Indistinguishability in Quantum Many-Body Dynamics: Why no Difference Makes a Difference

requirement has far-reaching consequences for the behaviour of many-particle systems. It must be

taken into account when counting states of identical particles, resulting in either Bose-Einstein or

Fermi-Dirac statistics for non-interacting systems in equilibrium. Out of equilibrium, particle

indiscernability additionally implies indistinguishability of many-particle paths between initial and final

states of a system: Because we cannot tell which particle of the final state corresponds to which

particle of the initial state, the transition amplitudes associated with the different alternatives must be

summed coherently. This gives rise to intricate many-particle interference effects in the dynamics.

In this talk, I will first introduce the concept of many-particle interference by explaining how it arises in

the paradigmatic Hong-Ou-Mandel effect. I will then discuss some of the more recent developments

in the theory of many-particle interference, focusing on our studies of its role in interacting many-body

dynamics. By endowing the particles with an internal degree of freedom, we can tune their degree of

indistinguishability and thus control the level of many-particle interference. In this way, we are able to

systematically assess the imprint of many-particle interference on many-body quantum evolution, e.g.

in the Bose-Hubbard model, and to set it apart from interaction-induced effects.