Nicolas Dupuis

LPTMC/UPMC, Université Pierre et Marie Curie (Paris)
Universal equation of state in Bose systems: from dilute gases to the Mott transition and critical Casimir forces

The equation of state of a dilute Bose gas at low temperatures depends on the boson mass and the s-wave scattering length and is otherwise universal. This universality can be understood from the presence of a quantum critical point at zero temperature and vanishing density. We compare renormalization-group calculations of the equation of state in a 2D dilute Bose gas with experiments in cold atoms. We then discuss the universal equation of state of a Bose gas in an optical lattice in the vicinity of the superfluid--Mott-insulator transition. Finally we show that the equation of state of a 2D quantum system is related to critical Casimir forces in a 3D classical system with periodic boundary conditions.