Low-energy properties of strongly interacting many-fermion systems can often be described in terms of one-particle excitations which behave almost like particles in a perfect Fermi gas. This is known as the Landau Fermi liquid concept which, however, fails in one dimension. Interacting particles in one dimension form a so called Luttinger liquid (LL) where there are no simple one-particle excitations. One of its peculiar properties is a hypersensitivity to defects: even a weak scattering from a single impurity totally destroys zero-temperature current through the LL made of fermions, while even a strong scattering makes no impact on the flow of the bosonic LL. On the other hand, scattering from two impurities may, under certain (resonant) conditions lead to an ideal fermionic current while destroying that of bosons. I emphasize the role of a duality between weak and strong scattering in these transport effects and show that – surprisingly – duality survives the addition of non-local and retarded interactions, which leads to some interesting consequences for electron transport in quantum wires and for flows of ultra-cold fermion-boson mixtures in one dimension.

Colloquium, May 23th, 2013