Kuipers, Jack and Hummel, Quirin and Richter, Klaus (2014) Quantum Graphs Whose Spectra Mimic the Zeros of the Riemann Zeta Function. PHYSICAL REVIEW LETTERS, 112 (7): 070406. ISSN 0031-9007, 1079-7114
Full text not available from this repository. (Request a copy)Abstract
One of the most famous problems in mathematics is the Riemann hypothesis: that the nontrivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that have the same oscillating part of the density of states as the Riemann zeros, offering an explanation of the overall minus sign. The smooth part is completely different, and hence also the spectrum, but the graphs pick out the low-lying zeros.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CHAOS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 26 Nov 2019 14:17 |
| Last Modified: | 26 Nov 2019 14:17 |
| URI: | https://pred.uni-regensburg.de/id/eprint/10654 |
Actions (login required)
 |
View Item |
