QLunch: Per Moosavi

Speaker: Per Moosavi, Stockholm University

Title: Inhomogeneous quantum liquids out of equilibrium

Abstract: Conformal field theory (CFT) in one spatial dimension is routinely used to describe the low-energy properties of a large class of gapless quantum many-body systems called Tomonaga-Luttinger liquids (TLLs). Examples include quasi-1D condensates of ultra-cold atoms, gapless quantum spin chains, and electron flows in quantum wires. For inhomogeneous systems, such as ultra-cold atoms in a trap or spin chains with smoothly varying couplings between sites, the standard CFT description of TLLs must be generalized so that the usual propagation velocity and Luttinger parameter depend on position.

In this talk, I will show how such inhomogeneous TLLs can be studied by exact analytical means, even out of equilibrium, using projective unitary representations of circle diffeomorphisms and path-ordered exponentials. The results reveal, among others, how inhomogeneities open up the possibility for diffusive contributions to transport in CFT (that otherwise would be purely ballistic) and for scattering known as Andreev reflections (that otherwise would be absent).