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SUMMARY:Quantitative Metastability in the Linear Becker-Döring Equations
DTSTART:20260929T091500Z
DTEND:20260929T101500Z
DTSTAMP:20261007T163100Z
UID:indico-event-16862@indico.math.cnrs.fr
DESCRIPTION:Speakers: Inmaculada Benítez Berral\n\nThe Becker-Döring equ
 ations describe the dynamics of cluster formation and have long been known
  to exhibit metastable behaviour near the critical monomer concentration. 
 In the linear setting\, where the monomer concentration is fixed\, Penrose
  [3\, 2] and Kreer [1] established fundamental results on the metastable r
 egime and the long-time behaviour of solutions.\nIn this talk\, we revisit
  this metastable behaviour from a quantitative perspective. We study the c
 onvergence of solutions to equilibrium in the subcritical and supercritica
 l regimes and obtain explicit estimates for the exponential relaxation rat
 e. Our approach combines entropy methods with discrete Hardy inequalities 
 and relates the convergence rate to the spectral properties of the associa
 ted linear operator.\nWe show that\, as the critical concentration is appr
 oached\, the relaxation rate becomes small\, providing a quantitative desc
 ription of the metastable time scale. In the supercritical regime\, we als
 o identify the role of the critical cluster size and the exponentially sma
 ll flux through it\, which provides a natural interpretation of the slow r
 elaxation.\nReferences\n[1] Markus Kreer. Classical Becker-Döring cluster
  equations: Rigorous results on metastability and long-time behaviour. Ann
 alen der Physik\, 505(4):398–417\, 1993.\n[2] Oliver Penrose. Metastable
  states for the Becker-Döring cluster equations. Communications in Mathem
 atical Physics\, 124(4):515–541\, 1989.\n[3] Oliver Penrose and Joel L. 
 Lebowitz. Towards a rigorous molecular theory of metastability. Fluctuatio
 n Phenomena\, 7:293–340\, 1987.\n\nhttps://indico.math.cnrs.fr/event/168
 62/
URL:https://indico.math.cnrs.fr/event/16862/
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