Manuscripts under review and preprints

A. Dietlein and A. Elgart, “Level spacing for continuum random Schrödinger operators with applications,” arxiv.org:1712.03925.

A. Elgart, A. Klein, G. Stolz, “Manifestations of dynamical localization in the disordered XXZ spin chain,” arxiv.org:1708.00474, submitted.

Publications in peer-reviewed journals

33. A. Elgart, A. Klein, G. Stolz, “Many-body localization in the droplet spectrum of the random XXZ quantum spin chain,” J. Funct. Anal., to appear. arXiv:1703.07483

32. A. Elgart, A. Klein, G. Stolz, “Droplet localization in the random XXZ model and its manifestations,” J. Phys. A: Math. Theor. 51, 01LT02 (2018). arXiv:1707.09665

31. A. Elgart and A. Klein, “Eigensystem multiscale analysis for Anderson localization in energy intervals,” J. Spectr. Theory, to appear. arxiv:1611.02650

30. A. Elgart and S. Sodin, “The trimmed Anderson model at strong disorder: localisation and its breakup,” J. Spectr. Theory 7, 87–110 (2017). arXiv:1409.8009

29. A. Elgart, L. Pastur, M. Shcherbina, “Large block properties of the entanglement entropy of disordered fermions,” J. Stat. Phys. 166, 1092–1127 (2017).  arXiv:1601.00294.

28. A. Elgart and A. Klein, “An eigensystem approach to Anderson localization,” J. Funct. Anal. 271, 3465–3512 (2016).  arXiv:1509.08521.

27. A. Elgart and D. Schmidt, “Eigenvalue counting inequalities, with applications to Schrödinger operators,”  J. Spectr.Theory 5, 251–278 (2015). arXiv:1306.3459

26. A. Elgart, M. Shamis, S. Sodin, “Localisation for non-monotone Schrödinger operators,”  JEMS, 16, 909–924 (2014). arXiv:1201.2211        

25. A. Elgart and A. Klein, “Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models,” J. Spectr. Theory, 4, 391–413 (2014). arXiv:1301.5268

24. Z. Cao and A. Elgart, “The weak localization for the alloy-type Anderson model on a cubic lattice,”  J. Stat. Phys., 148, 1006–1039 (2012). arXiv:1108.0196

23. A. Elgart and G. Hagedorn, “A note on the switching adiabatic theorem,” J. Math. Phys. 53, 102202 (2012). arXiv:1204.2318

22. Z. Cao and A. Elgart, “On the efficiency of Hamiltonian-based quantum computation for low-rank matrices,” J. Math. Phys. 53, 032201 (2012). arXiv:1004.4911

21. A. Elgart, M. Tautenhahn, I. Veselić, “Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method,”  Ann. Henri Poincaré 12, 1571–1599 (2011). arXiv:1011.5648

20. A. Elgart and G. Hagedorn, “An adiabatic theorem for resonances,” Comm. Pure and Appl. Math. 64, 1029–1058 (2011). arXiv:1002.1741 

19. A. Elgart, M. Tautenhahn, I. Veselić, “Localization via fractional moments for models on Z with single-site potentials of finite support,”  J. Phys. A: Math. Theor. 43, 474021 (2010). arXiv:math-ph/0903.0492

18. I. Sela, J. Aisenberg, T. Kottos, A. Elgart, D. Cohen,“Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum,” Phys. Rev. E 81, 036219 (2010). arXiv:1003.1645

17. J. Aisenberg, I. Sela, T. Kottos, D. Cohen, A. Elgart, “Quantum decay into a non-flat continuum,” J. Phys. A: Math. Theor. 43, 095301 (2010). arXiv:0905.4934

16. A. Elgart, “Lifshitz tails and localization in the three-dimensional Anderson model,” Duke Math. J., 146, 331–360, (2009). arXiv:0804.3347

15. A. Elgart and B. Schlein, “Mean Field Dynamics of Boson Stars,” Comm. Pure and Appl. Math., 60, 500–545 (2007). arXiv:0504051

14. M. Aizenman, A. Elgart, S. Naboko, J. H. Schenker, G. Stolz, “Moment analysis for localization in random Schrödinger operators,” Invent. Math., 163, 343–413 (2006). arXiv:math-ph/0308023 

13. A. Elgart, L. Erdos, B. Schlein, H-T. Yau, “Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons,” Arch. Rat. Mech. Anal., 179, 265–283, (2006).  arXiv:math-ph/0410038

12. A. Elgart, G.-M. Graf, J. H. Schenker, “Equality of edge and bulk Hall conductances in a mobility gap,” Comm. Math. Phys. 259, 185–221 (2005).  arXiv:math-ph/0409017

11. A. Elgart, L. Erdos, B. Schlein, H-T. Yau, “Nonlinear Hartree equation as the mean field limit of weakly coupled fermions,” J. Math. Pures Appl., 83, 1241–1273 (2004). arXiv:math-ph/0311043

10. J. E. Avron, A. Elgart, G.M. Graf, L. Sadun, “Transport and dissipation in quantum pumps,” J. Stat. Phys., 116, 425–473 (2004). arXiv:math-ph/0305049

9.   J. E. Avron, A. Elgart, G.M. Graf, L. Sadun, K. Schnee, “Adiabatic charge pumping in open quantum systems,” Comm. Pure and Appl. Math., 57, 528–561 (2004). arXiv:math-ph/0209029

8.  A. Elgart and B. Schlein, “Adiabatic charge transport and the Kubo formula for Landau type Hamiltonians,” Comm. Pure and Appl. Math., 57, 590–615 (2004). arXiv:math-ph/0304009

7.  J. E. Avron, A. Elgart, G.M. Graf, L. Sadun, “Time-Energy coherent states and adiabatic scattering,” J. Math. Phys., 43, 3415 (2002). arXiv:math-ph/0202021

6.  A. Elgart and J. H. Schenker, “A strong operator topology adiabatic theorem,” Rev. Math. Phys. 14, 569–584 (2002). arXiv:math-ph/0110002

5.  J. E. Avron, A. Elgart, G.M. Graf, L. Sadun, “Optimal quantum pumps,” Phys. Rev. Lett., 87, 236601 (2001). arXiv:math-ph/0105011

4.  J. E. Avron, A. Elgart, G.M. Graf, L. Sadun, “Geometry, statistics and asymptotics of quantum pumps,” Phys. Rev. B, 62, R10618(R) (2000). arXiv:math-ph/0002194

3.  J. E. Avron and A. Elgart, “Adiabatic theorem without a gap condition,” Comm. Math. Phys., 203, 445–463, (1999). arXiv:math-ph/9805022

2.  J. E. Avron and A. Elgart, “Smooth adiabatic evolutions with leaky power tails,” J. Phys. A: Math. Gen., 32, L537 (1999). arXiv:math-ph/9909063

1.  J. E. Avron and A. Elgart, “An adiabatic theorem without a gap condition: Two level system coupled to quantized radiation field,” Phys. Rev. A., 58, 4300–4306, (1998). arXiv:chao-dyn/9803153

Conference Proceedings

6.  A. Elgart, H. Krüger, M. Tautenhahn, I. Veselić, “Fractional moment methods for Anderson localization in the continuum,” Proceedings of the Spectral Days (Santiago 2010). arXiv:math-ph/1107.2800

5.  A. Elgart, “Equality of the bulk and edge Hall conductances in 2D,” Proceedings of the QMath9 (Giens 2004).

4.  A. Elgart, “Adiabatic transport, Kubo formula and Anderson localization in some lattice and continuum models,” Proceedings of the XIVth International Congress on Mathematical Physics (Lisbon 2003).

3.  G. M. Graf, A. Elgart, L. Sadun, K. Schnee, “Transport in adiabatic quantum pumps,” Proceedings of the XIVth International Congress on Mathematical Physics (Lisbon 2003).

2.  G. Stolz, M. Aizenman, A. Elgart, S. Naboko, J. H. Schenker, “Fractional moment methods for Anderson localization in the continuum,” Proceedings of the XIVth International Congress on Mathematical Physics (Lisbon 2003). arXiv:math-ph/0309018

1.   J. E. Avron and A. Elgart, “An Adiabatic Theorem without a Gap Condition,” Proceedings of the QMath7 (Prague 1998). arXiv:math-ph/9810004