Landau levels and Riemann zeros.
Germán Sierra1, Paul K Townsend
1Instituto de Física Teórica, CSIC-UAM, Facultad de Ciencias, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.
Physical Review Letters
|October 15, 2008
Summary
The Riemann zeta function
Area of Science:
- Number Theory
- Quantum Mechanics
- Mathematical Physics
Background:
- The Riemann zeta function's zeros are crucial in number theory.
- Existing models link its smooth part to semiclassical systems.
- Connes' model connects missing continuum states to zeta function regularization.
Purpose of the Study:
- To explore the connection between quantum mechanics and the Riemann zeta function.
- To investigate Connes' absorption spectrum model.
- To propose a role for Landau levels in zeta function fluctuations.
Main Methods:
- Analyzing a quantum-mechanical model of a charged particle in electromagnetic fields.
- Investigating the lowest Landau level limit of this model.
- Relating the model's absorption spectrum to Connes' model.
Main Results:
- The Connes absorption spectrum model emerges from the lowest Landau level limit.
- This quantum model provides a physical interpretation for Connes' regularization.
- Higher Landau levels are suggested to influence the fluctuation part of N(E).
Conclusions:
- Quantum mechanics offers a framework for understanding the Riemann zeta function's properties.
- The study links number theory and quantum field theory through Landau levels.
- Further research can explore the impact of higher Landau levels on zeta function fluctuations.
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