Hannover 2010 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 55: Poster II

Q 55.68: Poster

Thursday, March 11, 2010, 16:00–19:00, Lichthof

Zeta-States in Phase Space — •Cornelia Feiler, Rüdiger Mack, and Wolfgang P. Schleich — Institute for Quantum Physics, Ulm University

Wenn ich nach einem tausendjährigen Schlaf aufwachen würde, wäre meine erste Frage: Wurde die Riemann-Hypothese bewiesen?

D. Hilbert - Zur Hypothese von Bernhard Riemann

The Riemann hypothesis is a conjecture about the distribution of the so called non-trivial zeros of the Riemann ζ-function which 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 aproach the questions about the behavior of the ζ-function in the whole complex plane from a physical point of view. We construct so-called Zeta-states which contain properties connected to the Riemann ζ-function ζ(s). For example, the imaginary part t of the argument s=σ+1mui1mu t should be proportional to the time if we consider the time-evolution of the Zeta-state. Other properties, like the functional equation, and their influence on the phase space functions of these states are considered.

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