Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

Annals of Physics

Volumn 326, Issue 6, 2011, Pages 1479-1500

  Olendski, O ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Ginzburg Landau theory of superconductivity; Quantum disk; Quasibound states; Robin boundary condition; Wave scattering

Indexed keywords

EID: 79954715002     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2011.02.005     Document Type: Article

References (158)

1. Gustafson K., Abe T. Math. Intell. 1998, 20:63.
2. Morse P.M., Feshbach H. Methods of Theoretical Physics 1953, McGraw-Hill, New York, Pt. II, Chapter 9.2.
3. Strauss W.A. Partial Differential Equations 1992, Wiley, New York, Section 4.3.
4. Balian R., Bloch C. Ann. Phys. 1970, 60:401.
5. Balian R., Bloch C. Ann. Phys. 1971, 64:271.
6. Balian R., Bloch C. Ann. Phys. 1974, 84:559.
7. Fulling S.A. J. Phys. A 1983, 16:2615.
8. Ashwin P., Zhen M. J. Dyn. Differ. Equ. 1994, 6:487.
9. Sieber M., Primack H., Smilansky U., Ussishkin I., Schanz H. J. Phys. A 1995, 28:5041.
10. Lebedev S.L. Zh. Eksp. Teor. Fiz. 1996, 110:769.
11. Lebedev S.L. English Transl.: JETP 1996, 83:423.
12. Dancer E.N., Daners D. J. Diff. Equ. 1997, 138:86.
13. Daners D. Trans. Am. Math. Soc. 2000, 352:4207.
14. Minces P., Rivelles V.O. Nucl. Phys. B 2000, 572:651.
15. Solodukhin S.N. Phys. Rev. D 2001, 63:044002.
16. Romeo A., Saharian A.A. Phys. Rev. D 2001, 63:105019.
17. Lebedev S.L. Yadernaya Fiz. 2001, 64:1413.
18. Lebedev S.L. English Transl.: Phys. Atomic Nuclei 2001, 64:1337.
19. Berry M.V., Ishio H. J. Phys. A 2002, 35:5961.
20. Bordag M., Falomir H., Santangelo E.M., Vassilevich D.V. Phys. Rev. D 2002, 65:064032.
21. Zayed E.M.E. Appl. Math. Comp. 2003, 144:365.
22. Arendt W., Warma M. J. Evol. Equ. 2003, 3:119.
23. Fulling S.A. J. Phys. A 2003, 36:6857.
24. Arendt W., Warma M. Potential Anal. 2003, 19:341.
25. de Albuquerque L.C., Cavalcanti R.M. J. Phys. A 2004, 37:7039.
26. Bondurant J.D., Fulling S.A. J. Phys. A 2005, 38:1505.
27. Dowker J.S. J. Phys. A 2005, 38:4735.
28. Giorgi T., Smits R. Illinois J. Math. 2005, 49:1133.
29. Baelus B.J., Partoens B., Peeters F.M. Phys. Rev. B 2006, 73:212503.
30. Pankrashkin K. Rep. Math. Phys. 2006, 58:207.
31. Liu Z.H., Fulling S.A. New J. Phys. 2006, 8:234.
32. Freitas P., Krejčiřík D. Math. Phys. Anal. Geom. 2006, 9:335.
33. Mintz B., Farina C., Neto P.A.M., Rodrigues R.B. J. Phys. A 2006, 39:6559.
34. Mintz B., Farina C., Neto P.A.M., Rodrigues R.B. J. Phys. A 2006, 39:11325.
35. Farina C. Braz. J. Phys. 2006, 36:1137.
36. Daners D., Kennedy J. SIAM J. Math. Anal. 2007, 39:1191.
37. Giorgi T., Smits R. Z. Angew. Math. Phys. 2007, 58:224.
38. Jílek M. Symm. Integr. Geom. Meth. Appl. 2007, 3:108.
39. Berry M.V., Dennis M.R. J. Phys. A 2008, 41:135203.
40. Giorgi T., Smits R. Z. Angew. Math. Phys. 2008, 59:600.
41. Marlettta M., Rozenblum G. J. Phys. A 2009, 42:125204.
42. Berry M.V. J. Phys. A 2009, 42:165208.
43. Gesztesy F., Mitrea M. J. Differ. Equ. 2009, 247:2871.
44. Teo L.P. J. High Energy Phys. 2009, 11:095.
45. Dean D.S. Phys. Rev. E 2009, 79:011108.
46. Milovanovic G., Baumgartner O., Kosina H. Opt. Quant. Electron. 2009, 41:921.
47. Olendski O., Mikhailovska L. Phys. Rev. E 2010, 81:036606.
48. Behrndt J., Langer M., Lobanov I., Lotoreichik V., Popov I.Y. J. Math. Anal. Appl. 2010, 371:750.
49. Casimir H.B.G. Proc. K. Ned. Akad. Wet. 1948, 51:793.
50. Ginzburg V.L., Landau L.D. Zh. Eksp. Teor. Fiz. 1950, 20:1064.
51. Ginzburg V.L., Landau L.D. Men of physics 1965, vol. 1:138-167. Pergamon Press, London.
52. de Gennes P.G. Superconductivity of Metals and Alloys 1966, Benjamin, New York.
53. Olendski O., Mikhailovska L. Phys. Rev. B 2008, 77:174405.
54. Montevecchi E., Indekeu J.O. Europhys. Lett. 2000, 51:661.
55. Montevecchi E., Indekeu J.O. Phys. Rev. B 2000, 62:14359.
56. Olendski O., Mikhailovska L. Phys. Rev. E 2003, 67:056625.
57. Zaǐtsev R.O. Zh. Eksp. Teor. Phys. 1965, 48:1759.
58. Zaǐtsev R.O. English Transl.: Sov. Phys. - JETP 1965, 21:1178.
59. Andryushin E.A., Ginzburg V.L., Silin A.P. Usp. Fiz. Nauk 1993, 163(9):105.
60. Andryushin E.A., Ginzburg V.L. English Transl.: Phys. Usp. 1993, 36:854.
61. Andryushin E.A., Ginzburg V.L., Silin A.P. Usp. Fiz. Nauk 1993, 163(11):102.
62. Andryushin E.A., Ginzburg V.L., Silin A.P. English Transl.: Phys. Usp. 1993, 36:1086.
63. Lu K., Pan X.-B. J. Diff. Equ. 1996, 129:136.
64. Fink H.J., Joiner W.C.H. Phys. Rev. Lett. 1969, 23:120.
65. Kozhevnikov V.F., Van Bael M.J., Vinckx W., Temst K., Van Haesendonck C., Indekeu J.O. Phys. Rev. B 2005, 72:174510.
66. Khlyustikov I.N., Buzdin A.I. Adv. Phys. 1987, 36:271.
67. Bosma H. Proc. IEEE B 1962, 109:137.
68. Bosma H. IEEE Trans. Microwave Theory Tech. 1964, 12:61.
69. Fay C.E., Comstock R.L. IEEE Trans. Microwave Theory Tech. 1965, 13:15.
70. Gurevich A.G. Ferrites at Microwave Frequencies 1963, Consultants Bureau, New York.
71. Baden Fuller A.J. Ferrites at Microwave Frequencies 1987, Peter Peregrinus, London, UK.
72. Hurault J.-P. Phys. Lett. 1966, 20:587.
73. Takács S. Z. Phys. 1967, 199:495.
74. Takács S. Z. Phys. 1967, 203:226.
75. Takács S. Phys. Lett. A 1968, 28:349.
76. Takács S. Czech. J. Phys. B 1969, 19:1366.
77. Buisson O., Gandit P., Rammal R., Wang Y.Y., Pannetier B. Phys. Lett. A 1990, 150:36.
78. Masale M., Constantinou N.C., Tilley D.R. Supercond. Sci. Technol. 1993, 6:287.
79. Richardson G., Rubinstein J. Appl. Math. Lett. 2000, 13(3):97.
80. Hornberger K., Smilansky U. J. Phys. A 2000, 33:2829.
81. Baelus B.J., Yampolskii S.V., Peeters F.M., Montevecchi E., Indekeu J.O. Phys. Rev. B 2001, 65:024510.
82. Pogosov W.V. Phys. Rev. B 2002, 65:224511.
83. Hornberger K., Smilansky U. Phys. Rep. 2002, 367:249.
84. Pan X.-B. SIAM J. Math. Anal. 2003, 34:957.
85. Slachmuylders A.F., Partoens B., Peeters F.M. Phys. Rev. B 2005, 71:245405.
86. Kachmar A. C. R. Acad. Sci. Paris Ser. I 2006, 342:701.
87. Zhu B.-H., Zhou S.-P., Shi Y.-M., Zha G.-Q., Yang K. Phys. Rev. B 2006, 74:014501.
88. Kachmar A. J. Math. Phys. 2006, 47:072106.
89. Zha G.-Q., Zhou S.-P., Zhu B.-H., Shi Y.-M., Zhao H.-W. Phys. Rev. B 2006, 74:024527.
90. Kachmar A. J. Math. Phys. 2007, 48:019901.
91. Kachmar A. C. R. Acad. Sci. Paris Ser. I 2008, 346:297.
92. Kachmar A. Rev. Math. Phys. 2008, 20:901.
93. Barba J.J., de Souza Silva C.C., Cabral L.R.E., Aguiar J.A. Physica C 2008, 468:718.
94. Barba-Ortega J., Aguiar J.A. Physica C 2009, 469:754.
95. Barba-Ortega J., de Souza Silva C.C., Aguiar J.A. Physica C 2009, 469:852.
96. Krejčiřík D., Bíla H., Znojil M. J. Phys. A 2006, 39:10143.
97. Krejčiřík D. J. Phys. A 2008, 41:244012.
98. Krejčiřík D., Tater M. J. Phys. A 2008, 41:244013.
99. Borisov D., Krejčiřík D. Integral Equ. Oper. Theory 2008, 62:489.
100. Krejčiřík D., Siegl P. J. Phys. A 2010, 43:485204.
101. Bender C.M., Boettcher S. Phys. Rev. Lett. 1998, 80:5243.
102. Bender C.M. Contemp. Phys. 2005, 46:277.
103. Bender C.M. Rep. Prog. Phys. 2007, 70:947.
104. Davies E.B. Linear Operators and Their Spectra 2007, University Press, Cambridge, UK, Example 9.2.4.
105. Lakshtanov E., Vainberg B. J. Phys. A 2010, 43:415205.
106. Allard J.F., Atalla N. Propagation of Sound in Porous Media 2009, Wiley, New York.
107. Grigor'yan F.E. Akust. Zh. 1968, 14:376.
108. Grigor'yan F.E. English Transl.: Sov. Phys. Acoust. 1969, 14:315.
109. Grigor'yan F.E. Akust. Zh. 1970, 16:229.
110. Grigor'yan F.E. English Transl.: Sov. Phys. Acoust. 1970, 16:192.
111. Ko S.H., Ho L.T. J. Sound Vib. 1977, 53:189.
112. Ko S.-H. J. Sound Vib. 1979, 66:165.
113. Rostafinski W. J. Acoust. Soc. Am. 1982, 71:36.
114. Rienstra S.W. J. Fluid Mech. 1999, 380:279.
115. Rienstra S.W. J. Fluid Mech. 2003, 495:157.
116. Félix S., Pagneux V. J. Acoust. Soc. Am. 2004, 116:1921.
117. Bi W.P., Pagneux V., Lafarge D., Aurégan Y. J. Sound Vib. 2006, 289:1091.
118. Weston V.H. IEEE Trans. Antennas Propag. 1963, 11:578.
119. Katsenelenbaum B.Z. High-Frequency Electrodynamics 2006, Wiley, Weinheim, Germany.
120. Krupka J., Geyer R.G. IEEE Trans. Magn. 1996, 32:1924.
121. Kaiser H.-C., Neidhardt H., Rehberg J. Integral Equ. Oper. Theory 2003, 45:39.
122. Kaiser H.-C., Neidhardt H., Rehberg J. J. Math. Phys. 2002, 43:5325.
123. Kaiser H.-C., Neidhardt H., Rehberg J. Math. Nachr. 2003, 252:51.
124. Baro M., Neidhardt H., Rehberg J. SIAM J. Math. Anal. 2005, 37:941.
125. Lipavský P., Morawetz K., Koláček J., Yang T.J. Phys. Rev. B 2006, 73:052505.
126. Morawetz K., Lipavský P., Mareš J.J. New J. Phys. 2009, 11:023032.
127. Koláček J., Lipavský P. Int. J. Mod. Phys. B 2009, 23:4481.
128. Dingle R.B. Proc. R. Soc. London A 1952, 212:47.
129. Dingle R.B. Proc. R. Soc. London A 1953, 216:118.
130. Nakamura K., Thomas H. Phys. Rev. Lett. 1988, 61:247.
131. Geerinckx F., Peeters F.M., Devreese J.T. J. Appl. Phys. 1990, 68:3435.
132. Constantinou N.C., Masale M., Tilley D.R. J. Phys. Condens. Matter 1992, 4:4499.
133. Avishai Y., Kohmoto M. Phys. Rev. Lett. 1993, 71:279.
134. Saint-James D. Phys. Lett. 1965, 15:13.
135. Dalmasso C., Pagiola E. Nuovo Cimento 1965, 35:811.
136. Constantinou N.C., Masale M., Tilley D.R. J. Phys. Condens. Matter 1992, 4:L293.
137. Moshchalkov V.V., Qiu X.G., Bruyndoncx V. Phys. Rev. B 1997, 55:11793.
138. Benoist R., Zwerger W. Z. Phys. B 1997, 103:377.
139. Handbook of Mathematical Functions 1964, Dover, New York. M. Abramowitz, I.A. Stegun (Eds.).
140. Page L. Phys. Rev. 1930, 36:444.
141. Landau L.D., Lifshitz E.M. Quantum Mechanics (Non-Relativistic Theory) 1977, Pergamon, New York.
142. Newton R.G. Scattering Theory of Waves and Particles 1966, McGraw-Hill, New York.
143. Gradshteyn I.S., Ryzhik I.M. Series. Table of Integrals, Series, and Products 2000, Academic, New York.
144. Prudnikov A.P., Brychkov Y.A., Marichev O.I. Integrals and Series 1986, vol. 2. Gordon and Breach Science Publishers, New York.
145. Prudnikov A.P., Brychkov Y.A., Marichev O.I. Integrals and Series 1986, vol. 3. Gordon and Breach Science Publishers, New York.
146. Brychkov Y.A. Special Functions: Derivatives, Integrals, Series and Other Formulas 2008, Chapman, Boca Raton.
147. Jackson J.D. Classical Electrodynamics 1999, Wiley, New York.
148. Landau L.D., Lifshitz E.M. Fluid Mechanics 1993, Pergamon, New York.
149. Moshchalkov V.V., Gielen L., Strunk C., Jonckheere R., Qiu X., Van Haesendonck C., Bruynseraede Y. Nature 1994, 373:319.
150. Chibotaru L.F., Ceulemans A., Bruyndoncx V., Moshchalkov V.V. Nature 2000, 408:833.
151. Geim A.K., Grigorieva I.V., Dubonos S.V., Lok J.G.S., Maan J.C., Filippov A.E., Peeters F.M. Nature 1997, 390:259.
152. Deo P.S., Schweigert V.A., Peeters F.M., Geim A.K. Phys. Rev. Lett. 1997, 79:4653.
153. Chapman S.J., Du Q., Gunzburger M.D. Eur. J. Appl. Math. 1995, 6:97.
154. Giorgi T. Proc. R. Soc. Edinburgh A 2005, 135:331.
155. Kachmar A. Asymptotic Anal. 2007, 54:125.
156. Kachmar A. Asymptotic Anal. 2007, 55:145.
157. Fournais S., Kachmar A. J. Diff. Equ. 2009, 247:1637.
158. Nesvizhevsky V.V., Petukhov A.K., Protasov K.V., Voronin A.Y. Phys. Rev. A 2008, 78:033616.