Prof. Dr. Benjamin Schlein

Vita

Research

My research field is mathematical physics.

In particular, I am interested in the mathematical analysis of many-body quantum systems. A central question in my research is the derivation of effective theories describing properties of quantum system in interesting limiting regimes including, for example, the Gross-Pitaevskii limit for Bose-Einstein condensates and the mean-field limit for bosonic and fermionic systems.

Another area I am interested in is random matrix theory. In particular, I have been working to obtain a mathematically rigorous understanding of the universality properties of eigenvalue statistics for ensembles of Wigner matrices.

A list of my publications can be found

here

Publications

Morris Brooks, Jakob Felix Oldenburg, Diane Saint Aubin, Benjamin SchleinThird Order Upper Bound for the Ground State Energy of the Dilute Bose Gas.

Luca Fresta, Marcello Porta, Benjamin SchleinEffective Dynamics of Local Observables for Extended Fermi Gases in the High-Density Regime.

Florian Haberberger, Christian Hainzl, Arnaud Triay, Benjamin SchleinUpper Bound for the Free Energy of Dilute Bose Gases at Low Temperature.

Cristina Caraci, Alessandro Olgiati, Diane Saint Aubin, Benjamin SchleinThird order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime.

Cristina Caraci, Jakob Felix Oldenburg, Benjamin SchleinQuantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation.

Giulia Basti, Serena Cenatiempo, Alessandro Giuliani, Alessandro Olgiati, Giulio Pasqualetti, Benjamin SchleinUpper bound for the ground state energy of a dilute Bose gas of hard spheres.

Cristina Caraci, Serena Cenatiempo, Benjamin SchleinThe excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime.

Luca Fresta, Marcello Porta, Benjamin SchleinEffective Dynamics of Extended Fermi Gases in the High-Density Regime.

Marco Caporaletti, Andreas Deuchert, Benjamin SchleinDynamics of mean-field bosons at positive temperature.

Giulia Basti, Serena Cenatiempo, Alessandro Olgiati, Giulio Pasqualetti, Benjamin SchleinA second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime.

Benjamin SchleinBose gases in the Gross-Pitaevskii limit: a survey of some rigorous results.. The Physics and Mathematics of Elliott Lieb, Vol 2. Edited by Frank, Laptev, Lewin, Seiringer.

Christian Hainzl, Benjamin Schlein, Arnaud TriayBogoliubov Theory in the Gross-Pitaevskii Limit: a Simplified Approach.

Giulia Basti, Serena Cenatiempo, Alessandro Olgiati, Giulio Pasqualetti, Benjamin SchleinGround state energy of a Bose gas in the Gross-Pitaevskii regime.

Jürg Fröhlich, Antti Knowles, Benjamin Schlein, Vedran SohingerThe Euclidean phi_2^4 theory as a limit of an interacting Bose gas.

Christian Brennecke, Benjamin Schlein, Severin SchravenBogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime.

Niels Patriz Benedikter, Marcello Porta, Benjamin Schlein, Robert SeiringerCorrelation energy of a weakly interacting Fermi gas with large interaction potential.

Christian Brennecke, Marco Caporaletti, Benjamin SchleinExcitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime.

Niels Patriz Benedikter, Phan Thanh Nam, Marcello Porta, Benjamin Schlein, Robert SeiringerBosonization of Fermionic Many-Body Dynamics.

Christian Brennecke, Benjamin Schlein, Severin SchravenBose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime.

Benjamin SchleinBogoliubov theory for many-body quantum systems.. Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume. Edited by P. Exner, R.L. Frank, F. Gesztesy, H. Holden, T. Weidl.

Giulia Basti, Serena Cenatiempo, Benjamin SchleinA new second order upper bound for the ground state energy of dilute Bose gases.

Jürg Fröhlich, Antti Knowles, Benjamin Schlein, Vedran SohingerInteracting loop ensembles and Bose gases.

Cristina Caraci, Serena Cenatiempo, Benjamin SchleinBose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime.

Kay Kirkpatrick, Benjamin Schlein, Simone RademacherA large deviation principle in many-body quantum dynamics.

Benjamin Schlein, Niels Patriz Benedikter, Robert Seiringer, Phan Thanh Nam, Marcello PortaCorrelation energy of a weakly interacting Fermi gas.

Benjamin Schlein, Robert Seiringer, Simone Rademacher, Nikolai Leopold, David MitrouskasLandau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron.

Benjamin Schlein, Christian BrenneckeBose-Einstein condensation beyond the Gross-Pitaevskii regime.

Benjamin Schlein, Jürg Fröhlich, Vedran Sohinger, Antti KnowlesA path-integral analysis of interacting Bose gases and loop gases.

Benjamin SchleinThe mean-field limit of quantum Bose gases at positive temperature.

Benjamin Schlein, Simone Rademacher, Robert Seiringer, Nikolai LeopoldThe Landau-Pekar equations: Adiabatic theorem and accuracy.

Benjamin Schlein, Simone RademacherCentral limit theorem for Bose-Einstein condensates.

Benjamin Schlein, Chiara Boccato, Christian Brennecke, Serena CenatiempoOptimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.

Benjamin Schlein, Niels Patriz Benedikter, Phan Thanh Nam, Robert Seiringer, Marcello PortaOptimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.

Benjamin SchleinBogoliubov excitation spectrum for Bose-Einstein condensates

Benjamin Schlein, Chiara Boccato, Christian Brennecke, Serena CenatiempoBogoliubov Theory in the Gross-Pitaevskii Limit.

Benjamin Schlein, Phan Thanh Nam, Christian Brennecke, Marcin NapiórkowskiFluctuations of N-particle quantum dynamics around the nonlinear Schroedinger equation.

Benjamin Schlein, Simone Rademacher, Elia DietlerFrom Hartree dynamics to the relativistic Vlasov equation.

Benjamin Schlein, Serena Cenatiempo, Chiara Boccato, Christian BrenneckeThe excitation spectrum of Bose gases interacting through singular potentials.

Benjamin Schlein, Jürg Fröhlich, Antti Knowles, Vedran SohingerA microscopic derivation of time-dependent correlation functions of the 1D cubic nonlinear Schroedinger equation.

Benjamin Schlein, Chiara Boccato, Christian Brennecke, Serena CenatiempoComplete Bose-Einstein condensation in the Gross-Pitaevskii regime.

Benjamin Schlein, Christian Brennecke Gross-Pitaevskii dynamics for Bose-Einstein condensates.

Marcello Porta, Simone Rademacher, Chiara Saffirio, Benjamin SchleinMean field evolution of fermions with Coulomb interaction.

Benjamin Schlein, Jürg Fröhlich, Vedran Sohinger, Antti Knowles Gibbs measures of nonlinear Schroedinger equations as limits of
many-body quantum states in dimensions $d \leq 3$.

Serena Cenatiempo, Benjamin Schlein, Chiara Boccato Quantum many-body fluctuations around nonlinear Schrödinger dynamics

Benjamin Schlein, Rupert L. Frank, Christian Hainzl, Robert SeiringerIncompatibility of the time-dependent Bogoliubov-de Gennes and Ginzburg-Landau equations.

Marcello Porta, Niels Patriz Benedikter, Benjamin Schlein, Chiara SaffirioFrom the Hartree dynamics to the Vlasov equation.

Marcello Porta, Niels Patriz Benedikter, Benjamin SchleinEffective Evolution Equations from Quantum Dynamics.

Marcello Porta, Niels Patriz Benedikter, Vojkan Jaksic, Chiara Saffirio, Benjamin SchleinMean-field evolution of fermionic mixed states.

Marcello Porta, Niels Patriz Benedikter, Benjamin SchleinHartree-Fock dynamics for weakly interacting fermions.. Proceedings of the QMath12 conference.

Benjamin Schlein, Rupert L. Frank Dynamics of a strongly coupled polaron.

Marcello Porta, Niels Patriz Benedikter, Benjamin SchleinMean-field dynamics of fermions with relativistic dispersion.

Benjamin Schlein, Claudio Cacciapuoti, Anna MaltsevBounds on the Stieltjes transform of Wigner matrices.. Prob. Theory Rel. Fields. 163 (2015), no. 1-2, 1–59.

Benjamin Schlein, Chiara Saffirio, Simon BuchholzMultivariate central limit theorem in quantum dynamics. . J. Stat. Phys. 154 (2014), no. 1-2, 1130-152.

Benjamin Schlein, Mathieu Lewin, Phan Thanh NamFluctuations around Hartree states in the mean-field regime. . Am. J. Math. 137 (2015), no. 6, 1613-1650.

Marcello Porta, Niels Patriz Benedikter, Benjamin SchleinMean-field evolution of fermionic systems.

Benjamin SchleinQuantum dynamics, coherent states and Bogoliubov transformations.. XVII ICMP, World Sci. Publ., pages 197-216.

Benjamin Schlein, Niels Patriz Benedikter, Gustavo de OliveiraQuantitative derivation of the Gross-Pitaevskii equation.. Comm. Pure Appl. Math. 68 (2015), no. 8, 1399-1482.

Benjamin SchleinEffective equations for quantum dynamics.. Proceedings of 6-th ECM, Krakow, July 2012.

Benjamin Schlein, Anna Maltsev, Claudio CacciapuotiLocal Marchenko-Pastur law at the hard edge of sample covariance matrices.. J. Math. Phys. 54 (2013), 043302.

Benjamin Schlein, Christian HainzlDynamics of Bose-Einstein condensates of fermion pairs in the low density limit of BCS theory. . J. Funct. Anal. 265 (2013), no. 3, 399-423.

Benjamin Schlein, Kay Kirkpatrick, Gérard Ben ArousA central limit theorem in many-body quantum dynamics.. Comm. Math. Phys. 321 (2013), 371-417.

Benjamin SchleinEffective evolution equations in quantum physics.

Benjamin Schlein, Anna Maltsev A Wegner Estimate for Wigner Matrices. . Entropy and the Quantum II. American Mathematical Society, 2011, 145-160.

Benjamin Schlein, Ji Oon Lee, Li ChenRate of convergence towards Hartree dynamics. . J. Statist. Phys. 144 (2011), no. 4, 872-903.

Benjamin SchleinEffective evolution equations from many body quantum dynamics.. Proceedings of ``New Perspectives in Quantum Statistics and Correlations''.
Universitaetsverlag Winter, Heidelberg, 2012.

Benjamin Schlein, Anna Maltsev Average density of states for hermitian Wigner matrices. . Adv. Math. 228 (2011), 2797-2836.

Benjamin Schlein Spectral properties of Wigner matrices. . Proceedings of QMath 11. World Scientific, 2011, 79-94.

Benjamin Schlein, Alessandro MichelangeliDynamical description of gravitational collapse.. Comm. Math. Phys. 311 (2012), no. 3 , 645-687.

Benjamin Schlein, Jürg Fröhlich, Alessandro PizzoIonization of atoms by intense laser pulses.. Ann. Henri Poincare 11 (2010), no. 7, 1375-1407.

Benjamin Schlein, László Erdős, Horng-Tzer Yau, Jun YinThe local relaxation flow approach to universality of the local statistics for random matrices. . Ann. Inst. H. Poincare Probab. Statist. 48 (2012), no. 1, 1-46.

Benjamin SchleinDerivation of effective evolution equations from many body quantum dynamics.. XVI ICMP, World Sci. Publ., Hackensack, NJ, 2010, 406-416.

Benjamin Schlein, Christian Hainzl, Enno Lenzmann, Mathieu LewinOn blowup for time-dependent generalized Hartree-Fock equations.. Ann. Henri Poincare 11 (2010), no. 6, 1023-1052.

Benjamin Schlein, Bruno Nachtergaele, Robert Sims, Valentin Zagrebnov, Shannon StarrOn the existence of the dynamics for anharmonic quantum oscillator systems. . Rev. Math. Phys. 22 (2010), no. 2, 207--231.

Benjamin Schlein, László Erdős, Horng-Tzer Yau Universality of random matrices and local relaxation flow. . Invent. Math. 185 (2011), no. 1, 75-119.

Benjamin Schlein, László Erdős, Horng-Tzer Yau, Jose Ramirez, Terence Tao, Van VuBulk universality for Wigner hermitian matrices with subexponential decay.. Math. Res. Lett. 17 (2010), no. 4, 667-674.

Benjamin Schlein, László Erdős, Horng-Tzer Yau, Jose Ramirez, Sandrine PéchéBulk universality for Wigner matrices.. Comm. Pure Appl. Math. 63 (2010), no. 7, 895-925.

Benjamin Schlein, László Erdős, Horng-Tzer Yau, Jose RamirezUniversality of sine-kernel for Wigner matrices with a small Gaussian perturbation.. Electron. J. Probab. 15 (2010), no. 18, 526-603.

Benjamin Schlein, László Erdős, Horng-Tzer YauWegner estimate and level repulsion for Wigner random matrices.. Int. Math. Res. Not. 2010, no. 3, 436-479.

Benjamin Schlein, Kay Kirkpatrick, Gigliola Staffilani Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics.. Amer. J. Math. 133 (2011), no.1, 91-130.

Benjamin Schlein, László Erdős, Alessandro Michelangeli Dynamical formation of correlations in a Bose-Einstein condensate. . Comm. Math. Phys. 289 (2009), no. 3, 1171-1210.

Benjamin Schlein Derivation of effective evolution equations from microscopic quantum dynamics. . Clay Mathematics Proceedings 17, 2013, 511-572.

Benjamin Schlein, László Erdős, Horng-Tzer Yau The ground state energy of a low density Bose gas: a second order upper bound. . Phys. Rev. A 78 (2008), no. 5, 053627.

Benjamin Schlein, László Erdős Quantum dynamics with mean field interactions: a new approach. . J. Statist. Phys. 134 (2009), no. 5, 859-870.

Benjamin Schlein, Christian Hainzl Stellar collapse in the time dependent Hartree-Fock approximation.. Comm. Math. Phys. 287 (2009), no. 2, 705-717.

Benjamin Schlein, László Erdős, Horng-Tzer Yau Local semicircle law and complete delocalization for Wigner random matrices. . Comm. Math. Phys. 287 (2009), no. 2, 641-655.

Benjamin Schlein, László Erdős, Horng-Tzer YauRigorous derivation of the Gross-Pitaevskii equation with a large interaction potential.. J. Amer. Math. Soc. 22 (2009), no. 4, 1099-1156.

Benjamin Schlein, Bruno Nachtergaele, Hillel Raz, Robert SimsLieb-Robinson bounds for harmonic and anharmonic lattice systems.. Comm. Math. Phys. 286 (2009), no. 3, 1073-1098.

Benjamin Schlein, Igor RodnianskiQuantum fluctuation and rate of convergence towards mean field dynamics.. Comm. Math. Phys. 291 (2009), no. 1, 31-61.

Benjamin Schlein, László Erdős, Horng-Tzer YauSemicircle law on short scales and delocalization of eigenvectors for Wigner random matrices.. Ann. Probab. 37 (2009), no. 3, 815-852.

Benjamin SchleinDynamics of Bose-Einstein Condensates.. Proceedings of XV ICMP, Springer Verlag, 2009, 565-589.

Benjamin Schlein, László Erdős, Horng-Tzer YauRigorous derivation of the Gross-Pitaevskii equation.. Phys. Rev. Lett. 98 (2007), no. 4, 040404.

Benjamin Schlein, László Erdős, Horng-Tzer YauDerivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates. . Ann. of Math. (2) 172 (2010), no. 1, 291-370.

Benjamin Schlein, Jürg Fröhlich, Marcel GriesemerRayleigh scattering at atoms with dynamical nuclei.. Comm. Math. Phys. 271 (2007), no. 2, 387-430.

Benjamin Schlein, László Erdős, Horng-Tzer YauDerivation of the cubic non-linear Schroedinger equation from quantum dynamics of many-body systems.. Invent. Math. 167 (2007), no. 3, 515-614.

Benjamin Schlein, Carlo Albert, Jürg Fröhlich, Lucio FerrariMagnetism and the Weiss exchange field: a theoretical analysis of recent experiments.. J. Statist. Phys. 125 (2006), no. 1, 77-124.

Benjamin Schlein, Alexander ElgartMean field dynamics for boson stars. . Comm. Pure Applied Math. 60 (2007), no. 4, 500-545.

Benjamin Schlein, László Erdős, Horng-Tzer YauDerivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensates.. Comm. Pure Applied Math. 59 (2006), no. 12, 1659-1741.

Benjamin SchleinDerivation of the Gross-Pitaevskii hierarchy. . Proceedings of QMath 9, Gien. Lecture Notes in Phys. 690, Springer, Berlin, 2006.

Benjamin Schlein, Alexander Elgart, László Erdős, Horng-Tzer YauGross-Pitaevskii equation as the mean field limit of weakly coupled bosons.. Arch. Ration. Mech. Anal. 179 (2006), no. 2, 265-283.

Alexander Elgart, László Erdős, Benjamin Schlein, Horng-Tzer YauNonlinear Hartree equation as the mean field limit of weakly coupled fermions.. J. Math. Pures Appl. (9) 83 (2004), no. 10, 1241-1273.

Jürg Fröhlich, Marcel Griesemer, Benjamin Schlein Asymptotic completeness for Compton scattering.. Comm. Math. Phys. 252 (2004), 415-476.

Alexander Elgart, Benjamin Schlein Adiabatic charge transport and the Kubo formula for Landau type Hamiltonians. . Comm. Pure Appl. Math. 57 (2004), no. 5, 590-615.

Jürg Fröhlich, Marcel Griesemer, Benjamin Schlein Asymptotic completeness for Rayleigh scattering. . Ann. Henri Poincare 3 (2002), no. 1, 107-170.

Jürg Fröhlich, Marcel Griesemer, Benjamin Schlein Asymptotic electromagnetic fields in models of quantum-mechanical matter
interacting with the quantized radiation field. . Adv. Math. 164 (2001), no. 2, 349-398.