Huyghens, Bohr, Riemann and Galois: Phase-locking

International Journal of Modern Physics B

Volumn 20, Issue 11-13, 2006, Pages 1833-1850

  Planat, Michel ^a  

^a FEMTO ST INSTITUTE   (France)

Author keywords

1 f noise; Cyclotomic field; Galois fields; Incomplete Gauss sums; Phase states; Phase Locking; Prime numbers; Quantum complementarity

Indexed keywords

EID: 33744531267     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979206034340     Document Type: Conference Paper

References (31)

1. M. Planat, Fluct. and Noise Lett. 1, R65-R79 (2001).
2. M. Planat and E. Henry, Appl. Phys. Lett. 80, 2413-2415 (2002).
3. M. Planat and H. Rosu, Phys. Lett. A315, 1-5 (2003).
4. M. Planat and H. Rosu, Eur. Phys. J. D36, 133-139 (2005); DOI: 10.1140/epjd/e2005-00208-4.
5. M. S. Sargent, M. O. Scully and W. E. Lamb, Laser Physics, (Addison-Wesley, London, 1974), p. 52.
6. R. Adler, Proc. IRE 34, 351 (1946).
7. Reprinted in Proc. IEE 61, 1380 (1973).
8. J. Klapper and J. T. Frankle, Phase-locked and Frequency-Feedback Systems (Academic Press, New-York ,1972).
9. S. Dos Santos and M. Planat, Ann. of Telec. Paris 53, 488-494 (1998).
10. M. Planat and C. Eckert, IEEE Trans. on Ultrason. Ferroel. and Freq. Cont. 47, 1173-1182 (2000).
11. P. Cvitanovic, in From number theory to physics, ed. M. Waldschmidt, P. Moussa, J.M. Luck and C. Itzykson (Springer, Berlin, 1992), pp. 631-658.
12. R. Lynch, Physics Reports 256, 367-436 (1995).
13. E. Madelung, Z. Phys. 40, 332-336 (1926).
14. W. P. Schleich and S. M. Barnett Quantum phase and phase dependant measurements, (Special issue, Physica Scripta, T48, 1-142, 1993).
15. V. V. Dodonov and V. I. Man'ko, Theory of nonclassical states of light (Taylor & Francis, London, 2003).
16. L. Susskind and J. Glogower, Physics 1, 49-61 (1964).
17. V. Bouchiat, D. Vion, P. Joyez, D. Estve and M. H. Devoret, Physica Scripta 1, 165-170 (1998).
18. M. Planat and H. Rosu, J. Opt. B, Quant. and Semiclass. Opt. 6, S 583-590 (2004).
19. D. T. Pegg and S. M. Barnett, Phys. Rev. A 39, 1665-1675 (1989).
20. M. Planat, H. Rosu and S. Perrine, Phys. Rev. E 66, 56128-56134 (2002).
21. J. B. Bost and A. Connes, Selecta Mathematica 1, 411-457 (1995).
22. M. Planat, Neuroquantology 2, 292-308 (2004).
23. Quiprocone webside, http://www.imaph.tu-bs.de/qi/problems.
24. W.K. Wootters and B.D. Fields, Ann. Phys. 191, 363 (1989).
25. A. Klappenecker and M. Rötteler, in Proc. Applications of Finite Fields Fq7 (2003), quant-ph/0309120.
26. K.S. Gibbons, M.J. Hoffman and W.K. Wootters, Phys. Rev. A70, 062101 (2004).
27. M. Saniga, M. Planat and H. Rosu, J. Opt. B: Quantum Semiclass. Opt 6, L19 (2004).
28. M. Saniga and M. Planat, Hjelmslev Geometry of Mutually Unbiased Bases, mathph/0506057.
29. R. Lidl and H. Niederreiter, Finite Fields, (Addison-Wesley: Reading, Ma, 1983).
30. S. Konyagin and I. Shparlinski, Character sums with exponential functions and their applications (Cambridge Univ. Press, New York, 1999).
31. Henryk Iwaniec and Emmanuel Kowalski, Analytic Number Theory (Colloquium Publications, Vol. 53, Amer. Math. Soc. , 2004).