Department Mathematik



Phan Thành Nam

Research papers

49. (with Arnaud Triay) Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime. Preprint 2021. (arXiv)

48. (with Martin Ravn Christiansen and Christian Hainzl) The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime. Preprint 2021. (arXiv)

47. (with Niels Benedikter, Marcello Porta, Benjamin Schlein, and Robert Seiringer) Bosonization of Fermionic Many-Body Dynamics. Preprint 2021. (arXiv)

46. (with Rupert L. Frank) Existence and nonexistence in the liquid drop model. Preprint 2021. (arXiv)

45. (with Marcin Napiórkowski) Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas. Calc. Var. PDE 60, 99 (2021), pp. 1-30. (arXiv - article)

44. (with Kevin Kögler) The Lieb-Thirring inequality for interacting systems in strong-coupling limit. Arch. Ration. Mech. Anal. 240 (2021), 1169–1202. (arXiv - article)

43. (with Niels Benedikter, Marcello Porta, Benjamin Schlein, and Robert Seiringer) Correlation energy of a weakly interacting Fermi gas. Invent. Math. (2021), online first, 1-95. (arXiv - article)

42. (with Marcin Napiórkowski, Julien Ricaud, and Arnaud Triay) Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime. Analysis & PDE, in press. (arXiv)

41. (with Mathieu Lewin and Nicolas Rougerie) Classical field theory limit of many-body quantum Gibbs states in 2D and 3D. Invent. Math. 224 (2021), 315–444. (arXiv - article)

40. (with Nicolas Rougerie) Improved stability for 2D attractive Bose gases. J. Math. Phys. 61 (2020), 021901. (arXiv - article)

39. (with Debangana Mukherjee and Phuoc-Tai Nguyen) Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential. J. Funct. Anal. 281 (2021) 109092. (arXiv - article)

38. (with Simon Larson and Douglas Lundholm) Lieb-Thirring inequalities for wave functions vanishing on the diagonal set. Annales Henri Lebesgue 4 (2021), 251-282. (arXiv - article)

37. (with Robert Salzmann) Derivation of 3D energy-critical nonlinear Schrödinger equation and Bogoliubov excitations for Bose gases. Commun. Math. Phys. 375 (2020), 495–571. (arXiv - article)

36. (with Niels Benedikter, Marcello Porta, Benjamin Schlein, and Robert Seiringer) Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime. Commun. Math. Phys. 374 (2020), 2097–2150. (arXiv - article)

35. (with Rupert L. Frank, Dirk Hundertmark, and Michal Jex) The Lieb-Thirring inequality revisited. J. Eur. Math. Soc. 23 (2021), 2583-2600. (arXiv - article)

34. (with Nina Gottschling) Convergence of Levy-Lieb to Thomas-Fermi density functional. Calc. Var. PDE 57, 146 (2018), pp. 1-18. (arXiv - article)

33. (with Alessandro Michelangeli and Alessandro Olgiati) Ground state energy of mixture of Bose gases. Rev. Math. Phys. 31 (2019) 1950005. (arXiv - article)

32.(with Christian Brennecke, Marcin Napiórkowski, and Benjamin Schlein) Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation. Ann. Inst. H. Poincaré C, Anal. Non Linéaire 36 (2019), 1201-1235. (arXiv - article)

31. (with Marcin Napiórkowski) Norm approximation for many-body quantum dynamics: focusing case in low dimensions. Advances in Math. 350 (2019), 547-587. (arXiv - article)

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 and 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 and Hanne Van Den Bosch) The maximal excess charge in Müller density-matrix-functional theory. Ann. Henri Poincaré 19 (2018), 2839-2867. (arXiv - article)

26. (with Rupert L. Frank and Hanne Van Den Bosch) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Comm. Pure Appl. Math. 71 (2018), 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 and 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 and 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 and Jan Philip Solovej) Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. J. Funct. Anal. 270 (2016), 4340-4368. (arXiv - article)

19. (with Nicolas Rougerie and 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 and Fabian Portmann) Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems. Arch. Ration. Mech. Anal. 219 (2016), 1343-1382. (arXiv - article)

17. (with Mathieu Lewin and 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 and 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. Ration. Mech. Anal. 215 (2015), 381-417. (arXiv - article)

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

12. (with Mathieu Lewin and 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, and Jan Philip Solovej) Bogoliubov spectrum of interacting Bose gases. Comm. Pure Appl. Math. 68 (2015), 413-471. (arXiv - article )

10. (with Fabian Portmann and Jan Philip Solovej) Asymptotics for two dimensional atoms. Ann. Henri Poincaré 13 (2012), 333-362. (arXiv - article)

9. New bounds on the maximum ionization of atoms. Commun. Math. Phys. 312 (2012), 427-445. (arXiv - article)

8. (with Alain Pham Ngoc Dinh, Pham Hoang Quan and 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 and Phung Trong Thuc) The body force in a three-dimensional Lamé system: identification and regularization. Inverse Probl. Sci. Eng. 20 (2012), 517-532. (arXiv - article)

6. An approximate solution for nonlinear backward parabolic equations. J. Math. Anal. Appl. 367 (2010), 337-349. (preprint - article)

5. (with Dang Duc Trong and Nguyen Huy Tuan) The truncation method for a two-dimensional nonhomogeneous backward heat problem. Appl. Math. Comput. 216 (2010), 3423-3432. (preprint - article)

4. (with Dang Duc Trong, Mach Nguyet Minh, and Alain Pham Ngoc Dinh) Hölder-type approximation for the spatial source term of a backward heat equation. Numer. Funct. Anal. Optim. 31 (2010), 1386-1405. (preprint - article)

3. (with Dang Duc Trong and Alain Pham Ngoc Dinh) Determine the spatial term of a two-dimensional heat source. Applicable Analysis 88 (2009), 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, and Truong Trung Tuyen) Determination of the body force of a two-dimensional isotropic elastic body. J. Comput. Appl. Math. 229 (2009), 192-207. (arXiv - article)

Reviews / Proceedings of conferences / Book chapters

12. The Ionization Problem. EMS Newsletter, December 2020, pp. 22–27. (Full issue - article)

11. Direct methods to Lieb-Thirring kinetic inequalities. Proceedings of the Workshop on Density Functionals for Many-Particle Systems, September 2019, Singapore. (arXiv)

10. (with Mathieu Lewin and Nicolas Rougerie) Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases. J. Math. Phys. 60 (2019), 061901. Proceedings of the 19th ICMP, Montreal 2018. (arXiv - article)

9. Nonlinear Gibbs measure and Bose gases at positive temperature. IAMP News Bulletin, January 2019, 3-19. (pdf)

8. (with Mathieu Lewin and Nicolas Rougerie) The interacting 2D Bose gas and nonlinear Gibbs measures. Oberwolfach Reports, 15(2):1081–1116, 2018. (arXiv - report)

7. (with Mathieu Lewin and Nicolas Rougerie) Blow-up profile of rotating 2D focusing Bose gases. In: Macroscopic Limits of Quantum Systems, D. Cadamuro, et al. (eds.), Springer 2018, pp. 145–170. Conference in honor of Herbert Spohn 70th birthday, Munich 2017. (arXiv - book)

6. (with Rupert L. Frank and Hanne van den Bosch) A short proof of the ionization conjecture in Müller theory. In: Mathematical Problems in Quantum Physics, F. Bonetto, et al. (eds.), AMS Contemporary Mathematics 717 (2018), pp. 1-12. (arXiv - book)

5. (with Marcin Napiórkowski) Norm approximation for many-body quantum dynamics and Bogoliubov theory. In: Advances in Quantum Mechanics, A. Michelangeli and G. Dell'Antonio (eds.), Springer-INdAM Volume 18 (2017), pp. 223-238. (arXiv - book)

4. (with Rupert L. Frank and Hanne van den Bosch) Maximum ionization in Thomas-Fermi-Dirac-Weizsäcker theory. Oberwolfach Reports, 13(3):2500-2502, 2016. (report)

3. (with Mathieu Lewin and 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: XVIIth International Congress on Mathematical Physics, A. Jensen (ed.), World Scientific 2013, pp. 504-511. (arXiv - book)

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

PhD Thesis

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