Benjamin Schlein

Research

Research Interests

Our research field is mathematical physics. We are interested in the dynamical properties of quantum mechanical systems (quantum dynamics). In particular, we study the derivation of effective evolution equations for interacting many body systems, as well as the behavior of the solutions of these macroscopic evolution equations.

A related subject we are interested in is the derivation of Lieb-Robinson bounds for the time evolution of anharmonic lattice systems; these bounds establish the locality of the dynamics.

A further research subject concerns the spectral properties of random matrices; in particular, we are interested in universality properties of eigenvalue statistics for ensembles of Wigner matrices.


Publications

1) J. Froehlich, M. Griesemer, and 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.

2) J. Froehlich, M. Griesemer, and B. Schlein. Asymptotic completeness for Rayleigh scattering. Ann. Henri Poincaré 3 (2002), no. 1, 107-170.

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

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

5) A. Elgart, L. Erdos, B. Schlein, and 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.

6) A. Elgart, L. Erdos, B. Schlein, and 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.

7) 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.

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

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

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

11) L. Erdos, B. Schlein, and 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.

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

13) L. Erdos, B. Schlein, and 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.

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

15) B. Schlein. Dynamics of Bose-Einstein Condensates. New Trends in Mathematical Physics. Selected contributions of the XVth International Congress on Mathematical Physics, edited by V. Sidoravicius, Springer Verlag, 2009, 565-589.

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

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

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

19) L. Erdos, B. Schlein, and 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.

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

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

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

23) L. Erdos, B. Schlein, and 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.

24) B. Schlein. Derivation of effective evolution equations from microscopic quantum dynamics. To appear in the Proceedings of the 2008 CMI Summer School in Zurich. Preprint arXiv: 0807.4307.

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

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

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

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

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

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

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

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

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

34) B. Schlein. Derivation of effective evolution equations from many body quantum dynamics. XVIth International Congress on Mathematical Physics. World Sci. Publ., Hackensack, NJ, 2010,  406-416.

35) L. Erdos, B. Schlein, H.-T. Yau, J. Yin. The local relaxation flow approach to universality of the local statistics for random matrices. Ann. Inst. H. Poincaré Probab. Statist. 48 (2012), no. 1, 1-46.

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

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

38) 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.

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

40) B. Schlein. Effective evolution equations from many body quantum dynamics. New Perspectives in Quantum Statistics and Correlations.  Moritz Hiller, Fernando de Melo, Peter Pickl, Thomas Wellens, Sandro Wimberger (Eds.). Universitätsverlag Winter, Heidelberg, 2012. ISBN: 978-3-8253-6001-6.

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

42) A. Maltsev and 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.

43) B. Schlein. Effective evolution equations in quantum physics. To appear in the Proceedings of the Conference "Days in PDE" held in Biarritz, June 2011. Preprint arXiv:1111.6995.

44) G. Ben Arous, K. Kirkpatrik, B. Schlein. A central limit theorem in many-body quantum dynamics. Comm. Math. Phys. 321 (2013), no. 2, 371-417.

45) 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.

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

47) B. Schlein. Effective equations for quantum dynamics.  Contribution to Proceedings of 6-th European Congress of Mathematics, Krakow, July 2012. Preprint arXiv:1208.0185. 

48) N. Benedikter, G. de Oliveira, B. Schlein. Quantitative derivation of the Gross-Pitaevskii equation. Preprint  arXiv:1208.0373.

49) B. Schlein. Quantum dynamics, coherent states and Bogoliubov transformations. Contribution to Proceedings of International Conference on Mathematical Physics, Aalborg, August 2012. Preprint arXiv:1210.1603.

50) N. Benedikter, M. Porta, B. Schlein. Mean-field evolution of fermionic systems. Preprint arXiv:1305.2768.

51) M. Lewin, P.T. Nam, B. Schlein. Fluctuations around Hartree states in the mean-field regime. Preprint arXiv:1307.0665.

52) S. Buchholz, C. Saffirio, B. Schlein. Multivariate central limit theorem in quantum dynamics. J. Statist. Phys. 154 (2014), no. 1-2, 113-152.

53) C. Cacciapuoti, A. Maltsev, B. Schlein. Optimal bounds on the Stieltjes transform of Wigner matrices. Preprint arXiv:1311.0326.

54) R.L. Frank, B. Schlein. Dynamics of a strongly coupled polaron. Preprint arXiv:1311.5814.

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