A Uniqueness Result for Minimizers of the 1D Log-gas Renormalized Energy

2014/08/10 by Leblé, Thomas · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1408.2283

Abstract

Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice \mathbbz is a minimizer for the so-called renormalized energy which they obtained as a limit of the N-particle Log-gas Hamiltonian for N → ∞. However, this minimizer is not unique among infinite point configurations (for example small perturbations of \mathbbz leave the renormalized energy unchanged). In this paper, we establish that uniqueness holds at the level of (stationary) point processes, the only minimizer being given by averaging \mathbbz over a choice of the origin in [0,1]. This is proved by showing a quantitative estimate on the two-point correlation function of a process in terms of its renormalized energy.

Cited by

• Periodic ground states for a one-parameter family of nonlocal energies on the real line
• Dynamics of screened particles towards equi-spaced ground states

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