Coulomb and Riesz gases: The known and the unknown

DOI10.1063/5.0086835OpenAlexW4281674100MaRDI QIDQ5883511

Mathieu Lewin

Publication date: 21 March 2023

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.09240

Mathematics Subject Classification ID

Gas dynamics (general theory) (76N15) Classical equilibrium statistical mechanics (general) (82B05) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21)

Related Items (13)

An exact formula for the variance of linear statistics in the one-dimensional jellium model ⋮ Gap probability and full counting statistics in the one-dimensional one-component plasma ⋮ Number-rigidity and \(\beta\)-circular Riesz gas ⋮ The random Weierstrass zeta function. I: Existence, uniqueness, fluctuations ⋮ Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies ⋮ Determinantal Coulomb Gas Ensembles with a Class of Discrete Rotational Symmetric Potentials ⋮ Preface to the Special Collection in Honor of Freeman Dyson ⋮ Dirac cones for a mean-field model of graphene ⋮ Asymptotics of \(k\)-nearest neighbor Riesz energies ⋮ Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble ⋮ Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials ⋮ Classical density functional theory: representability and universal bounds ⋮ Improved Lieb-Oxford bound on the indirect and exchange energies

Cites Work

• Equilibrium configurations of particles on a sphere: the case of logarithmic interactions
• Universality of local spectral statistics of random matrices
• Density Functional Theory and Optimal Transportation with Coulomb Cost
• Floating Wigner crystal and periodic jellium configurations
• Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs
• The <scp>One‐Dimensional Log‐Gas</scp> Free Energy Has a Unique Minimizer
• DLR Equations and Rigidity for the Sine‐Beta Process
• An invitation to Kähler–Einstein metrics and random point processes
• Edge fluctuations and third-order phase transition in harmonically confined long-range systems
• Gap probability and full counting statistics in the one-dimensional one-component plasma
• Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture
• Existence of Gibbs point processes with stable infinite range interaction
• Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry
• Microscopic description of Log and Coulomb gases
• Discrete Energy on Rectifiable Sets
• Renormalized Energy Equidistribution and Local Charge Balance in 2D Coulomb Systems
• Quantum Chaos, Random Matrix Theory, and the Riemann ζ-function
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]
• Statistical Ensembles of Complex, Quaternion, and Real Matrices
• A lemma about the Epstein zeta-function
• Notes on two lemmas concerning the Epstein zeta-function
• Statistical Theory of the Energy Levels of Complex Systems. IV
• Statistical Theory of the Energy Levels of Complex Systems. V
• A Dynamical Approach to Random Matrix Theory
• Lattice Sums Then and Now
• Universality for random matrices and log-gases
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• An Extension Problem Related to the Fractional Laplacian
• Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets
• Large-Nexpansion for the 2D Dyson gas
• A model for the bus system in Cuernavaca (Mexico)
• The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
• Random Matrices in Physics
• Rigorous Statistical Mechanics for Nonuniform Systems
• A Statistical Mechanical Approach to the Problem of a Fluid in an External Field
• Proof of a Conjecture by Dyson
• Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces. III. Statistics of the Electric Field
• Long-Range Correlations in a Closed System with Applications to Nonuniform Fluids
• Convergence of Fugacity Expansions for Fluids and Lattice Gases
• NEXT ORDER ASYMPTOTICS AND RENORMALIZED ENERGY FOR RIESZ INTERACTIONS
• A quantum mechanical investigation of the cohesive forces of metallic copper
• Quelques Propriétés Générales De L'intégrale De Configuration D'un Système De Particules Avec Interaction
• Sur L'intégrale de Configuration Pour Les Systèmes De Particules À Une Dimension
• A Minimum Problem for the Epstein Zeta-Function
• Effect of Short Wavelength Interference on Neuteron Scattering by Dense Systems of Heavy Nuclei
• Local Properties of Riesz Minimal Energy Configurations and Equilibrium Measures
• Harmonically confined long-ranged interacting gas in the presence of a hard wall
• Liouville perturbation theory for Laughlin state and Coulomb gas
• Ginzburg-Landau vortices
• Bounded fluctuations and translation symmetry breaking in one-dimensional particle systems
• Bounded fluctuations and translation symmetry breaking: a solvable model
• Replica treatment of the Calogero-Sutherland model
• On the thermodynamic limit for Hartree-Fock type models
• Classical and quantum statistical mechanics in one and two dimensions: two-component Yukawa- and Coulomb systems.
• On the \(1/n\) expansion for some unitary invariant ensembles of random matrices
• Observables at infinity and states with short range correlations in statistical mechanics
• Regularity theory for general stable operators
• Logarithmic, Coulomb and Riesz energy of point processes
• Exact energy computation of the one component plasma on a sphere for even values of the coupling parameter
• Mean-field models for disordered crystals
• Wigner crystallization in the quantum 1D jellium at all densities
• Quasi-uniformity of minimal weighted energy points on compact metric spaces
• From the Ginzburg-Landau model to vortex lattice problems
• Level statistics for one-dimensional Schrödinger operators and Gaussian beta ensemble
• Riesz external field problems on the hypersphere and optimal point separation
• Gap universality of generalized Wigner and \(\beta\)-ensembles
• Infinite-body optimal transport with Coulomb cost
• 1D log gases and the renormalized energy: crystallization at vanishing temperature
• Quantum Hall effect and Quillen metric
• Diameter bounded equal measure partitions of Ahlfors regular metric measure spaces
• Some open problems in random matrix theory and the theory of integrable systems. II
• Number rigidity in superhomogeneous random point fields
• Gibbs measures and phase transitions.
• Random matrices: universality of local eigenvalue statistics
• Symmetry breaking in quasi-1D Coulomb systems
• Universality of random matrices and local relaxation flow
• Fekete points and convergence towards equilibrium measures on complex manifolds
• Kosterlitz-Thouless transition line for the two dimensional Coulomb gas
• Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
• Application of an idea of Voronoĭ to lattice zeta functions
• Characteristic vectors of bordered matrices with infinite dimensions
• On the distribution of the roots of certain symmetric matrices
• Entropy, large deviations, and statistical mechanics.
• Continuum limits of random matrices and the Brownian carousel
• Strongly correlated phases in rapidly rotating Bose gases
• Riesz spherical potentials with external fields and minimal energy points separation
• The phase transition in the one-dimensional Ising model with \(1/r^2\) interaction energy
• Determinantal processes and completeness of random exponentials: the critical case
• The crystallization conjecture: a review
• An application of the modular function in nonlocal variational problem
• Gibbsian random fields for lattice systems with pairwise interactions.
• Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles
• The thermodynamic limit of quantum Coulomb systems. I: General theory
• On potential and field fluctuations in classical charged systems
• Analyticity for one-dimensional systems with long-range superstable interactions
• On the absence of phase transition in continuous one-dimensional Gibbs systems with no hard core
• Absence of crystalline ordering in two dimensions
• The thermodynamic limit for a crystal
• Equilibrium equations and symmetries of classical Coulomb systems
• Surface effects in Debye screening
• Thermodynamics for Coulomb systems: A problem at vanishing particle densities
• Extremals of determinants of Laplacians
• The existence of the thermodynamic limit in Coulomb-like systems
• Quadrature domains
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
• Three integrable Hamiltonian systems connected with isospectral deformations
• Homogeneous random fields and statistical mechanics
• On the distribution of Fekete points
• The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei.
• The Thomas-Fermi theory of atoms, molecules and solids
• A note on the eigenvalue density of random matrices
• Two-dimensional Coulomb systems on a surface of constant negative curvature
• Large deviations and the maximum entropy principle for marked point random fields
• Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction
• Distributing many points on a sphere
• The thermodynamic limit for jellium
• Pressures for a one-component plasma on a pseudosphere
• Mathematical problems for the next century
• The equivalence of ensembles for classical systems of particles.
• Characterization of functions on \(\mathbb{R}^3\) with bounded Newtonian potential
• Hyperuniform states of matter
• Local microscopic behavior for 2D Coulomb gases
• Large deviation principle for empirical fields of log and Riesz gases
• Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere
• Equidistribution of jellium energy for Coulomb and Riesz interactions
• Next-order asymptotic expansion for \(N\)-marginal optimal transport with Coulomb and Riesz costs
• Local incompressibility estimates for the Laughlin phase
• Rigidity of the \(\operatorname{Sine} _{\beta }\) process
• Fluctuations, large deviations and rigidity in hyperuniform systems: a brief survey
• Repulsion in low temperature \({\beta}\)-ensembles
• On the stationary BBGKY hierarchy for equilibrium states
• Minimal Riesz energy point configurations for rectifiable \(d\)-dimensional manifolds
• Rigidity of the Laughlin liquid
• Perturbation theory for linear operators.
• Chaotic eigenfunctions in phase space.
• Analysis of certain lattice sums
• The Coulomb gas at low temperature and low density
• On the question of final \(\zeta\)-optimality of lattices providing the closest lattice packing of \(n\)-dimensional spheres
• Lattice point problems and values of quadratic forms
• Action-angle maps and scattering theory for some finite-dimensional integrable systems. III: Sutherland type systems and their duals
• The free energy of systems with net charge
• On the molecular limit of Coulomb gases
• Generalized Hartree-Fock theory and the Hubbard model
• Debye screening for two-dimensional Coulomb systems at high temperatures
• Zeros of principal \(L\)-functions and random matrix theory
• Asymptotic expansion of \(\beta \) matrix models in the one-cut regime
• Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
• Coulomb systems at low density: a review.
• Exact finite-size study of the 2D OCP at \(\Gamma=4\) and \(\Gamma=6\)
• Local optimality of cubic lattices for interaction energies
• Large deviations for Gibbs measures with singular Hamiltonians and emergence of Kähler-Einstein metrics
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• A localization theorem for the planar Coulomb gas in an external field
• Fluctuation and entropy in spectrally constrained random fields
• Almost impossible \(E_8\) and Leech lattices
• The classical Jellium and the Laughlin phase
• Emergence of Haldane pseudo-potentials in systems with short-range interactions
• Lattices with finite renormalized Coulombian interaction energy in the plane
• Local laws and rigidity for Coulomb gases at any temperature
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• A uniqueness result for minimizers of the 1D log-gas renormalized energy
• On the calculation of an integral
• Bulk universality for Wigner Hermite matrices with subexponential decay
• The local density approximation in density functional theory
• Some connections between the classical Calogero-Moser model and the log-gas
• On lattice sums and Wigner limits
• Existence and stability for a non-local isoperimetric model of charged liquid drops
• 2D Coulomb gases and the renormalized energy
• Renormalized energy concentration in random matrices
• Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues
• The \(\mathrm{Sine}_{\beta}\) operator
• Boundary regularity estimates for nonlocal elliptic equations in \(C^1\) and \(C^{1,\alpha }\) domains
• Local density for two-dimensional one-component plasma
• Large deviation principles for hypersingular Riesz gases
• Universality for conditional measures of the sine point process
• Universality of general \(\beta\)-ensembles
• Selected topics on quadrature domains
• Large charge fluctuations in classical Coulomb systems
• Minima of Epstein's zeta function and heights of flat tori
• Is the two-dimensional one-component plasma exactly solvable?
• Symmetry breaking in Laughlin's state on a cylinder
• The problem of uniqueness of a Gibbsian random field and the problem of phase transitions
• Gibbsian random fields. The general case
• Superstable interactions in classical statistical mechanics
• The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem
• Determinantal random point fields
• Higher-Dimensional Coulomb Gases and Renormalized Energy Functionals
• Bulk universality of general β-ensembles with non-convex potential
• Physics of Long-Range Interacting Systems
• Periodic discrete energy for long-range potentials
• Generating Point Configurations via Hypersingular Riesz Energy with an External Field
• Large Deviations of Empirical Measures of Zeros of Random Polynomials
• Gibbs' States for Moser-Calogero Potentials
• ASYMPTOTIC LINEAR PROGRAMMING LOWER BOUNDS FOR THE ENERGY OF MINIMIZING RIESZ AND GAUSS CONFIGURATIONS
• Über eine Punktverteilung auf der Kugel
• Zero-Point Energy of an Electron Lattice
• On a problem of Rankin about the Epstein zeta-function
• Statistical Theory of the Energy Levels of Complex Systems. I
• Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces. II. The Method of Functional Integration
• The Riesz energy of the N th roots of unity: an asymptotic expansion for large N
• The virial expansion of a classical interacting system
• Universally optimal distribution of points on spheres
• Vortex Lattices in Rotating Bose–Einstein Condensates
• Large-NAsymptotic Expansion for Mean Field Models with Coulomb Gas Interaction
• Multi-marginal optimal transport: Theory and applications
• Theoretical Practice: the Bohm-Pines Quartet
• An Introduction to Random Matrices
• Convergence of lattice sums and Madelung’s constant
• Minimal theta functions
• Energy of static electron lattices
• Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels
• Statistical Thermodynamics of Nonuniform Fluids
• Locally minimal Epstein zeta functions
• The local regularity of solutions of degenerate elliptic equations
• Gibbs States on Countable Sets
• Statistical mechanics of classical particles with logarithmic interactions
• Semiclassical theory of spectral rigidity
• Asymptotics for minimal discrete energy on the sphere
• Density Functionals for Non-relativistic Coulomb Systems in the New Century
• ‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle
• Statistical Mechanics for a Class of Quantum Statistics
• Thermodynamics of a One-Dimensional Ideal Gas with Fractional Exclusion Statistics
• Stability of Matter. I
• Stability of Matter. II
• The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles
• Statistical mechanics of the uniform electron gas
• Next Order Energy Asymptotics for Riesz Potentials on Flat Tori
• On the Distribution of Spacings Between Zeros of the Zeta Function
• The Optimal Lattice Quantizer in Three Dimensions
• On the Interaction of Electrons in Metals
• Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝ^d
• Matrix models for beta ensembles
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