Hamburg 2009 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 30: Poster II

Q 30.49: Poster

Tuesday, March 3, 2009, 16:30–19:00, VMP 9 Poster

The Riemann ζ-Function in Phase Space — •Cornelia Feiler, Rüdiger Mack, and Wolfgang P. Schleich — Institute for Quantum Physics, Ulm University

The Riemann hypothesis, a conjecture about the distribution of the so called non-trivial zeros of the Riemann ζ-function, is at the very heart of number theory. The distribution of these zeros is strongly connected with the distribution of primes [1]. Prime numbers, on the other hand, play a crucial role for example in cryptography or factorization.

We propose a new physical approach to the Riemann ζ-function. We consider the states of an harmonic oscillator with a logarithmic coupling to an external field. With an appropriate projection we obtain the values ζ(s) for ℜ s>1. With the help of an entangled system, similar to the Jaynes-Cummings-Model [3], we managed to reach into the critical strip, where the non-trivial zeros of the ζ-function are expected to be.

[1] E. C. Titchmarsh. The Theory of the Riemann Zeta-Function. Oxford, Charlendon Press, 1967.

[2] Wolfgang P. Schleich. Quantum Optics in Phase Space. Wiley-VCH Verlag, Berlin, 2001.