Department Mathematik



Phan Thành Nam

Research papers

51. (with Julien Ricaud and Arnaud Triay) Ground state energy of the low density Bose gas with three-body interactions. Preprint 2022. Contribution to a special issue honoring Freeman Dyson. (arXiv)

50. (with Julien Ricaud and Arnaud Triay) The condensation of a trapped dilute Bose gas with three-body interactions. Preprint 2021. (arXiv)

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. Ann. Henri Poincaré (2021). (arXiv - article)

46. (with Rupert L. Frank) Existence and nonexistence in the liquid drop model. Calc. Var. Partial Differential Equations, 60, 223 (2021), pp. 1-12. (arXiv - article)

45. (with Marcin Napiórkowski) Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas. Calc. Var. Partial Differential Equations 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. 225 (2021), pp. 885-979. (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. Partial Differential Equations 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

15. The ionization problem in quantum mechanics. Contribution to a book in honour of Elliott H. Lieb's 90th birthday, edited by R. L. Frank, A. Laptev, M. Lewin and R. Seiringer, EMS Publishing House (2022). (pdf)

14. (with J. Ricaud and A. Triay) Dilute Bose gas with three-body interaction: recent results and open questions. Contribution to the Proceedings of the 20th ICMP, Geneva 2021. (arXiv)

13. Bogoliubov excitation spectrum of Bose gases. Proceedings of the 8th European Congress of Mathematics, Portorož 2021. (pdf)

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 International Congress on Mathematical Physics, 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)