Geodesic
Uncertainty relation for multidimensional correlation functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 3, pp. 427-434 
N. V. Karelin; A. M. Lazaruk. Uncertainty relation for multidimensional correlation functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 3, pp. 427-434. http://geodesic.mathdoc.fr/item/TMF_1998_117_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Partially coherent fields (mixed states) described by correlation functions (density matrices) are considered. The lower bound for the product of the uncertainties in the wave spatial localization and in its Fourier transform localization is obtained as a function of the space dimensionality. For the state with minimum uncertainty, it is shown that increasing the dimensionality leads to decreasing the phase volume corresponding to one mode in the canonical distribution of the correlation function as compared with the phase volume in the case of a coherent field (pure state).

[1] G. Veil, Teoriya grupp i kvantovaya mekhanika, Nauka, M., 1986 | MR

[2] A. Papulis, Teoriya sistem i preobrazovanii v optike, Mir, M., 1971

[3] M. J. Bastiaans, Opt. Acta, 28 (1981), 1215 | DOI | MR

[4] M. J. Bastiaans, J. Opt. Soc. Amer., 72 (1982), 1441 | DOI

[5] M. J. Bastiaans, J. Opt. Soc. Amer., 73 (1983), 251 | DOI | MR

[6] L. D. Landau, E. M. Livshits, Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1989 | MR

[7] B. R. Levin, Teoreticheskie osnovy statisticheskoi radiotekhniki, Radio i svyaz, M., 1989 | MR | Zbl

[8] H. Gamo, “Matrix treatment of coherence”, Progress in Optics, 3, ed. E. Wolf, North-Holland, Amsterdam, 1964, 1 | DOI

[9] E. Wolf, J. Opt. Soc. Amer., 72 (1982), 343 | DOI | MR

[10] N. V. Karelin, A. M. Lazaruk, Izv. vuzov. Radiofizika, 40 (1997), 903

[11] R. Feinman, Statisticheskaya mekhanika, Mir, M., 1978

[12] L. D. Landau, E. M. Livshits, Statisticheskaya fizika, ch. I, Nauka, M., 1974

[13] V. V. Dodonov, V. I. Manko, Trudy FIAN, 183 (1987), 5

[14] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, T. 2, Nauka, M., 1974 | MR

[15] V. I. Levin, DAN SSSR, 59 (1948), 635 | Zbl

[16] D. S. Mitrinović, Analytic inequalities, Springer-Verlag, Berlin, 1970 | MR | Zbl