Scale and Conformal Invariance in Ultracold Gases

The fourth lecture is devoted to the consequences of scale and conformal invariance in ultracold gases. Following a brief discussion of elementary examples like electrodynamics, it is shown that scale and conformal invariance appears for ultracold gases in 1D and 3D with unitarity limited scattering and generically in 2D. The additional symmetries give rise to universal features in both equilibrium properties and in dynamics. An example is the observation of breathers in 2D Bose gases at Collège de France, whose theoretical understanding is still incomplete. Finally, the implications of scale and conformal invariance for quantum limited transport coefficients like viscosity are discussed briefly.