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arXiv:2409.15079 · New Journal of Physics

Fourier analysis of many-body transition amplitudes and states

Gabriel Dufour, Andreas Buchleitner

Published Aug 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract Particle-exchange symmetry shapes the counting statistics of many-body systems by giving rise to multiple alternative evolutions whose transition amplitudes interfere. Here, we apply a Fourier transform over the symmetric group S N to the collection of N ! many-body transition amplitudes connecting two states of an N -particle system. This provides a decomposition of the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. As a first application of our formalism, we consider bosons or fermions which are rendered partially distinguishable from one another through unobserved degrees of freedom, and whose state is also subjected to a Fourier analysis. We thereby obtain a systematic description of partial distinguishability, which is both an important experimental noise source and a possible handle for the control of many-body interference. As a second application, we identify mechanisms responsible for completely destructive interference in many-body systems with other exchange symmetries than those of bosons or fermions. For an interferometer implementing the discrete Fourier transform unitary, we predict many instances of such suppressed transitions.

DOI
10.1088/1367-2630/ae98a9

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Abstract Particle-exchange symmetry shapes the counting statistics of many-body systems by giving rise to multiple alternative evolutions whose transition amplitudes interfere. Here, we apply a Fourier transform over the symmetric group S N to the collection of N ! many-body transition amplitudes connecting two states of an N -particle system. This provides a decomposition of the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. As a first application of our formalism, we consider bosons or fermions which are rendered partially distinguishable from one another through unobserved degrees of freedom, and whose state is also subjected to a Fourier analysis. We thereby obtain a systematic description of partial distinguishability, which is both an important experimental noise source and a possible handle for the control of many-body interference. As a second application, we identify mechanisms responsible for completely destructive interference in many-body systems with other exchange symmetries than those of bosons or fermions. For an interferometer implementing the discrete Fourier transform unitary, we predict many instances of such suppressed transitions.
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