Non-Archimedean Coulomb gases
W. A. Zúñiga‐Galindo, Sergii M. Torba
Abstract
This article aims to study the Coulomb gas model over the d-dimensional p-adic space. We establish the existence of equilibrium measures and the Γ-limit for the Coulomb energy functional when the number of configurations tends to infinity. For a cloud of charged particles confined into the unit ball, we compute the equilibrium measure and the minimum of its Coulomb energy functional. The p-adic Coulomb energy is the continuum limit of the minus a hierarchical Hamiltonian attached to a spin glass model with a p-adic coupling.
Topics & Concepts
CoulombCoulomb's constantPhysicsHamiltonian (control theory)Electric potential energyLimit (mathematics)Quantum mechanicsCoulomb barrierEnergy (signal processing)MathematicsMathematical analysisElectronMathematical optimizationadvanced mathematical theoriesTopological and Geometric Data AnalysisMathematical Dynamics and Fractals