Dresden 2011 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 15: Poster 1: Quanteninformation, Quanteneffekte, Laserentwicklung, Laseranwendungen, Ultrakurze Pulse, Photonik

Q 15.92: Poster

Montag, 14. März 2011, 16:30–19:30, P1

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

In 1859 Bernhard Riemann mentioned in his seminal paper “Ueber die Anzahl der Primzahlen unter einer gegeben Grösse” [1], the by now famous conjecture: all non-trivial zeros of the zeta function have real part one-half without giving a proof for it. Although the Riemann hypothesis was studied by many famous mathematicians and lately was attacked by physicists, no rigorous proof exists today.

Our approach towards the Riemann zeta function takes advantage of the time evolution of two interacting quantum systems followed by a joint measurement. The states which reproduce the zeta function in the different parts of the complex plane inherit the properties of the different representations [2] of the zeta function. To understand their behavior we investigate the Wigner functions of these so-called zeta states.

[1] B. Riemann. Monatsbericht der Berliner Akademie, 1859.

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