Some contributions to many-body quantum mathematics
arXiv:1607.03833
Abstract
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The main tools are mostly those of the mathematical analyst: partial differential equations, functional analysis, spectral theory, calculus of variations, with some incursions into probability theory. A running thread is the construction, by rigorous asymptotic analysis most of the time, of bridges between different levels of mathematical modeling of physical phenomena. This is the manuscript for the author's habilitation thesis, summarizing results obtained between 2011 and 2016, in collaboration with: Michele Correggi, Mathieu Lewin, Douglas Lundholm, Phan Thành Nam, Robert Seiringer, Sylvia Serfaty and Jakob Yngvason.
arXiv comment118 pages, "habilitation à diriger des recherches" thesis. The defense took place in Grenoble on November 8th, 2016. The composition of the committee has been added on the front page
References in corpus (59)
- Many-Body Physics with Ultracold Gases
- Theory of Bose-Einstein condensation in trapped gases
- Vortex formation in a stirred Bose-Einstein condensate
- Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
- Rapidly Rotating Atomic Gases
- Unknown Quantum States: The Quantum de Finetti Representation
- Vortex Nucleation in a Stirred Bose-Einstein Condensate
- Proof of Bose-Einstein Condensation for Dilute Trapped Gases
- Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
- Symmetry implies independence
- Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
- One-and-a-half quantum de Finetti theorems
- Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
- A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas
- On Kac's Chaos And Related Problems
- A Composite Fermion Description of Rotating Bose-Einstein Condensates
- Vortex patterns in a fast rotating Bose-Einstein condensate
- The excitation spectrum for weakly interacting bosons in a trap
- Yrast line for weakly interacting trapped bosons
- Erratum: Exact Ground State Energy of the Strong-Coupling Polaron
- Geometric methods for nonlinear many-body quantum systems
- Experimental studies of equilibrium vortex properties in a Bose-condensed gas
- Signatures of fractional statistics in noise experiments in quantum Hall fluids
- A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
- Next Order Asymptotics and Renormalized Energy for Riesz Interactions
- Quantum Hall fractions for spinless Bosons
- Bose condensates at high angular momenta
- Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation
- Rotational spectra of weakly interacting Bose-Einstein condensates
- Ground State Energy of the Low Density Fermi Gas
- Emergence of fractional statistics for tracer particles in a Laughlin liquid
- Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement
- The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
- Strongly correlated phases in rapidly rotating Bose gases
- Fractional angular momentum in cold atom systems
- Non-perturbative embedding of local defects in crystalline materials
- A Perspective on Constructive Quantum Field Theory
- Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps
- Vortex distribution in the Lowest Landau Level
- Quantum statistics and locality
- The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution
- Local exclusion principle for identical particles obeying intermediate and fractional statistics
- Mean-field limit of Bose systems: rigorous results
- The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime
- Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
- Quantum Hall states of bosons in rotating anharmonic traps
- Composite fermion theory of rapidly rotating two-dimensional bosons
- Bi-Polaron and N-Polaron Binding Energies
- Lowest Landau Level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap
- Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases
- Parafermionic states in rotating Bose-Einstein condensates
- Anyons and lowest Landau level Anyons
- On the anyon description of the Laughlin hole states
- Magnetic Moment and Perturbation Theory with Singular Magnetic Fields
- Geometric extensions of many-particle Hardy inequalities
- Finite-size anyons and perturbation theory
- Hot Topics in Cold Gases
- Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
- Bose Gases at Positive Temperature and Non-Linear Gibbs Measures