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 Schlein. Third Order Upper Bound for the Ground State Energy of the Dilute Bose Gas.

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

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

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

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

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

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

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

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

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

Benjamin Schlein. Bose 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 Triay. Bogoliubov Theory in the Gross-Pitaevskii Limit: a Simplified Approach.

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

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

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

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

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

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

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

Benjamin Schlein. Bogoliubov 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 Schlein. A new second order upper bound for the ground state energy of dilute Bose gases.

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

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

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

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

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

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

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

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

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

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

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

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

Benjamin Schlein. Bogoliubov excitation spectrum for Bose-Einstein condensates

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

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

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

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

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

Benjamin Schlein, Chiara Boccato, Christian Brennecke, Serena Cenatiempo. Complete 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 Schlein. Mean 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 Seiringer. Incompatibility of the time-dependent Bogoliubov-de Gennes and Ginzburg-Landau equations.

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

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

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

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

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

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

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

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

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

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

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

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

Benjamin Schlein, Christian Hainzl. Dynamics 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 Arous. A central limit theorem in many-body quantum dynamics.. Comm. Math. Phys. 321 (2013), 371-417.

Benjamin Schlein. Effective 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 Chen. Rate of convergence towards Hartree dynamics. . J. Statist. Phys. 144 (2011), no. 4, 872-903.

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

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

Benjamin Schlein, László Erdős, Horng-Tzer Yau, Jun Yin. The 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 Schlein. Derivation 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 Lewin. On 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 Starr. On 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 Vu. Bulk 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 Péché. Bulk universality for Wigner matrices.. Comm. Pure Appl. Math. 63 (2010), no. 7, 895-925.

Benjamin Schlein, László Erdős, Horng-Tzer Yau, Jose Ramirez. Universality 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 Yau. Wegner 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 Yau. Rigorous 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 Sims. Lieb-Robinson bounds for harmonic and anharmonic lattice systems.. Comm. Math. Phys. 286 (2009), no. 3, 1073-1098.

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

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

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

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

Benjamin Schlein, László Erdős, Horng-Tzer Yau. Derivation 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 Griesemer. Rayleigh scattering at atoms with dynamical nuclei.. Comm. Math. Phys. 271 (2007), no. 2, 387-430.

Benjamin Schlein, László Erdős, Horng-Tzer Yau. Derivation 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 Ferrari. Magnetism and the Weiss exchange field: a theoretical analysis of recent experiments.. J. Statist. Phys. 125 (2006), no. 1, 77-124.

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

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

Benjamin Schlein. Derivation 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 Yau. Gross-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 Yau. Nonlinear 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.