Unitarization of the classical statistical s matrix for systems with localization

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 5, 2007, Pages

  Weaver, Richard L ^a  

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BACKSCATTERING; DIFFUSION; RANDOM PROCESSES; STATISTICAL METHODS;

MESOSCOPIC BEHAVIORS; REVERBERANT CAVITIES;

MATRIX ALGEBRA;

EID: 36549003614     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.051122     Document Type: Article

References (27)

1. Thomas Guhr, Axel Muller-Groeling, and H. A. Weidnemuller, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00088-4 299, 189 (1998).
2. Y. V. Fyodorov, D. V. Savin, and H.-J. Sommers J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/49/017 38, 10731 (2005).
3. Oleg Lobkis, Igor Rozhkov, and Richard Weaver, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.194101 91, 194101 (2003).
4. R. H. Lyon and R. G. DeJong, Theory and Application of Statistical Energy Analysis (Butterworths-Heimann, Boston, MA, 1995).
5. R. S. Langley and P. G. Bremner, J. Acoust. Soc. Am. JASMAN 0001-4966 10.1121/1.426705 105, 1657 (1999).
6. M. L. Lai and A. Soom, J. Vibr. Acoust. JVACEK 0739-3717 112, 127 (1990).
7. P. Morse and R. Bolt, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.16.69 16, 69 (1944).
8. Lothar Cremer and Helmut A. Müller, J. Acoust. Soc. Am. JASMAN 0001-4966 76, 1277 (1984).
9. Diffuse Waves in Complex Media, NATO ASI, Ser. C., edited by, J.-P. Fouque, (Kluwer Academic, Dordrecht, 1999), Vol. 531.
10. Richard L. Weaver and Oleg I. Lobkis, Geophysics GPYSA7 0016-8033 71, S15 (2006).
11. R. L. Weaver and W. Sachse, J. Acoust. Soc. Am. JASMAN 0001-4966 10.1121/1.412002 97, 2094 (1995).
12. Richard L. Weaver, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/1/ 008 9, 8 (2007).
13. J. P. Keating and S. Müller, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 463, 3241 (2007).
14. Richard L. Weaver and Oleg I. Lobkis, J. Sound Vib. JSVIAG 0022-460X 10.1006/jsvi.1999.2725 231, 1111 (2000).
15. C. Dembowski, H.-D. Gräf, R. Hofferbert, H. Rehfeld, A. Richter, and T. Weiland, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.3942 60, 3942 (1999).
16. U. Kuhl, H.-J. Stockmann, and R. Weaver, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/49/001 38, 10433 (2005).
17. The restriction to minimum phase has an interpretation based on Robinson's energy delay theorem, which says that the energy t=0 T st2 summed to any time T is no less for a minimum phase function st than for any other causal function with the same spectrums(ω).
18. The theorem for the more general matrix case may be seen in Y. Inouye, IEEE Trans. Circuits Syst. ICSYBT 0098-4094 10.1109/TCS.1987.1086102 34, 188 (1987).
19. A. H. Sayed and T. Kailath, Numer. Linear Algebra Appl. ZZZZZZ 1070-5325 8, 467 (2001).
20. V. N. Prigodin, B. Altshuler, K. B. Efetov, and S. Ida, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.546 72, 546 (1994).
21. D. Vollhardt and P. Wolfle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45.842 45, 842 (1980);
22. D. Vollhardt and P. Wolfle, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.22.4666 22, 4666 (1980);
23. D. Vollhardt and P. Wolfle, in Electronic Phase Transitions, edited by, W. Hanke, and, Yu. V. Kopaev, (Elsevier, Amsterdam, 1992).
24. B. A. van Tiggelen, A. Lagendijk, and D. S. Wiersma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4333 84, 4333 (2000);
25. S. E. Skipetrov and B. A. van Tiggelen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.113901 92, 113901 (2004);
26. S. E. Skipetrov and B. A. van Tiggelen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.043902 96, 043902 (2006).
27. O. I. Lobkis and R. L. Weaver, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.011112 71, 011112 (2005).