ELFT HÍRADÓ

[<juhasz.robert AT wigner.hu>]

Dear Colleagues,

Our next Wigner Colloquium will be held as follows:

The Riemann Zeta Function and Quantum Mechanics

by Prof. Dr. Wolfgang P. Schleich (Institut für Quantenphysik, Center for
Integrated Quantum Science and Technology, Universität Ulm)

Thursday, 28 October 2021 from 10:00 to 11:00 (Europe/Budapest)
at KFKI campus Bldg. 1 ( Meeting Room )
Budapest, Konkoly-Thege Miklós út 29-33.

Wearing a mask is mandatory.
The event will be streamed online on Zoom:

Join Zoom Meeting
https://wigner-hu.zoom.us/j/96663948362?pwd=UnJta1l2VjA3UVE2NGRHM2ZWTDFtdz09

Meeting ID: 966 6394 8362
Passcode: 780159


Abstract

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. We also analyze the Newton flows [3, 4] of ζ
as well as of the closely related function ξ. Both provide additional insight
[5] into the Riemann hypothesis.


[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).
[3] J. Neuberger, C. Feiler, H. Maier, and W.P. Schleich, Newton flow of the
Riemann zeta function: Separatrices control the appearance of zeros, New J.
Phys. 16, 103023 (2014).
[4] J.W. Neuberger, C. Feiler, H. Maier, and W.P. Schleich, The Riemann
hypothesis illuminated by the Newton flow of ζ, Phys. Scr. 90, 108015 (2015).
[5] W.P. Schleich, I. Bezděková, M.B. Kim, P.C. Abbott, H. Maier, H.
Montgomery, and J.W. Neuberger, Equivalent formulations of the Riemann
hypothesis based on lines of constant phase, Phys. Scr. 93, 065201 (2018).

Sincerely Yours

Tamás Kiss (organizer)