Institute of Mathematics


Prof. Dr. Benjamin Schlein

Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

Phone: +41 44 635 58 42
Fax: +41 44 635 57 06
Office: Y27K32
Field of Research:
Mathematische Physik
Shang-Chi Hsiao

+41 44 635 58 51


Here you can find my cv.


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

Fall 23 Fall 24

Lecture & Seminar

Research seminars
PDE and Mathematical Physics
Peter Hintz, Mikaela Iacobelli, Benjamin Schlein, Klaus Widmayer
Zurich Colloquium in Mathematics
Rémi Abgrall, Joseph Ayoub, Afonso Bandeira, Mikaela Iacobelli, Alessandra Iozzi, Siddhartha Mishra, Rahul Pandharipande, Benjamin Schlein


N. Benedikter, P. T. Nam, M. Porta, B. Schlein, R. Seiringer
Correlation energy of a weakly interacting Fermi gas.
Preprint arXiv:2005.08933

N. Leopold, D. Mitrouskas, S. Rademacher, B. Schlein, R. Seiringer
Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron.
Preprint arXiv:2005.02098

C. Brennecke, B. Schlein
Bose-Einstein condensation beyond the Gross-Pitaevskii regime.
Preprint arXiv:2002.03406

J. Fröhlich, A. Knowles, B. Schlein, V. Sohinger
A path-integral analysis of interacting Bose gases and loop gases.
Preprint arXiv:2001.11714.

B. Schlein
The mean-field limit of quantum Bose gases at positive temperature.
Preprint arXiv:2001.01546.

N. Leopold, S. Rademacher, B. Schlein, R. Seiringer
The Landau-Pekar equations: Adiabatic theorem and accuracy.
Preprint arXiv:1904.12532

S. Rademacher, B. Schlein
Central limit theorem for Bose-Einstein condensates.
J. Math. Phys. 60 (2019), no. 7, 071902.

C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.
Comm. Math. Phys. 376 (2020), 1311-1395.

N. Benedikter, P. T. Nam, M. Porta, B. Schlein, R. Seiringer
Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.
Comm. Math. Phys. 374 (2020), 2097-2150.

B. Schlein
Bogoliubov excitation spectrum for Bose-Einstein condensates
Proc. Int. Cong. of Math. - 2018. Rio de Janeiro, Vol. 2 (2655-2672).

C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
Bogoliubov Theory in the Gross-Pitaevskii Limit.
Acta Math. 222 (2019), no. 2, 219-335

C. Brennecke, P. T. Nam, M. Napiórkowski, B. Schlein
Fluctuations of N-particle quantum dynamics around the nonlinear Schroedinger equation.
Ann. Inst. H. Poincare' Anal. Non Lin. 36 (2019), no. 5, 1201-1235.

E. Dietler, S. Rademacher, B. Schlein
From Hartree dynamics to the relativistic Vlasov equation.
Jour. Stat. Phys. 172 (2018), no. 2, 398-433

C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
The excitation spectrum of Bose gases interacting through singular potentials.
Jour. EMS 22 (2020), no. 7, 2331-2403

J. Fröhlich, A. Knowles, B. Schlein, V. Sohinger
A microscopic derivation of time-dependent correlation functions of the 1D cubic nonlinear Schroedinger equation.
Adv. Math. 353 (2019), 67-115.

C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
Complete Bose-Einstein condensation in the Gross-Pitaevskii regime.
Comm. Math. Phys. 359 (2018), no. 3, 975-102

C. Brennecke, B. Schlein
Gross-Pitaevskii dynamics for Bose-Einstein condensates.
Anal. PDE 12 (2019), no. 6, 1513-1596.

M. Porta, S. Rademacher, C. Saffirio, B. Schlein
Mean field evolution of fermions with Coulomb interaction.
J. Stat. Phys. 166, 1345-1364 (2017).

J. Fröhlich, A. Knowles, B. Schlein, V. Sohinger
Gibbs measures of nonlinear Schroedinger equations as limits of
many-body quantum states in dimensions $d \leq 3$.

Comm. Math. Phys. 356 (2017), no. 3, 883-980.

C. Boccato, S. Cenatiempo, B. Schlein
Quantum many-body fluctuations around nonlinear Schrödinger dynamics
Ann. Henri Poincare 18 (2017), 113.

R. L. Frank, C. Hainzl, B. Schlein, R. Seiringer
Incompatibility of the time-dependent Bogoliubov-de Gennes and Ginzburg-Landau equations.
Lett. Math. Phys. 106 (2016), 913-923.

N. Benedikter, M. Porta, C. Saffirio, B. Schlein
From the Hartree dynamics to the Vlasov equation.
Arch. Rational Mech. Anal. 221, 273-334 (2016)

N. Benedikter, M. Porta, B. Schlein
Effective Evolution Equations from Quantum Dynamics.
SpringerBriefs in Mathematical Physics (2015)

N. Benedikter, V. Jaksic, M. Porta, C. Saffirio, B. Schlein
Mean-field evolution of fermionic mixed states.
Comm. Pure Appl. Math. 69 (2016), no. 12, 2250-2303.

N. Benedikter, M. Porta, B. Schlein
Hartree-Fock dynamics for weakly interacting fermions.
Proceedings of the QMath12 conference.   
Preprint arXiv:1404.7769.

R. L. Frank, B. Schlein
Dynamics of a strongly coupled polaron.
Lett. Math. Phys. 104 (2014), no. 8, 911-929.

N. Benedikter, M. Porta, B. Schlein
Mean-field dynamics of fermions with relativistic dispersion.
J. Math. Phys. 55, 021901 (2014).

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

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

M. Lewin, P. T. Nam, B. Schlein
Fluctuations around Hartree states in the mean-field regime.
Am. J. Math. 137 (2015), no. 6, 1613-1650.   

N. Benedikter, M. Porta, B. Schlein
Mean-field evolution of fermionic systems.
Comm. Math. Phys. 331, 1087 - 1131 (2014).

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

N. Benedikter, G. de Oliveira, B. Schlein
Quantitative derivation of the Gross-Pitaevskii equation.
Comm. Pure Appl. Math. 68 (2015), no. 8, 1399-1482.   

B. Schlein
Effective equations for quantum dynamics.
Proceedings of 6-th ECM, Krakow, July 2012.   
Preprint arXiv:1208.0185

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

C. Hainzl, B. Schlein
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.   

G. Ben Arous, K. Kirkpatrick, B. Schlein
A central limit theorem in many-body quantum dynamics.
Comm. Math. Phys. 321 (2013), 371-417.   

B. Schlein
Effective evolution equations in quantum physics.
Journees equations aux derivees partielles (2011), Exp. No. 11.

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

L. Chen, J.O. Lee, B. Schlein
Rate of convergence towards Hartree dynamics.
J. Statist. Phys. 144 (2011), no. 4, 872-903.   

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

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

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

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

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

L. Erdős, B. Schlein, H.-T. Yau, J. 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.   

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

C. Hainzl, E. Lenzmann, M. Lewin, B. Schlein
On blowup for time-dependent generalized Hartree-Fock equations.
Ann. Henri Poincare 11 (2010), no. 6, 1023-1052.   

B. Nachtergaele, B. Schlein, R. Sims, S. Starr, V. Zagrebnov
On the existence of the dynamics for anharmonic quantum oscillator systems.
Rev. Math. Phys. 22 (2010), no. 2, 207--231.   

L. Erdős, B. Schlein, H.-T. Yau
Universality of random matrices and local relaxation flow.
Invent. Math. 185 (2011), no. 1, 75-119.   

L. Erdős, J. Ramirez, B. Schlein, T. Tao, V. Vu, H.-T. Yau
Bulk universality for Wigner hermitian matrices with subexponential decay.
Math. Res. Lett. 17 (2010), no. 4, 667-674.   

L. Erdős, S. Péché, J. Ramirez, B. Schlein, H.-T. Yau
Bulk universality for Wigner matrices.
Comm. Pure Appl. Math. 63 (2010), no. 7, 895-925.   

L. Erdős, J. Ramirez, B. Schlein, H.-T. Yau
Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation.
Electron. J. Probab. 15 (2010), no. 18, 526-603.   

L. Erdős, B. Schlein, H.-T. Yau
Wegner estimate and level repulsion for Wigner random matrices.
Int. Math. Res. Not. 2010, no. 3, 436-479.   

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

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

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

L. Erdős, B. Schlein, H.-T. Yau
The ground state energy of a low density Bose gas: a second order upper bound.
Phys. Rev. A 78 (2008), no. 5, 053627.   

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

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

L. Erdős, B. Schlein, H.-T. Yau
Local semicircle law and complete delocalization for Wigner random matrices.
Comm. Math. Phys. 287 (2009), no. 2, 641-655.   

L. Erdős, B. Schlein, H.-T. Yau
Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential.
J. Amer. Math. Soc. 22 (2009), no. 4, 1099-1156.   

B. Nachtergaele, H. Raz, B. Schlein, R. Sims
Lieb-Robinson bounds for harmonic and anharmonic lattice systems.
Comm. Math. Phys. 286 (2009), no. 3, 1073-1098.   

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

L. Erdős, B. Schlein, H.-T. Yau
Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices.
Ann. Probab. 37 (2009), no. 3, 815-852.   

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

L. Erdős, B. Schlein, H.-T. Yau
Rigorous derivation of the Gross-Pitaevskii equation.
Phys. Rev. Lett. 98 (2007), no. 4, 040404.   

L. Erdős, B. Schlein, H.-T. Yau
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates.
Ann. of Math. (2) 172 (2010), no. 1, 291-370.   

J. Fröhlich, M. Griesemer, B. Schlein
Rayleigh scattering at atoms with dynamical nuclei.
Comm. Math. Phys. 271 (2007), no. 2, 387-430.   

L. Erdős, B. Schlein, H.-T. Yau
Derivation of the cubic non-linear Schroedinger equation from quantum dynamics of many-body systems.
Invent. Math. 167 (2007), no. 3, 515-614.   

C. Albert, L. Ferrari, J. Fröhlich, B. Schlein
Magnetism and the Weiss exchange field: a theoretical analysis of recent experiments.
J. Statist. Phys. 125 (2006), no. 1, 77-124.   

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

L. Erdős, B. Schlein, H.-T. Yau
Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensates.
Comm. Pure Applied Math. 59 (2006), no. 12, 1659-1741.   

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

A. Elgart, L. Erdős, B. Schlein, H.-T. Yau
Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons.
Arch. Ration. Mech. Anal. 179 (2006), no. 2, 265-283.   

A. Elgart, L. Erdős, B. Schlein, H.-T. Yau
Nonlinear Hartree equation as the mean field limit of weakly coupled fermions.
J. Math. Pures Appl. (9) 83 (2004), no. 10, 1241-1273.   

J. Fröhlich, M. Griesemer, B. Schlein
Asymptotic completeness for Compton scattering.
Comm. Math. Phys. 252 (2004), 415-476.   

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

J. Fröhlich, M. Griesemer, B. Schlein
Asymptotic completeness for Rayleigh scattering.
Ann. Henri Poincare 3 (2002), no. 1, 107-170.   

J. Fröhlich, M. Griesemer, B. Schlein
Asymptotic electromagnetic fields in models of quantum-mechanical matter
interacting with the quantized radiation field.

Adv. Math. 164 (2001), no. 2, 349-398.   


Prof. Dr. Michael Loss, Georgia Tech (Atlanta, GA)
Talk: [Video Seminar] The phase diagram of the Caffarelli-Kohn-Nirenberg inequalities
02.12.15 - 05.12.15Schlein, Benjamin
Prof. Dr. Marcin Napiórkowski, University of Warsaw (Wasaw)
Talk: Bogoliubov Free Energy Functional
23.11.15 - 27.11.15Schlein, Benjamin
Prof. Dr. Laurent Desvillettes, ENS Cachan (Cachan)
Talk: Speed of convergence of the solutions of the Landau equation of plasmas towards equilibrium
29.10.15 - 30.10.15Schlein, Benjamin
Prof. Dr. Didier Smets, Sorbonne Université (Paris)
Talk: On the leapfrogging phenomenon in fluid mechanics
08.10.15 - 09.10.15Schlein, Benjamin
Prof. Dr. Alexander Elgart, VirginiaTech (Blacksburg)
28.06.15 - 02.07.15Schlein, Benjamin
Dr. Jan Maas, Institute for Applied Mathematics, Hausdorff Center for Mathematics, University of Bonn (Bonn)
Talk: Entropic gradient flows in Markov chains and chemical reaction networks
05.05.15 - 07.05.15Schlein, Benjamin
Prof. Dr. Simone Warzel, Fakultät für Mathematik, TU München (Garching)
Talk: Resonant delocalization
21.04.15 - 22.04.15Schlein, Benjamin
Dr. Julien Sabin, (Paris Sud)
Talk: Optimal trace ideals properties of the Fourier restriction operator and applications
17.03.15 - 20.03.15Schlein, Benjamin
Prof. Dr. Christian Hainzl, Eberhard Karls Universität Tübingen (Tübingen)
03.03.15 - 05.03.15Schlein, Benjamin
Prof. Dr. Mario Pulvirenti, University La Sapienza (Roma)
Talk: Scaling limits and effective equations for large particle systems
18.02.15 - 21.02.15Schlein, Benjamin
Dr. Renato Lucá, Consejo Superior de Investigaciones Científicas (Madrid)
09.02.15 - 13.02.15Schlein, Benjamin
Dr. Daniele Valeri, SISSA-ISAS (Trieste)
09.02.15 - 11.02.15Schlein, Benjamin