Publications and Preprints



B. Schlein.
Derivation of effective evolution equations from many body quantum dynamics.

C. Hainzl, E. Lenzmann, M. Lewin, B. Schlein.
On blowup for time-dependent generalized Hartree-Fock equations.

B. Nachtergaele, B. Schlein, R.Sims, S.Starr, V. Zagrebnov.
On the existence of the dynamics for anharmonic quantum oscillator systems.

L. Erdös, B. Schlein, H.-T. Yau.
Universality of random matrices and local relaxation flow.

L. Erdös, J. Ramirez, B. Schlein, T. Tao, V. Vu, H.-T. Yau.
Bulk universality for Wigner hermitian matrices with subexponential decay.
To appear in Math. Res. Lett.

L. Erdös, J. Ramirez, B. Schlein, H.-T. Yau.
Bulk universality for Wigner matrices.

L. Erdös, J. Ramirez, B. Schlein, H.-T. Yau.
Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation.

L. Erdös, B. Schlein, H.-T. Yau.
Wegner estimate and level repulsion for Wigner random matrices.
To appear in Int. Math. Res. Not.

K. Kirkpatrick, B. Schlein, G. Staffilani.
Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics.
To appear in Amer. J. Math.

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.
Lecture notes for the minicourse held at the 2008 CMI Summer School in Zurich.

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, and H.-T. Yau.
Rigorous derivation of the Gross-Pitaevskii equation: the case of a strong potential.
To appear in J. Amer. Math. Soc.

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, 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.

B. Schlein.
Dynamics of Bose-Einstein Condensates.
Proceedings article for ICMP, Rio de Janeiro, 2006.

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

L. Erdös, B. Schlein, and H.-T. Yau.
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates.
To appear in Ann. of Math.

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, and H.-T. Yau.
Derivation of the cubic non-linear Schrödinger 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 and B. Schlein.
Mean field dynamics of boson stars.
Comm. Pure Applied Math. 60 (2007), no. 4, 500-545.

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

B. Schlein.
Derivation of the Gross-Pitaevskii hierarchy.
Mathematical Physics of Quanum Mechanics, Lecture Notes in Physics 690 (2006), Springer. (Proceedings of QMath 9).

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

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

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

A. Elgart and B. Schlein.
Adiabatic charge transport and the Kubo formula for Landau type Hamiltonians.
Comm. Pure Appl. Math. 57 (5): 590-615, 2004.

J. Fröhlich, M. Griesemer, and B. Schlein.
Asymptotic completeness for Rayleigh scattering.
Ann. Henry Poincaré 3: 107-170, 2002.

J. Fröhlich, M. Griesemer, and B. Schlein.
Asymptotic electromagnetic fields in models of quantum-mechanical matter interacting with the quantized radiation field.
Adv. Math. 164 (2): 349-398, 2001.