Gaussian. However, at sufficiently large. lambda(H) over bar < 0 the spatially uniform solution becomes sub-optimal and gives way to non-uniform optimal paths. We study these, and the resulting non-Gaussian distribution P(<(H)over bar>, L, T), analytically and numerically. The loss of optimality of the uniform solution occurs via a dynamical phase transition of either first or second order, depending on the rescaled system size l = L/root nu T, at a critical value (H) over bar = (H) over bar (c)(l). At large but finite l the transition is of first order. Remarkably, it becomes an 'accidental' second-order transition in the limit of l ->infinity, where a large-deviation behavior - ln P((H) over bar H, L, T) similar or equal to (L/T) f((H) over bar) (in the units lambda = nu = D = 1) is observed. At small l the transition is of second order, while at l = O(1) transitions of both types occur.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/EF16_019%2F0000789" target="_blank" >EF16_019/0000789: Pokročilý výzkum s využitím fotonů a částic vytvořených vysoce intenzivními lasery</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Statistical Mechanics - Theory and Experiment

ISSN

1742-5468

e-ISSN

1742-5468

Svazek periodika

2023

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

30

Strana od-do

123202 (1-30)

Kód UT WoS článku

001123037900001

EID výsledku v databázi Scopus

2-s2.0-85180359707