Institut für Mathematik


Prof. Dr. Benjamin Schlein

Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

Tel.: +41 44 635 58 42
Fax: +41 44 635 57 06
Büro: Y27K32
Mathematische Physik
Iva Kabosch

+41 44 635 58 51
Tatjana Pacheco McCormick

+41 44 635 58 76


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

FS 20

Vorlesungen & Seminare

Stochastische Prozesse
Erwin Bolthausen, Ashkan Nikeghbali, Pierre Nolin, Benjamin Schlein, Alain-Sol Sznitman, Wendelin Werner
PDE and Mathematical Physics
Xavier Ros-Oton, Benjamin Schlein
Zurich Colloquium in Mathematics
Rémi Abgrall, Joseph Ayoub, Afonso Bandeira, Mikaela Iacobelli, Alessandra Iozzi, Siddhartha Mishra, Rahul Pandharipande, Benjamin Schlein

Stability of quantum mechanical matter

Exercises Stability of quantum mechanical matter


C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
The excitation spectrum of Bose gases interacting through singular potentials.
Preprint arXiv:1704.04819.   

J. Fröhlich, A. Knowles, B. Schlein, V. Sohinger
A microscopic derivation of time-dependent correlation functions of the 1D cubic nonlinear Schroedinger equation.
Preprint arXiv:1703.04465.   

C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
Complete Bose-Einstein condensation in the Gross-Pitaevskii regime.
Preprint arXiv:1703.04452. To appear in Comm. Math. Phys.   

C. Brennecke, B. Schlein
Gross-Pitaevskii dynamics for Bose-Einstein condensates.
Preprint arXiv:1702.05625.   

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 $d \leq 3$.
Preprint arXiv:1605.07095. To appear in Comm. Math. Phys.   

C. Boccato, S. Cenatiempo, B. Schlein
Quantum many-body fluctuations around nonlinear Schrödinger dynamics
Ann. Henri Poincare 18 (2017), 113.    arXiv:1509.03837

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.
Lecture notes of the course held at the summer school "Mathematical Physics, Analysis and Stochastics" at the University of Heidelberg in July 2014.    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.
Mathematical Results in Quantum Mechanics. Proceedings of the QMath12 Conference held in Berlin in Sept. 2013. World Scientific, Singapur, 2015.    Arxiv preprint.

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, Phan Thanh 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.
Contribution to Proceedings of 6-th European Congress of Mathematics, Krakow, July 2012.   

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. Available in electronic form at   

A. Maltsev, B. Schlein
A Wegner Estimate for Wigner Matrices.
Entropy and the Quantum II. Arizona School of Analysis with Applications. R. Sims, D. Ueltschi Editors, American Mathematical Society, 2011, 145-160.   

Li 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'', Hiller, de Melo, Pickl, Wellens, Wimberger (Eds.). 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.
Mathematical Results in Quantum Physics. Proceedings of the QMath 11 conference. Edited by P. Exner. 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,  Pizzo, B. Schlein
Ionization of atoms by intense laser pulses.
Ann. Henri Poincare 11 (2010), no. 7, 1375-1407.   

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

L. Erdös, 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. Erdös, 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. Erdös, 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. Erdös, 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. Erdös, 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.
Evolution Equations, CMI Summer School, ETH 2008. Clay Mathematics Proceedings, 17, 2013. Edited by D. Ellwood, I. Rodnianski, G. Staffilani, J. Wunsch. 511-572.   

L. Erdös, 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. Erdös, 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. Erdös, 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. Erdös, 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. Erdös, 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.
New Trends in Mathematical Physics. Selected contributions of the XV ICMP, edited by V. Sidoravicius, Springer Verlag, 2009, 565-589.   

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

L. Erdös, 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. Erdös, 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. Erdös, 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.
Mathematical Physics of Quantum Mechanics, 279-293. Proceedings of the conference QMath 9, Gien. Lecture Notes in Phys., 690, Springer, Berlin, 2006.   

A. Elgart, L. Erdös, 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. Erdös, 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. Marcello Porta, Universität Zürich (Zürich)
19.06.20 - 20.07.20Schlein, Benjamin
Dr. Robin Reuvers, University of Cambridge (Cambridge)
16.03.20 - 20.03.20Schlein, Benjamin
Dr. Vedran Sohinger, University of Warwick (Coventry)
24.01.20 - 26.01.20Schlein, Benjamin