Japanese version
Dr. Sarnak's Lecture Notes:
Some Lecture notes by Dr. Sarnak
I read D. Schumayer and D. A. W. Hutchinson's paper (arxiv:1101.3116)
Physics of the Riemann Hypothesis
and become to think that Number Theory is not pure Math. but Phys. of the world of numbers. I gather some related article and build menu as follows:
Riemann Zeta Function and Functional Equation II (Hilbert Polya's proposal)
Riemann Zeta Function and Functional Equation III (From Selberg to Quantum Chaos)
Riemann Zeta Function and Functional Equation IV (H=xp model and Landau level)
V reserved.
Riemann Zeta Function and Functional Equation VI (A Short Story of Automorphic Forms)
Riemann Zeta Function and Functional Equation VII (Hardy-Ramanujan fomula and the central charge of 3-
dimensional black holes)
Riemann Zeta Function and Functional Equation VIII (Lee-Yang theorem and Riemann zeta function)
Riemann Zeta Function and Functional Equation IX（On Mertens Conjecture）
The following article I (partially) translate into Japanese:
Zeta functions, statistical mechanics and Haar measure (prologue)
Zeta functions, statistical mechanics and Haar measure
Walks on graphs and statistical mechanics
arxiv:1101.3116 "Physics of the Riemann Hypothesis" tells us the history ow physics and Riemann hypothesis, as its title.
ReplyDeleteIts contents as follows:
I Introduction
II Historical background and 'Mathematical necessities'
III Connections to physics
A. Classical mechanics
B. Quantum mechanics
1. Scattering state models
2. Bound State models
C. Nuclear physics
D. Condensed matter physics
E. Statistical physics
IV Concluseion
They cover all field of physics and very intresting.
Arithmetic Quantum Caologsts say that Riemann zeta's nontrivial zeros distribute GUE, which means breaking time reversal symmetry.
ReplyDeleteWhat is the arthmetical meaning of the breaking time reversal symmetry?
Arithmetic Quantum Chaologsts say that Riemann zeta's nontrivial zeros distribute GUE, which means breaking time reversal symmetry.
ReplyDeleteWhat is the arthmetical meaning of the breaking time reversal symmetry?