Living on the edge of instability

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405369" target="_blank" >RIV/00216208:11320/19:10405369 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wxr0mJIjeX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wxr0mJIjeX</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1742-5468/ab333f" target="_blank" >10.1088/1742-5468/ab333f</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Living on the edge of instability

Popis výsledku v původním jazyce

Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from theory of Q-processes and quasi-stationary distributions, we analyze position statistics of non-diverging trajectories. We discuss two limit distributions which can be considered as (formal) generalizations of the Gibbs canonical distribution to highly unstable systems. Even though the associated effective potentials differ only slightly, properties of the two distributions are fundamentally different for all highly unstable system. The distribution for trajectories conditioned to diverge in an infinitely distant future is localized and light-tailed. The other distribution, describing trajectories surviving in the meta-stable region at the instant of conditioning, is heavy-tailed. The exponent of the corresponding power-law tail is determined by the leading divergent term of the unstable potential. We discuss different equivalent forms of the two distributions and derive properties of the effective statistical force arising in the ensemble of non-diverging trajectories after the Doob h-transform. The obtained explicit results generically apply to non-linear dynamical models with meta-stable states and fast kinetic transitions.

Název v anglickém jazyce

Living on the edge of instability

Popis výsledku anglicky

Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from theory of Q-processes and quasi-stationary distributions, we analyze position statistics of non-diverging trajectories. We discuss two limit distributions which can be considered as (formal) generalizations of the Gibbs canonical distribution to highly unstable systems. Even though the associated effective potentials differ only slightly, properties of the two distributions are fundamentally different for all highly unstable system. The distribution for trajectories conditioned to diverge in an infinitely distant future is localized and light-tailed. The other distribution, describing trajectories surviving in the meta-stable region at the instant of conditioning, is heavy-tailed. The exponent of the corresponding power-law tail is determined by the leading divergent term of the unstable potential. We discuss different equivalent forms of the two distributions and derive properties of the effective statistical force arising in the ensemble of non-diverging trajectories after the Doob h-transform. The obtained explicit results generically apply to non-linear dynamical models with meta-stable states and fast kinetic transitions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GA17-06716S" target="_blank" >GA17-06716S: Stochastická termodynamika molekulárních systémů: od klasické ke kvantové</a><br>

Návaznosti

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

Rok uplatnění

2019

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

—

Svazek periodika

Neuveden

Číslo periodika v rámci svazku

August 2019

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

18

Strana od-do

084014

Kód UT WoS článku

000482548900003

EID výsledku v databázi Scopus

2-s2.0-85072301090