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These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics.
Plancks Gesetz und Lichtquantenhypothese
Bose · 1924
Earlier work this paper cites.
Quantentheorie des einatomigen idealen Gases
Einstein, A · 1924
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Funzione caratteristica di un fenomeno aleatorio
de Finetti, B · 1931
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Sur les classes d’évènements équivalents
Khintchine, A. Y · 1932
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La prévision, ses lois logiques, ses sources subjectives
de Finetti, B · 1937
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Classes of equivalent random quantities
Dynkin, E. B · 1953
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Symmetric measures on Cartesian products
Hewitt, E., and Savage, L. J · 1955
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Bose-Einstein Condensation and Liquid Helium
Penrose, O., and Onsager, L · 1956
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Ground-state energy of a hard-sphere gas
Dyson, F. J · 1957
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Norm Ideals of Completely Continuous Operators
Schatten, R · 1960
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Statistical theory of the energy levels of a complex system. part I
Dyson, F. J · 1962
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Statistical theory of the energy levels of a complex system. part II
Dyson, F. J · 1962
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Statistical theory of the energy levels of a complex system. part III
Dyson, F. J · 1962
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Statistical ensembles of complex, quaternion, and real matrices
Ginibre, J · 1965
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On the limits of sequences of normal states
dell’Antonio, G · 1967
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Mean entropy of states in classical statistical mechanics
Robinson, D., and Ruelle, D · 1967
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Nonsaturation of gravitational forces
Lévy-Leblond, J.-M · 1969
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Symmetric states of infinite tensor products of C ∗ C^{\ast} -algebras
Størmer, E · 1969
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Normal and locally normal states
Robinson, D. W · 1970
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Propagation of chaos for the Boltzmann equation
Grünbaum, S. A · 1971
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Convex functions of operators
Berezin, F. A · 1972
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The classical limit of quantum spin systems
Lieb, E. H · 1973
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The classical limit for quantum mechanical correlation functions
Hepp, K · 1974
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The P ( ϕ ) 2 P(\phi)_{2} Euclidean (quantum) field theory
Simon, B · 1974
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Integration in Hilbert space
Skorokhod, A · 1974
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Locally normal symmetric states and an analogue of de Finetti’s theorem
Hudson, R. L., and Moody, G. R · 1975
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Methods of Modern Mathematical Physics. II. Fourier analysis, self-adjointness
Reed, M., and Simon, B · 1975
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The stability of matter
Lieb, E. H · 1976
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A note on Hunziker’s theorem
Enss, V · 1977
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A remark on the difference between sampling with and without replacement
Freedman, D · 1977
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Geometric methods in multiparticle quantum systems
Simon, B · 1977
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Classical bounds and limits for energy distributions of Hamilton operators in electromagnetic fields
Combes, J., Schrader, R., and Seiler, R · 1978
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Asymptotic completeness for quantum mechanical potential scattering. I. Short range potentials
Enss, V · 1978
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Über äquivalente normierung der anisotropen Funktionalraüme H μ ( ℝ n ) H^{\mu}(\mathbb{R}^{n})
Masja, W., and Nagel, J · 1978
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Methods of Modern Mathematical Physics. IV. Analysis of operators
Reed, M., and Simon, B · 1978
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The classical field limit of scattering theory for nonrelativistic many-bosons systems. I
Ginibre, J., and Velo, G · 1979
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The classical field limit of scattering theory for nonrelativistic many-bosons systems. II
Ginibre, J., and Velo, G · 1979
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Trace ideals and their applications
Simon, B · 1979
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Finite exchangeable sequences
Diaconis, P., and Freedman, D · 1980
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Equilibrium states for mean field models
Fannes, M., Spohn, H., and Verbeure, A · 1980
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The classical limit of quantum partition functions
Simon, B · 1980
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Kinetic equations from Hamiltonian dynamics: Markovian limits
Spohn, H · 1980
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On the Vlasov hierarchy
Spohn, H · 1981
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Statistical mechanics of the isothermal Lane-Emden equation
Messer, J., and Spohn, H · 1982
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Geometric methods in the quantum many-body problem. Non existence of very negative ions
Sigal, I. M · 1982
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Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle
Benguria, R., and Lieb, E. H · 1983
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Nonlinear Schrödinger equations and sharp interpolation estimates
Weinstein, M. I · 1983
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Gravitational collapse in quantum mechanics with relativistic kinetic energy
Lieb, E. H., and Thirring, W. E · 1984
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The concentration-compactness principle in the calculus of variations. The locally compact case, Part I
Lions, P.-L · 1984
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The concentration-compactness principle in the calculus of variations. The locally compact case, Part II
Lions, P.-L · 1984
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Exchangeability and Related Topics
Aldous, D · 1985
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Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods
Gallavotti, G · 1985
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Coherent States, Applications in Physics and Mathematical Physics
Klauder, J., and Skagerstam, B · 1985
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The concentration-compactness principle in the calculus of variations. The limit case. I
Lions, P.-L · 1985
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The concentration-compactness principle in the calculus of variations. The limit case. II
Lions, P.-L · 1985
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Quantum Physics: A Functional Integral Point of View
Glimm, J., and Jaffe, A · 1987
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The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics
Lieb, E. H., and Yau, H.-T · 1987
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Statistical mechanics of the nonlinear Schrödinger equation
Lebowitz, J. L., Rose, H. A., and Speer, E. R · 1988
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On the equilibrium statistical mechanics of isothermal classical self-gravitating matter
Kiessling, M. K.-H · 1989
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Uniqueness of positive solutions of Δ u − u + u p = 0 in ℝ n {\Delta}u-u+u^{p}=0\mbox{ in }{\mathbb{R}}^{n}
Kwong, M. K · 1989
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Asymptotics of Varadhan-type and the Gibbs variational principle
Petz, D., Raggio, G. A., and Verbeure, A · 1989
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Quantum statistical mechanics of general mean field systems
Raggio, G. A., and Werner, R. F · 1989
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Coherent states : theory and some applications
Zhang, W., Feng, D., and Gilmore, R · 1990
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A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description
Caglioti, E., Lions, P.-L., Marchioro, C., and Pulvirenti, M · 1992
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Statistical mechanics of classical particles with logarithmic interactions
Kiessling, M. K.-H · 1993
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Periodic nonlinear Schrödinger equation and invariant measures
Bourgain, J · 1994
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On the statistical mechanics approach in the random matrix theory: integrated density of states
Boutet de Monvel, A., Pastur, L., and Shcherbina, M · 1995
Cited alongside, same era.
Invariant measures for the 2d-defocusing nonlinear Schrödinger equation
Bourgain, J · 1996
Cited alongside, same era.
Large deviations for Wigner’s law and Voiculescu’s noncommutative entropy
Ben Arous, G., and Guionnet, A · 1997
Cited alongside, same era.
Large deviations from the circular law
Ben Arous, G., and Zeitouni, O · 1998
Cited alongside, same era.
Ground state energy of the low density Bose gas
Lieb, E. H., and Yngvason, J · 1998
Cited alongside, same era.
Theory of Bose-Einstein condensation in trapped gases
Dalfovo, F., Giorgini, S., Pitaevskii, L. P., and Stringari, S · 1999
Cited alongside, same era.
An introduction to random matrices
Anderson, G., Guionnet, A., and Zeitouni, O · 2010
Later among the works it cites.
Critical temperature of dilute bose gases
Betz, V., and Ueltschi, D · 2010
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Mean-field dynamics: singular potentials and rate of convergence
Knowles, A., and Pickl, P · 2010
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The Stability of Matter in Quantum Mechanics
Lieb, E. H., and Seiringer, R · 2010
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On the symmetry of the ground states of nonlinear Schrödinger equation with potential
Maeda, M · 2010
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Derivation of the time dependent Gross Pitaevskii equation with external fields
Pickl, P · 2010
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Asymptotic completeness in quantum field theory. Massive Pauli-Fierz Hamiltonians
Dereziński, J., and Gérard, C · 1999
Cited alongside, same era.
A note on the eigenvalue density of random matrices
Kiessling, M. K.-H., and Spohn, H · 1999
Cited alongside, same era.
Weak coupling limit of the N N -particle Schrödinger equation
Bardos, C., Golse, F., and Mauser, N. J · 2000
Cited alongside, same era.
Reduced Density Matrices: Coulson’s Challenge
Coleman, A., and Yukalov, V · 2000
Cited alongside, same era.
Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional
Lieb, E. H., Seiringer, R., and Yngvason, J · 2000
Cited alongside, same era.
Another look at Sobolev spaces
Bourgain, J., Brézis, H., and Mironescu, P · 2001
Cited alongside, same era.
Derivation of the time dependent Gross-Pitaevskii equation without positivity condition on the interaction
Pickl, P · 2010
Later among the works it cites.
Gibbs measure for the periodic derivative nonlinear Schrödinger equation
Thomann, L., and Tzvetkov, N · 2010
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Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
Ammari, Z., and Nier, F · 2011
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On quantum estimation, quantum cloning and finite quantum de Finetti theorems
Chiribella, G · 2011
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Artificial gauge potentials for neutral atoms
Dalibard, J., Gerbier, F., Juzeliūnas, G., and Öhberg, P · 2011
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Invariant measure for the cubic wave equation on the unit ball of ℝ 3 \mathbb{R}^{3}
de Suzzoni, A.-S · 2011
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Geometric methods for nonlinear many-body quantum systems
Lewin, M · 2011
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Estimation quantitative et uniforme en temps de la propagation du chaos et introduction aux limites de champ moyen pour des systèmes de particules
Mischler, S · 2011
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A simple derivation of mean-field limits for quantum systems
Pickl, P · 2011
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The excitation spectrum for weakly interacting bosons
Seiringer, R · 2011
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Bulk universality of general β \beta -ensembles with non-convex potential
Bourgade, P., Erdös, L., and Yau, H.-T · 2012
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The Hartree limit of Born’s ensemble for the ground state of a bosonic atom or ion
Kiessling, M. K.-H · 2012
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unpublished, 2012
Lewin, M., and Rougerie, N · 2012
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Disordered Bose-Einstein condensates with interaction in one dimension
Seiringer, R., Yngvason, J., and Zagrebnov, V. A · 2012
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Large scale dynamics of interacting particles
Spohn, H · 2012
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A Perspective on Constructive Quantum Field Theory
Summers, S. J · 2012
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Systèmes hamiltoniens en théorie quantique des champs : dynamique asymptotique et limite classique
Ammari, Z · 2013
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Quantum de Finetti theorems under local measurements with applications
Brandão, F., and Harrow, A · 2013
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Long time dynamics for the one dimensional non linear Schrödinger equation
Burq, N., Thomann, L., and Tzvetkov, N · 2013
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On the Dynamics of Large Particle Systems in the Mean Field Limit
Golse, F · 2013
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Empirical measures and Vlasov hierarchies
Golse, F., Mouhot, C., and Ricci, V · 2013
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The excitation spectrum for weakly interacting bosons in a trap
Grech, P., and Seiringer, R · 2013
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The church of the symmetric subspace
Harrow, A · 2013
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Quantum and thermal fluctuations in bosonic Josephson junctions
Juliá-Díaz, B., Gottlieb, A., Martorell, J., and Polls, A · 2013
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Bogoliubov spectrum of interacting Bose gases
Lewin, M., Nam, P. T., Serfaty, S., and Solovej, J. P · 2013
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unpublished, 2013
Lewin, M., and Rougerie, N · 2013
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Kac’s Program in Kinetic Theory
Mischler, S., and C., M · 2013
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Sur la modélisation de l’interaction entre polarons et cristaux quantiques
Rougerie, N · 2013
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Quantum Hall phases and plasma analogy in rotating trapped bose gases
Rougerie, N., Serfaty, S., and Yngvason, J · 2013
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Quantum Hall states of bosons in rotating anharmonic traps
Rougerie, N., Serfaty, S., and Yngvason, J · 2013
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Quantitative Derivation of the Gross-Pitaevskii Equation
Benedikter, N., de Oliveira, G., and Schlein, B · 2014
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Universality of general β \beta -ensembles
Bourgade, P., Erdös, L., and Yau, H.-T · 2014
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Stability estimates for the lowest eigenvalue of a Schrödinger operator
Carlen, E., Frank, R., and Lieb, E · 2014
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First order asymptotics for confined particles with singular pair repulsions
Chafaï, D., Gozlan, N., and Zitt, P.-A · 2014
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On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
Chen, T., Hainzl, C., Pavlovíc, N., and Seiringer, R · 2014
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Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti
Chen, T., Hainzl, C., Pavlovíc, N., and Seiringer, R · 2014
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Quantum fields with classical perturbations
Dereziński, J · 2014
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Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
Dereziński, J., and Napiórkowski, M · 2014
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Ground states of semi-linear PDEs
Frank, R. L · 2014
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Symmetry breaking and collapse in Bose-Einstein condensates with attractive interactions
Guo, Y., and Seiringer, R · 2014
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On Kac’s chaos and related problems
Hauray, M., and Mischler, S · 2014
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Derivation of Hartree’s theory for generic mean-field Bose systems
Lewin, M., Nam, P. T., and Rougerie, N · 2014
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Derivation of nonlinear Gibbs measures from many-body quantum mechanics
Lewin, M., Nam, P. T., and Rougerie, N · 2014
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The mean-field approximation and the non-linear Schrödinger functional for trapped bose gases
Lewin, M., Nam, P. T., and Rougerie, N · 2014
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Remarks on the quantum de Finetti theorem for bosonic systems
Lewin, M., Nam, P. T., and Rougerie, N · 2014
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Collective excitations of Bose gases in the mean-field regime
Nam, P.-T., and Seiringer, R · 2014
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Next order asymptotics and renormalized energy for Riesz interactions
Petrache, M., and Serfaty, S · 2014
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Higher dimensional Coulomb gases and renormalized energy functionals
Rougerie, N., and Serfaty, S · 2014
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1d Log Gases and the Renormalized Energy: Crystallization at vanishing temperature
Sandier, E., and Serfaty, S · 2014
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2d coulomb gases and the renormalized energy
Sandier, E., and Serfaty, S · 2014
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Coulomb gases and Ginzburg-Landau vortices
Serfaty, S · 2014
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Effective Evolution Equations from Quantum Dynamics
Benedikter, N., Porta, M., and Schlein, B · 2015
Closest in time.
Large Deviation Principle for Empirical Fields of Log and Riesz Gases
Leblé, T., and Serfaty, S · 2015
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The average field approximation for almost bosonic extended anyons
Lundholm, D., and Rougerie, N · 2015
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Ground states of large Bose systems: The Gross-Pitaevskii limit revisited
Nam, P. T., Rougerie, N., and Seiringer, R · 2015
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Incompressibility estimates for the Laughlin phase
Rougerie, N., and Yngvason, J · 2015
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Incompressibility estimates for the Laughlin phase, part ii
Rougerie, N., and Yngvason, J · 2015
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On two properties of the fisher information
Rougerie, N · 2019
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Propagation of chaos for fractional Keller Segel equations in diffusion dominated and fair competition cases
Salem, S · 2019
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Propagation of chaos for the boltzmann equation with moderately soft potentials
Salem, S · 2019
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