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  • Letter
  • Open Access

Computing Riemann zeros with light scattering

Sunkyu Yu1,*, Xianji Piao2,†, and Namkyoo Park3,‡

  • 1Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
  • 2Wave Engineering Laboratory, School of Electrical and Computer Engineering, University of Seoul, Seoul 02504, Korea
  • 3Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea

  • *Contact author: sunkyu.yu@snu.ac.kr
  • †Contact author: piao@uos.ac.kr
  • ‡Contact author: nkpark@snu.ac.kr
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Phys. Rev. B 110, L220201 – Published 23 December, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.L220201

Abstract

Finding hidden order within disorder is a common interest in material science, wave physics, and mathematics. The Riemann hypothesis, stating the locations of nontrivial zeros of the Riemann zeta function, tentatively characterizes statistical order in the seemingly random distribution of prime numbers. This famous conjecture has inspired various connections with different branches of physics, recently with non-Hermitian physics, quantum field theory, trapped-ion qubits, and hyperuniformity. Here we develop the computing platform for the Riemann zeta function by employing classical scattering of light. We show that the Riemann hypothesis suggests the landscape of semi-infinite optical scatterers for the perfect reflectionless condition under the Born approximation. To examine the validity of the scattering-based computation, we investigate the asymptotic behaviors of suppressed reflections with the increasing number of scatterers and the emergence of multiple scattering. The result provides another bridge between classical physics and the Riemann zeros, exhibiting the design of wave devices inspired by number theory.

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Phys. Rev. B 110, L220201– Published 23 December, 2024
  • Received 2 September 2024
  • Revised 21 November 2024
  • Accepted 26 November 2024
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