Phan Thành Nam


Research Papers

30. Lieb-Thirring inequality with semiclassical constant and gradient error term. J. Funct. Anal.  (2017), in press. (arXiv - article)

29. Binding energy of homogeneous Bose gas. Preprint (2017). (arXiv)

28. (with Mathieu Lewin & Nicolas Rougerie) Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits. Preprint (2017). (arXiv)

27. (with Rupert L. Frank & Hanne Van Den Bosch) The maximal excess charge in Müller density-matrix-functional theory. Preprint (2016). (arXiv)

26. (with Rupert L. Frank & Hanne Van Den Bosch) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Comm. Pure Appl. Math. (2017), in press. (arXiv)

25. (with Marcin Napiórkowski) A note on the validity of Bogoliubov correction to mean-field dynamics. J. Math. Pures Appl. (2017), in press. (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. (2016), to appear. (arXiv)

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)


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

4. Maximum ionization in Thomas-Fermi-Dirac-Weizsäcker theory, Oberwolfach Reports (2016), Workshop "Many-Body Quantum Systems and Effective Theories".

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. In 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. In 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)