Nonclassical degrees of freedom in the Riemann Hamiltonian

Physical Review Letters

Volumn 107, Issue 10, 2011, Pages

  Srednicki, Mark ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREE OF FREEDOM; DENSITY OF STATE; EIGENVALUES; IMAGINARY PARTS; PERIODIC ORBITS; PHASE FACTOR; QUANTUM HAMILTONIANS; RIEMANN ZETA FUNCTIONS; SIGN PROBLEM; UNIVERSALITY CLASS;

EIGENVALUES AND EIGENFUNCTIONS; QUANTUM OPTICS;

HAMILTONIANS;

EID: 80052243639     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.107.100201     Document Type: Article

References (18)

1. S.J. Miller and R. Takloo-Bighash, An Invitation to Modern Number Theory (Princeton University Press, Princeton, 2006).
2. J. Derbyshire, Prime Obsession (Joseph Henry Press, Washington, DC, 2003).
3. J.B. Conrey, Not. Am. Math. Soc. AMNOAN 0002-9920 50, 341 (2003).
4. M.L. Mehta, Random Matrices (Elsevier, Amsterdam, 2004).
5. O. Bohigas, M.-J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984). PRLTAO 0031-9007 10.1103/PhysRevLett.52.1
6. M.V. Berry, Proc. R. Soc. A 400, 229 (1985); PRLAAZ 0080-4630 10.1098/rspa.1985.0078
7. M.V. Berry, in Quantum Chaos and Statistical Nuclear Physics, edited by, T.H. Seligman, and, H. Nishioka, (Springer, Berlin, 1986).
8. N.M. Katz and P. Sarnak, Bull. Am. Math. Soc. 36, 1 (1999); BAMOAD 0002-9904 10.1090/S0273-0979-99-00766-1
9. N.M. Katz P. Sarnak Random Matrices, Frobenius Eigenvalues, and Monodromy (Am. Math. Soc., Providence, 1999).
10. M.O. Rubinstein, Ph.D. thesis, Princeton University, 1998.
11. A. Altland and M.R. Zirnbauer, Phys. Rev. B PRBMDO 0163-1829 55, 1142 (1997). 10.1103/PhysRevB.55.1142
12. W. Pauli, Z. Phys. 31, 765 (1925). ZEPYAA 0044-3328 10.1007/BF02980631
13. F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 2001).
14. S. Gnutzmann, B. Seif, F. von Oppen, and M.R. Zirnbauer, Phys. Rev. E PLEEE8 1063-651X 67, 046225 (2003). 10.1103/PhysRevE.67.046225
15. Note that orbit repetitions were not included in the formulas of Ref. 14, since primitive orbits are expected to dominate [S. Gnutzmann (private communication)].
16. A. Connes, Sel. Math. New Ser. 1022-1824 5, 29 (1999). 10.1007/s000290050042
17. M.V. Berry and J.P. Keating, in Supersymmetry and Trace Formulae: Chaos and Disorder, edited by, J.P. Keating, D.E. Khmelnitskii, and, I.V. Lerner, (Plenum, New York, 1999);
18. M.V. Berry J.P. Keating SIAM Rev. 41, 236 (1999). SIREAD 0036-1445 10.1137/S0036144598347497