Simple WaveOptical Superpositions as Prime Number Sieves
Abstract
We encode the sequence of prime numbers into simple superpositions of identical waves, mimicking the archetypal prime number sieve of Eratosthenes. The primes are identified as zeros accompanied by phase singularities in a physically generated wave field for integer valued momenta. Similarly, primes are encoded in the diffraction pattern from a simple single aperture and in the harmonics of a single vibrating resonator. Further, diffraction physics connections to number theory reveal how to encode all Gaussian primes, twin primes, and how to construct wave fields with amplitudes equal to the divisor function at integer spatial frequencies. Remarkably, all of these basic diffraction phenomena reveal that the naturally irregular sequence of primes can arise from trivially ordered wave superpositions.
 Publication:

Physical Review Letters
 Pub Date:
 March 2019
 DOI:
 10.1103/PhysRevLett.122.090201
 arXiv:
 arXiv:1812.04203
 Bibcode:
 2019PhRvL.122i0201P
 Keywords:

 Physics  Optics
 EPrint:
 4 figures