## 126 Citations

Ground state energy of dilute Bose gases in 1D

- Physics
- 2022

We study the ground state energy of a gas of 1D bosons with density ρ , interacting through a general, repulsive 2-body potential with scattering length a , in the dilute limit ρ | a | ≪ 1. The ﬁrst…

The free energy of a dilute two-dimensional Bose gas

- Physics, Mathematics
- 2020

We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem…

Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger

- Physics
- 2020

How and why may an interacting system of many particles be described assuming that all particles are independent and identically distributed ? This question is at least as old as statistical…

Ground states of large bosonic systems: The gross-pitaevskii limit revisited

- Physics, Mathematics
- 2015

We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive non-linear Schr\"odinger functional whose quartic term is…

The Quantum-Mechanical Many-Body Problem: The Bose Gas

- Physics
- 2004

Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by…

The ground state of the Bose gas

- Physics
- 2001

Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas…

Dilute Bose gas with three-body interaction: Recent results and open questions

- PhysicsJournal of Mathematical Physics
- 2022

We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schrödinger…

Bounds for Interacting Bose Gases ∗

- Physics
- 2018

We study interacting Bose gases and prove lower bounds for the kinetic plus interaction energy of a many-body wave function in terms of its particle density. These general estimates are then applied…

Lieb-Thirring Bounds for Interacting Bose Gases

- Physics
- 2015

We study interacting Bose gases and prove lower bounds for the kinetic plus interaction energy of a many-body wave function in terms of its particle density. These general estimates are then applied…

Lieb-Thirring Bounds for Interacting Bose Gases∗

- Physics
- 2014

We study interacting Bose gases and prove lower bounds for the kinetic plus interaction energy of a many-body wave function in terms of its particle density. These general estimates are then applied…