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"The Riemann Zeta Function and Quantum Mechanics"

Dr. Wolfgang P. Schleich
Universität Ulm, Germany
Texas A&M University, U.S.A.


The Riemann zeta function ζ plays a crucial role in number theory as well as physics. Indeed, the distribution of primes is intimately connected to the non-trivial zeros of this function. We briefly summarize the essential properties of the Riemann zeta function and then present a quantum mechanical system which when measured appropriately yields ζ. We emphasize that for the representation in terms of a Dirichlet series interference [1] suffices to obtain ζ. However, in order to create ζ along the critical line where the non-trivial zeros are located we need two entangled quantum systems [2]. In this way entanglement may be considered the quantum analogue of the analytical continuation of complex analysis.

[1] R. Mack, J. P. Dahl, H. Moya-Cessa, W.T. Strunz, R. Walser and W. P. Schleich, Riemann ζ-function from wave packet dynamics, Phys. Rev. A. 82, 032119 (2010).
[2] C. Feiler and W.P. Schleich, Entanglement and analytical continuation: an intimate relation told by the Riemann zeta function, New J. Phys. 15, 063009 (2013).

Wednesday, April 2, 2014
IQSE 578, 12:30 noon
Mitchell Physics Building

Institute for Quantum Science and Engineering
Texas A&M University

(Pizza, salad, and soda to be served at 12:00 noon)

Host: Dr. Marlan Scully