Fourier analysis of many-body transition amplitudes and states
Abstract
We decompose the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. To do so, we perform a Fourier transform over the symmetric group SN on the collection of N! many-body transition amplitudes connecting two states of a system of N particles. We apply our formalism to the interference of partially distinguishable bosons and fermions and describe mechanisms responsible for completely destructive interference in many-body systems obeying specific exchange symmetries, including, but not limited to, bosons and fermions.
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