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August 14, 2026New Journal of PhysicsOpen Access

Fourier analysis of many-body transition amplitudes and states

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Authors

GDGabriel DufourABAndreas Buchleitner

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Overview

Theoretical study reveals a group Fourier decomposition of many-body transition amplitudes, providing tools to quantify partial distinguishability and predict suppressed quantum interference.

Key Points

  • Decompose many-body quantum transition amplitudes and counting statistics using Fourier analysis over the symmetric group to systematically characterize particle-exchange symmetries.
  • Applied a Fourier transform over the symmetric group $S_N$ to the $N!$ transition amplitudes connecting two states in an $N$-particle system.
  • Evaluated partially distinguishable bosons and fermions with unobserved degrees of freedom and modeled transmission through discrete Fourier transform interferometers.
  • Provided a mathematical decomposition of multi-particle counting statistics into distinct irreducible exchange symmetry components.
  • Derived a systematic description of partial distinguishability as an experimental noise source and control parameter in quantum interference.
  • Identified suppression mechanisms causing completely destructive interference and predicted specific zero-probability transition instances in discrete Fourier transform unitaries.

Cite This Study

Dufour et al. (2026) studied this question.

synapsesocial.com/papers/6a7ec69fb70b84ec8b912b72https://doi.org/10.1088/1367-2630/ae98a9
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