Dyson, F.J.: Ground state energy of a hard-sphere gas. Phys. Rev. 106, 20–26 (1957)

Article  ADS  Google Scholar 

Lieb, E.H., Yngvason, J.: Ground state energy of the low density Bose gas. Phys. Rev. Lett. 80(12) (1998)

Nam, P.T., Ricaud, J., Triay, A.: Ground state energy of the low density Bose gas with three-body interactions. J. Math. Phys. 63, 071903 (2022). Special collection in honor of Freeman Dyson

Nam, P.T., Ricaud, J., Triay, A.: Dilute Bose gas with three-body interaction: recent results and open questions. J. Math. Phys. 63(6) (2022)

Pieniazek, P.A., Tainter, C.J., Skinner, J.L.: Surface of liquid water: Three-body interactions and vibrational sum-frequency spectroscopy. J. Am. Chem. Soc. 133, 10360–10363 (2011)

Article  ADS  Google Scholar 

Ujevic, S., Vitiello, S.A.: Three-body interactions in the condensed phases of helium atom systems. J. Phys.: Condens. Matter 19, 116212 (2007)

ADS  Google Scholar 

Gammal, A., Frederico, T., Tomio, L., Chomaz, P.: Atomic Bose-Einstein condensation with three-body interactions and collective excitations. J. Phys. B 33(19), 4053 (2000)

Article  ADS  Google Scholar 

Koch, T., Lahaye, T., Metz, J., Fröhlich, B., Griesmaier, A., Pfau, T.: Stabilization of a purely dipolar quantum gas against collapse. Nat. Phys. 4(3), 218–222 (2008)

Article  Google Scholar 

Petrov, D.S.: Beyond-mean-field effects in mixtures: few-body and many-body aspects (2023). https://arxiv.org/abs/2312.05336

Basti, G., Cenatiempo, C., Schlein, B.: A new second order upper bound for the ground state energy of dilute Bose gases. Forum Math. Sigma 9, 74 (2021)

Article  MathSciNet  Google Scholar 

Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Ann. of Math. 192, 893–976 (2020)

Article  MathSciNet  Google Scholar 

Fournais, S., Solovej, J.P.: The energy of dilute Bose gases II: the general case. Invent. Math. 232, 863–994 (2023)

Article  MathSciNet  ADS  Google Scholar 

Yau, H.-T., Yin, J.: The second order upper bound for the ground state energy of a Bose gas. J. Stat. Phys. 136, 453–503 (2009)

Article  MathSciNet  ADS  Google Scholar 

Adami, R., Lee, J.: Microscopic derivation of a Schrödinger equation in dimension one with a nonlinear point interaction. J. Funct. Anal. 288(10), 110866 (2025)

Article  Google Scholar 

Chen, T., Pavlović, N.: The quintic NLS as the mean field limit of a boson gas with three-body interactions. J. Funct. Anal. 260(4), 959–997 (2011)

Article  MathSciNet  Google Scholar 

Chen, X.: Second order corrections to mean field evolution for weakly interacting bosons in the case of three-body interactions. Arch. Ration. Mech. Anal. 203(2), 455–497 (2012)

Article  MathSciNet  Google Scholar 

Chen, X., Holmer, J.: The derivation of the \(\mathbb ^\) energy-critical NLS from quantum many-body dynamics. Invent. Math. 217, 433–547 (2019)

Article  MathSciNet  ADS  Google Scholar 

Lee, J.: Rate of convergence towards mean-field evolution for weakly interacting bosons with singular three-body interactions (2021). https://arxiv.org/abs/2006.13040

Li, Y., Yao, F.: Derivation of the nonlinear Schrödinger equation with a general nonlinearity and Gross-Pitaevskii hierarchy in one and two dimensions. J. Math. Phys. 62(2), 021505 (2021)

Article  MathSciNet  ADS  Google Scholar 

Nam, P.T., Salzmann, R.: Derivation of 3D energy-critical nonlinear Schrödinger equation and Bogoliubov excitations for Bose gases. Commun. Math. Phys. 375, 495–571 (2019)

Article  ADS  Google Scholar 

Rout, A., Sohinger, V.: A microscopic derivation of Gibbs measures for the 1D focusing quintic nonlinear Schrödinger equation. Commun. Partial Differ. Equ. 48, 1008–1055 (2023)

Article  Google Scholar 

Yuan, J.: Derivation of the quintic NLS from many-body quantum dynamics in \(T^2\). Commun. Pure Appl. Anal. 14(5), 1941–1960 (2015)

Article  MathSciNet  Google Scholar 

Nam, P.T., Ricaud, J., Triay, A.: The condensation of a trapped dilute Bose gas with three-body interactions. Prob. Math. Phys 4, 91–149 (2023)

Article  MathSciNet  Google Scholar 

Nguyen, D.-T., Ricaud, J.: On one-dimensional Bose gases with two-body and (critical) attractive three-body interactions. SIAM J. Math. Anal. 56(3), 3203–3251 (2024)

Article  MathSciNet  Google Scholar 

Nguyen, D.-T., Ricaud, J.: Stabilization against collapse of 2D attractive Bose-Einstein condensates with repulsive, three-body interactions. Lett. Math. Phys. 115(31), 1–46 (2025)

MathSciNet  ADS  Google Scholar 

Ruelle, D.: Statistical Mechanics. Rigorous Results. Singapore: World Scientific. London: Imperial College Press, London (1999)

Lieb, E.H., Loss, M.: Analysis. Graduate Studies in Mathematics, vol. 14. American Mathematical Society, second ed., Providence (2001)

Lee, T.D., Huang, K., Yang, C.N.: Eigenvalues and eigenfunctions of a bose system of hard spheres and its low temperature properties. Phys. Rev. 106, 1135–1145 (1957)

Article  MathSciNet  ADS  Google Scholar 

Haberberger, F., Hainzl, C., Nam, P.T., Seiringer, R., Triay, A.: The free energy of dilute Bose gases at low temperatures (2023). https://arxiv.org/abs/2304.02405

Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional Bose gas. Commun. Math. Phys. 405(59) (2024)

Nam, P.T., Rougerie, N., Seiringer, R.: Ground states of large bosonic systems: the Gross-Pitaevskii limit revisited. Anal. PDE 9, 459–485 (2016)

Article  MathSciNet  Google Scholar 

Lieb, E.H., Seiringer, R., Sobolev, J.P., Yngvason, J.: The Mathematics of the Bose Gas and Its Condensation: Series: Oberwolfach Semin, vol. 34. Birkhäuser Verlag, Basel (2005)

Google Scholar 

Junge, L., Visconti, F.L.A.: Ground state energy of a dilute Bose gas with three-body hard-core interactions (2024). https://arxiv.org/abs/2406.09019

Nam, P.T., Triay, A.: Bogoliubov excitation spectrum of trapped Bose gas in the Gross-Pitaevskii regime. J. Math. Pures Appl. 176, 18–101 (2022)

Article  Google Scholar 

Temple, G.: The theory of Rayleigh’s principle as applied to continuous systems. In: Proc. Roy. Soc. London A, vol. 119, p. 276 (1928)

Reed, M.C., Simon, B.: Methods of Modern Mathematical Physics vol. 4: Analysis of operators. Academic Press, New York (1978)

Bijl, A.: The lowest wave function of the symmetrical many particles system. Physica 7(9), 869–886 (1940)

Article  ADS  Google Scholar 

Dingle, R.: The zero-point energy of a system of particles. Philos. Mag. 40(304), 573–578 (1949)

Article  Google Scholar 

Jastrow, R.: Many-body problem with strong forces. Phys. Rev. 98, 1479–1484 (1955)

Article  ADS  Google Scholar 

Basti, G., Cenatiempo, S., Olgiati, A., Pasqualetti, G., Schlein, B.: Ground state energy of a Bose gas in the Gross–Pitaevskii regime. J. Math. Phys. 63(4) (2022)