Research Papers

34. (with Nina Gottschling) Convergence of Levy-Lieb to Thomas-Fermi density functional. Preprint  2018. (arXiv)

33. (with  Alessandro Michelangeli & Alessandro Olgiati) Ground state energy of mixture of Bose gases. Preprint  2018. (arXiv)

32. (with Christian Brennecke, Marcin Napiórkowski & Benjamin Schlein) Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation. Preprint  2017. (arXiv)

31. (with Marcin Napiórkowski) Norm approximation for many-body quantum dynamics: focusing case in low dimensions. Preprint  2017. (arXiv)

30. Lieb-Thirring inequality with semiclassical constant and gradient error term. J. Funct. Anal. 274 (2018), 1739-1746. (arXiv - article)

29. Binding energy of homogeneous Bose gas. Lett. Math. Phys. 108 (2018), 141-159. (arXiv - article)

28. (with Mathieu Lewin & Nicolas Rougerie) Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits. J. Math. Phys. 59 (2018), 041901. (arXiv - article)

27. (with Rupert L. Frank & Hanne Van Den Bosch) The maximal excess charge in Müller density-matrix-functional theory. Ann. Henri Poincaré (2018), in press. (arXiv - article)

26. (with Rupert L. Frank & Hanne Van Den Bosch) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Comm. Pure Appl. Math. 71 (2018), no. 3, 577-614. (arXiv - article)

25. (with Marcin Napiórkowski) A note on the validity of Bogoliubov correction to mean-field dynamics. J. Math. Pures Appl. 108 (2017), 662-688. (arXiv - article)

24. (with Rupert L. Frank & Rowan Killip) Nonexistence of large nuclei in the liquid drop model. Lett. Math. Phys. 106 (2016), 1033-1036. (arXiv - article)

23. (with Hanne Van Den Bosch) Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Math. Phys. Anal. Geom. (2017), 20:6. (arXiv - article)

22. (with Mathieu Lewin & Nicolas Rougerie) A note on 2D focusing many-boson systems. Proc. Amer. Math. Soc. 145 (2017), 2441-2454. (arXiv - article)

21. (with Marcin Napiórkowski) Bogoliubov correction to the mean-field dynamics of interacting bosons. Adv. Theor. Math. Phys.  21 (2017), 683-738. (arXiv - article)

20. (with Marcin Napiórkowski & Jan Philip Solovej) Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. J. Funct. Anal.  270 (2016), 4340-4368. (arXiv - article)

19. (with Nicolas Rougerie &  Robert Seiringer) Ground states of large bosonic systems: The Gross-Pitaevskii limit revisited. Analysis & PDE 9 (2016),  459-485. (arXiv - article)

18. (with Douglas Lundholm &  Fabian Portmann) Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems. Arch. Rational Mech. Anal219 (2016), 1343-1382. (arXiv - article)

17. (with Mathieu Lewin & Nicolas Rougerie) Derivation of nonlinear Gibbs measures from many-body quantum mechanics. Journal de l'École polytechnique — Mathématiques 2 (2015), 65-115. (arXiv - article)

16. (with Mathieu Lewin & Nicolas Rougerie) The mean-field approximation and the nonlinear Schrödinger functional for trapped Bose gases. Trans. Amer. Math. Soc. 369 (2016), 6131-6157(arXiv - article)

15. (with Robert Seiringer) Collective excitations of Bose gases in the mean-field regime. Arch. Rational Mech. Anal. 215 (2015), 381-417. (arXiv - article)

14. (with Mathieu Lewin & Nicolas Rougerie) Remarks on the quantum de Finetti theorem for bosonic systems. Appl. Math. Res. Express (AMRX) 1 (2015),  48–63(arXiv - article)

13. (with Mathieu Lewin & Benjamin Schlein) Fluctuations around Hartree states in the mean-field regime. Amer. J. Math. 137 (2015), 1613-1650. (arXiv - article)

12. (with Mathieu Lewin & Nicolas Rougerie) Derivation of Hartree's theory for generic mean-field Bose systems. Advances in Math. 254 (2014), 570-621. (arXiv - article)

11. (with Mathieu Lewin, Sylvia Serfaty & Jan Philip Solovej) Bogoliubov spectrum of interacting Bose gases. Comm. Pure Appl. Math. 68 (2015), no. 3, 413–471. (arXiv - article )

10. (with Fabian Portmann & Jan Philip Solovej) Asymptotics for two dimensional atoms. Ann. Henri Poincaré 13 (2012), no. 2, 333-362. (arXiv - article)

9. New bounds on the maximum ionization of atoms. Commun. Math. Phys. 312 (2012), no. 2, 427-445. (arXiv - article)

8. (with Alain Pham Ngoc Dinh, Pham Hoang Quan & Dang Duc Trong) Ice formation in the Arctic during summer: false-bottoms. Appl. Math. Comput. 227 (2014), 857–870. (arXiv - article)

7. (with Dang Duc Trong & Phung Trong Thuc) The body force in a three-dimensional Lamé system: identification and regularization. Inverse Probl. Sci. Eng. 20 (2012), no. 4, 517-532. (arXiv - article)

6. An approximate solution for nonlinear backward parabolic equations. J. Math. Anal. Appl. 367 (2010), no. 2,  337-349. (preprint - article)

5. (with Dang Duc Trong & Nguyen Huy Tuan) The truncation method for a two-dimensional nonhomogeneous backward heat problem. Appl. Math. Comput. 216 (2010), no. 12, 3423-3432. (preprint - article)

4. (with Dang Duc Trong, Mach Nguyet Minh & Alain Pham Ngoc Dinh) Hölder-type approximation for the spatial source term of a backward heat equation. Numer. Funct. Anal. Optim. 31 (2010), no. 12, 1386-1405. (preprint - article)

3. (with Dang Duc Trong & Alain Pham Ngoc Dinh) Determine the spatial term of a two-dimensional heat source. Applicable Analysis 88 (2009), no. 3, 457-474. (arXiv - article)

2. (with Mach Nguyet Minh) Proof of a conjecture on general means. J. Inequal. Pure Appl. Math. 9 (2008), no. 3, Article 86. (article)

1. (with Dang Duc Trong, Alain Pham Ngoc Dinh & Truong Trung Tuyen) Determination of the body force of a two-dimensional isotropic elastic body. J. Comput. Appl. Math. 229 (2009), no. 1, 192-207. (arXiv - article)

Proceedings of conferences/Book chapters

8. (with Mathieu Lewin & Nicolas Rougerie) The interacting 2d Bose gas and nonlinear Gibbs measures. Oberwolfach Reports (2018): mini-workshop Gibbs measures for nonlinear dispersive equations. (arXiv)

7. (with Mathieu Lewin & Nicolas Rougerie) Blow-up profile of rotating 2D focusing Bose gases. Macroscopic Limits of Quantum Systems, Proceedings in Mathematics and Statistics, Springer, 2018. Conference in honor of Herbert Spohn 70th birthday, Munich 2017. (arXiv)

6. (with Rupert L. Frank & Hanne van den Bosch) A short proof of the ionization conjecture in Müller theory. Proceedings of QMath 13: Mathematical Results in Quantum Physics, Georgia 2016. (arXiv)

5. (with Marcin Napiórkowski) Norm approximation for many-body quantum dynamics and Bogoliubov theory. Advances in Quantum Mechanics: contemporary trends and open problems, A. Michelangeli and G. Dell'Antonio (editors), Springer-INdAM volume 18 (2017). (arXiv)

4. (with Rupert L. Frank and Hanne Van Den Bosch) Maximum ionization in Thomas-Fermi-Dirac-Weizsäcker theory. Oberwolfach Reports (2016): workshop Many-Body Quantum Systems and Effective Theories. (pdf)

3. (with Mathieu Lewin & Nicolas Rougerie) Bose Gases at Positive Temperature and Non-Linear Gibbs Measures. In Proceedings of the 18th International Congress on Mathematical Physics, Santiago 2015. (arXiv)

2. On the number of electrons that a nucleus can bind. Proceedings of the 17th International Congress on Mathematical Physics, Aalborg 2012. A. Jensen (ed.), World Scientific, Singapore (2013), 504-511. (arXiv)

1. (with Dang Duc Trong &  Mach Nguyet Minh) Recovering a class of entire functions and application to heat equations.  Proceedings of the Vietnamese Congress of Mathematicians, Quy Nhon 2008. Vietnam J. Math. 37 (2009), no 2&3, 1-19. (pdf)

PhD Thesis 

Contributions to the rigorous study of the structure of atoms. University of Copenhagen, September 2011. (pdf)