Shape-sensitive spectral asymptotics for overdamped Langevin dynamics

Analysis and simulation of quantum and molecular systems, RWTH, Aachen

Noé Blassel, joint work with Tony Lelièvre and Gabriel Stoltz (École des Ponts)

Mathematics for Materials, Institute of Mathematics, EPFL

2026-05-26

Kinetic properties in Molecular dynamics

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Let \(V:\mathbb{R}^d\to\mathbb{R}\) be an interaction potential, we consider the overdamped Langevin dynamics \[ \mathrm{d}X_t = -\nabla V(X_t)\,\mathrm{d}t + \sqrt{\frac2\beta}\,\mathrm{d}W_t \]

  • Measuring static properties = sampling the Gibbs measure \[ \mu(\mathrm{d}x) = \frac1{Z_\beta}\mathrm{e}^{-\beta V(x)}\,\mathrm{d}x\in\mathcal P_1(\mathbb{R}^d) \]
  • Measuring kinetic properties = sampling paths of \(X\).Time-correlation functions, transport coefficients, reaction rates…
  • Separation of timescales: bond oscillations/thermal fluctuations (\(\mathrm{fs}\)–\(\mathrm{ps}\)) macroscopic transitions (\(\mu\mathrm{s}\)–\(\mathrm{ms}\)). Signature of metastability