Noise, chaos, and the Josephson voltage standard

Reports on Progress in Physics

Volumn 59, Issue 8, 1996, Pages 935-992

  Kautz, R L ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001501428     PISSN: 00344885     EISSN: None     Source Type: Journal    
DOI: 10.1088/0034-4885/59/8/001     Document Type: Article

References (182)

1. Aeillo A, Barone A and Ovsyannikov A 1984 Phys. Rev. B 30 456-8
2. Ambika G 1992 J. Phys.: Condens. Matter 4 4829-38
3. Alstrøm P, Christiansen B, Hyldgaard P, Levinsen M T and Rasmussen R 1986 Phys. Rev. A 34 2220-33
4. Alstrøm P and Levinsen M T 1985 Phys. Rev. B 32 1503-11
5. Alvarez G, Russel G J and Taylor K N R 1990 Physica 171C 415-18
6. Ambegaokar V and Halperin B I 1969 Phys. Rev. Lett. 22 1364-6
7. Arnold V I 1965 AMS Transl. Series 2 46 213-84
8. Bak P, Bohr T, Jensen M H and Christiansen P V 1984 Solid State Commun. 51 231-4
9. Barone A and Paterǹ G 1982 Physics and Applications of the Josephson Effect (New York: Wiley)
10. Battuccelli M, Christiansen P L, Pedersen N F and Soerensen M P 1986 Phys. Rev. B 33 4686-91
11. Belykh V N, Pedersen N F and Soerensen O H 1977 Phys. Rev. B 16 4860-71
12. Ben-Jacob E, Braiman Y and Shainsky R 1981 Appl. Phys. Lett. 38 822-4
13. Ben-Jacob E, Goldhirsch I, Irnry Y and Fishman S 1982 Phys. Rev. Lett. 49 1599-602
14. Biswas A C and Jha S S 1970 Phys. Rev. B 2 2543-7
15. Blackburn J A, Yang Z, Vik S, Smith H J T and Nerenberg M A H 1987 Physica 26D 385-95
16. Bohr T, Bak P and Jensen M H 1984 Phys. Rev. A 30 1970-81
17. Bryant P J and Miles J W 1990 J. Austral. Math. Soc. Ser. B 32 1-22
18. Callen H B and Welten T A 1951 Phys. Rev. 83 34-40
19. Chandrasekhar S 1943 Rev. Mod. Phys. 15 1-89
20. Chi C C and Vanneste C 1990 Phys. Rev. B 42 9875-95
21. Cicogna G 1987 Phys. Lett. 121A 403-6
22. Cicogna G and Fronzoni L 1990 Phys. Rev. A 42 1901-6
23. Cirillo M and Pedersen N F 1982 Phys. Lett. 90A 150-2
24. Coddington E A and Levinson N 1955 Theory of Ordinary Differential Equations (New York: McGraw-Hill)
25. Costabile G, Monaco R and Pagano S 1988 J. Appl. Phys. 63 5406-10
26. Costabile G, Monaco R, Pagano S and Rotoli G 1990 Phys. Rev. B 42 2651-4
27. Cronemeyer D C, Chi C C, Davidson A and Pedersen N F 1985 Phys. Rev. B 31 2667-74
28. Danchi W C, Golightly W J and Sutton E C 1989 J. Appl. Phys. 65 2772-86
29. Davidson A, Dueholm B and Beasely M R 1986 Phys. Rev. B 33 5127-30
30. Davidson A and Pedersen N F 1987 Phys. Rev. A 36 2455-9
31. de Lange G. Kuipers J J, Klapwijk T M, Panhuyzen R A, van de Stadt H and de Graauw M W M 1994 J. Appl. Phys. 76 8016-21
32. D'Humieres D, Beasely M R, Huberman B A and Libchaber A 1982 Phys. Rev. A 26 3483-96
33. Endo T, Koyanagi M and Nakamura A 1983 IEEE Trans. Instrum. Meas. 32 267-71
34. Feigenbaum M J 1978 J. Stat. Phys. 19 25-52
35. _1979 J. Stat. Phys. 21 669-706
36. Feynman R P, Leighton R B and Sands M 1965 The Feynman Lectures on Physics vol III (Reading, MA: Addison-Wesley)
37. Field B F, Finnegan T F and Toots J 1973 Metrologia 9 155-66
38. Filatrella G, Malomed B A and Parmentier R D 1993 Phys. Lett. 180A 346-9
39. Frank B and Meyer H G 1992 J. Appl Phys. 72 2973-7
40. Freidlin M I and Wentzell A D 1984 Random Perturbations of Dynamical Systems (New York: Springer)
41. Geisel T, Nierwetberg J and Zacherl A 1985 Phys. Rev. Lett. 54 616-9
42. Genchev Z D, Ivanov Z G and Todorov B N 1983 IEEE Trans. Circuits Syst. 30 633-6
43. Goldhirsch I, Imry Y, Wasserman G and Ben-Jacob E 1984 Phys. Rev. B 29 1218-30
44. Graham R 1973 Springer Tracts in Modern Physics vol 66, ed G Höhler (Berlin: Springer) pp 1-97
45. Graham R and Tel T 1986 Phys. Rev. A 33 1322-37; erratum 38 5944
46. Grassberger P 1989 J. Phys. A: Math. Gen. 22 3283-90
47. Grebogi C, Ott E, Romeiras F and Yorke J A 1987a Phys. Rev. A 36 5365-80
48. Grebogi C, Ott E and Yorke J A 1986 Phys. Rev. Lett. 56 1011-4
49. _1987b Physica 24D 243-62
50. Gubankov V N, Konstantinyan K I, Koshelets V P and Ovsyannikov G A 1982 Pis. Zh. Tekh. Fiz. 8 1332-5 (1982 Sov. Tech. Phys. Lett. 8 574-5)
51. Gubankov V N, Konstantinyan K I, Koshelets V P and Ovsyannikov G A 1982 Pis. Zh. Tekh. Fiz. 8 1332-5 (1982 Sov. Tech. Phys. Lett. 8 574-5)
52. _1983 IEEE Trans. Magn. 19 637-9
53. Gubankov V N, Ziglin S L, Konstantinyan K I, Koshelets V P and Ovsyannikov G A 1984 7h. Eksp. Teor. Fiz. 86 343-351 (1984 Sov. Phys.-JETP 59 198-203)
54. Gubankov V N, Ziglin S L, Konstantinyan K I, Koshelets V P and Ovsyannikov G A 1984 7h. Eksp. Teor. Fiz. 86 343-351 (1984 Sov. Phys.-JETP 59 198-203)
55. Gwinn E G and Westervelt R M 1985 Phys. Rev. Lett. 54 1613-6
56. _1986 Phys. Rev. A 33 4143-55
57. Hamilton C A 1972 Phys. Rev. B 5 912-23
58. Hamilton C A, Kautz R L, Steiner R L and Lloyd F L 1985 IEEE Electron Device Lett. 6 623-5
59. Hamilton C A, Kautz R L, Stieg M, Kao C, Arvin W F and Simmonds M 1991 IEEE Trans. Instrum. Meas. 40 301-4
60. Hamilton C A and Shapiro S 1970 Phys. Rev. B 2 4494-503
61. Hanggi P 1986 J. Stat. Phys. 42 105-48
62. He D R, Yeh W J and Kao Y H 1984 Phys. Rev. B 30 172-8
63. _1985 Phys. Rev. B 31 1359-73
64. Hockett K and Holmes P 1986 Ergod. Th. & Dynam. Sys. 6 205-39
65. Holmes P 1989 Chaos and Fractals: The Mathematics Behind the Computer Graphics ed R L Devaney and L Keen (Providence, RI: American Mathematical Society) pp 25-39
66. Holmes P 1990 Phys. Rep. 193 137-63
67. Hu Q, Free J U, lansiti M, Liengme O and Tinkham M 1985 IEEE Trans. Magn. 21 590-3
68. Hu Q, Lobb C J and Tinkham M 1987 Phys. Rev. B 35 1687-91
69. Huberman B A, Crutchfield J P and Packard N H 1980 Appl. Phys. Lett. 37 750-2
70. lansiti M, Hu Q, Westervelt R M and Tinkham M 1985 Phys. Rev. Lett. 55 746-9
71. Imai S, Shinagawa M, Monta S, Takeuti Y and Mikoshiba N 1992 Japan. J. Appl. Phys. 31 3546-58
72. Irnry Y 1983 Statics and Dynamics of Nonlinear Systems ed G Benedek, H Bilz and R Zeyher (Berlin: Springer) pp 170-88
73. Inoue M and Fujisaka H 1985 Phys. Rev. B 32 277-9
74. Inoue M, Kawaguchi T and Fujisaka H 1986 Phys. Lett. 115A 139-42
75. Inoue M and Koga H 1982 Prog. Theor. Phys. 68 2184-7
76. Ivanchenko Y M and Zil'berman L A 1968 Zh. Eksp. Teor. Fiz. 55 2395-402 (1969 Sov. Phys.-JETP 28 1272-6) Josephson B D 1962 Phys. Lett. 1 251-3
77. Ivanchenko Y M and Zil'berman L A 1968 Zh. Eksp. Teor. Fiz. 55 2395-402 (1969 Sov. Phys.-JETP 28 1272-6) Josephson B D 1962 Phys. Lett. 1 251-3
78. Ivanchenko Y M and Zil'berman L A 1968 Zh. Eksp. Teor. Fiz. 55 2395-402 (1969 Sov. Phys.-JETP 28 1272-6) Josephson B D 1962 Phys. Lett. 1 251-3
79. Jung P 1993 Phys. Rep. 234 175-295
80. Jung P and Hanggi P 1990 Phys. Rev. Lett. 65 3365-8
81. Kajanto M J and Salomaa 1985 Solid State Commun. 53 99-106
82. Kao Y H, Huang J C and Gou Y S 1986 J. Low Temp. Phys. 63 287-305
83. Kautz R L 1980 Appl. Phys. Lett. 36 386-8
84. _1981a J. Appl. Phys. 52 3528-41
85. _1981b J. Appl. Phys. 52 6241-6
86. _1983 IEEE Trans. Magn. 19 465-74
87. _1985 J. Appl. Phys. 58 424-40
88. _1987a J. Appl. Phys. 62 198-211
89. _1987b Phys. Lett. 125A 315-9
90. _1988 Phys. Rev. A 38 2066-80
91. _1989 Structure, Coherence and Chaos in Dynamical Systems ed P L Christiansen and R D Parmentier (Manchester: Manchester University Press) pp 207-26
92. _1992 Metrology at the Frontiers of Physics and Technology ed L Crovini and T J Quinn (Amsterdam: NorthHolland) pp 259-96
93. _1994 J. Appl. Phys. 76 5538-44
94. Kautz R L and Costabile G 1981 IEEE Trans. Magn. 17 780-3
95. Kautz R L, Hamilton C A and Lloyd F L 1987 IEEE Trans. Magn. 23 883-90
96. Kautz R L and Lloyd F L 1987 Appl. Phys. Lett. 51 2043-5
97. Kautz R L and Macfarlane J C 1986 Phys. Rev. A 33 498-509
98. Kautz R L and Monaco R 1985 J. Appl. Phys. 57 875-89
99. _1989 IEEE Trans. Magn. 25 1399-403
100. Kerr W C, Williams M B, Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1985 Z. Phys. B 59 103-10
101. Klein U, Hinken J H, Günther T and Teklenburg D 1989 IEEE Trans. Magn. 25 1092-5
102. Klein U, Schröder S and Hinken J H 1991 IEEE Trans. Instrum. Meas. 40 291-4
103. Knuth DE 1981 The Art of Computer Programming vol 2 (Reading, MA: Addison-Wesley)
104. Koga H, Fujisaka H and Inoue M 1983 Phys. Rev. A 28 2370-3
105. Kramers H A 1940 Physica 7 284-304
106. Kurkijärvi J 1985 SQUID '85 ed H D Hahlbohm and H Lübbig (Berlin: Walter de Gruyter) pp 377-407
107. Kuznik J and Odehnal M 1986 J. Low Temp. Phys. 65 353-74
108. Kuznfk J, Odehnal M and Seidel P 1988 J. Low Temp. Phys. 72 391-406
109. Kuznik J and Rogacki K 1993 Phys. Lett. 176A 144-8
110. Lee P A 1971 J. Appl. Phys. 42 325-34
111. Levi M 1988 Phys. Rev. A 37 927-31
112. Levinsen M T 1982 J. Appl. Phys. 53 4294-9
113. Levinsen M T, Chiao R Y, Feldman M J and Tucker B A 1977 Appl. Phys. Lett. 31 776-8
114. Lloyd F L, Hamilton C A, Beall J A, Go D, Ono R H and Harris R E 1987 IEEE Electron Device Lett. 8 449-50
115. Ludwig D 1975 SIAM Rev. 17 605-40
116. MacDonald A H and Plischke M 1983 Phys. Rev. B 27 201-11
117. Matkowsky B J and Schuss Z 1977 SIAM J. Appl. Math. 33 365-82
118. McCumber D E 1968 J. Appl. Phys. 39 3113-8
119. Mel'nikov V K 1963 Trans. Moscow Math. Soc. 12 1-57
120. Mikolajczak B, Meyer H G and Seidel P 1989 J. Appl. Phys 66 735-40
121. Monaco R and Kautz R L 1986 Josephson Effect-Achievement and Trends ed A Barone (Singapore: World Scientific) pp 498-509
122. Müller F and Köhler H J 1988 Phys. Status Solidi b 106 K165-8
123. Naito S and Higashino Y 1984 Japan. J. Appl. Phys. 23 861-6
124. Niemeyer J, Grimm L, Meier W, Hinken J H and Vollmer E 1985 Appl. Phys. Lett. 47 1222-3
125. Niemeyer J, Hinken J H and Kautz R L 1984 Appl. Phys. Lett. 45 478-80
126. Noeldeke C, Gross R, Bauer M, Reiner G and Seifert H 1986 J. Low Temp. Phys. 64 235-68
127. Nöldeke C 1985 Phys. Lett. 112A 178-82
128. Nöldeke C and Seifert H 1985 Phys. Lett. 109A 401-4
129. Octavio M 1984 Phys. Rev. B 29 1231-42
130. _1990 Physica A 163 248-57
131. Octavio M and Nasser C R 1984 Phys. Rev. B 30 1586-8
132. Odyniec M and Chua L O 1985 IEEE Trans. Circuits Syst. 32 34-45
133. Okuyama K, Hartfuss H J and Gundlach K H 1981 J. Low Temp. Phys. 44 283-93
134. Ott E 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)
135. Ovsyannikov G A and Smimov I V 1985 Zh. Teich. Fiz. 55 2410-3 (1986 Sov. Phys.-Tech. Phys. 30 1434-6)
136. Ovsyannikov G A and Smimov I V 1985 Zh. Teich. Fiz. 55 2410-3 (1986 Sov. Phys.-Tech. Phys. 30 1434-6)
137. Pedersen N F 1986 Phys. Scr. T13 129-34
138. Pedersen N F and Davidson A 1981 Appl. Phys. Lett. 39 830-2
139. Pegrum C M, Gurney W S C and Nisbet R M 1989 IEEE Trans. Magn. 25 1404-7
140. Popel R 1992 Metrologia 29 153-74
141. Qian M and Shen W X 1990 Science in China 33 409-22
142. Qian M, Shen W X and Zhang J 1988 J. Diff. Equations 71 315-33
143. Renne M J and Polder D 1974 Revue Phys. Appl. 9, 25-8
144. Rogvin D and Scalapino D J 1974 Ann. Phys. 86 1-90
145. Sakai K and Yamaguchi Y 1984 Phys. Rev. B 30 1219-30
146. Salam F M A and Sastry S S 1985 IEEE Trans. Circuits Syst. 32 784-96
147. Salemo M, Samueisen M R, Filatrella G, Pagano S and Parmentier R D 1990 Phys. Rev. B 41 6641-54
148. Schecter S 1987 SIAM J. Math. Anal. 18 1699-715
149. Seifert H 1983 Phys. Lett. 98B 213-6
150. _1984 Phys. Lett. 101B 230-4
151. Shapiro S 1963 Phys. Rev. Lett. 11 80-2
152. Shapiro S, Janus A R and Holly S 1964 Rev. Mod. Phys. 36 223-5
153. Shen W X 1991 Chin. Ann. Math. 12B 137-46
154. Soerensen M P, Davidson A, Pedersen N F and Pagano S 1988 Phys. Rev. A 38 5384-90
155. Steeb W H and Kunick A 1982 Phys. Rev. A 25 2889-92
156. Stephen M J 1969 Phys. Rev. 186 393-7
157. Stewart W C 1968 Appl. Phys. Lett. 12 277-80
158. Stratonovich R L 1963 Topics in the Theory of Random Noise vol 1 (New York: Gordon and Breach)
159. Swift J W and Wiesenfeld K 1984 Phys. Rev. Lett. 52 705-8
160. Talkner P, Hänggi P, Freidkin E and Trautmann D 1987 J. Stat. Phys. 48 231-54
161. Tao H, Lu L and Yang Q 1986 Chin. Phys. Lett. 3 349-52
162. Tinkham M 1989 Structure, Coherence and Chaos in Dynamical Systems ed P L Christiansen and R D Parmentier (Manchester: Manchester University Press) pp 427-39
163. Tsai J S, Jain A K and Lukens J E 1983 Phys. Rev. Lett. 51 315-9
164. Vanneste C, Chi C C and Cronemeyer D C 1985 Phys. Rev. B 32 4796-9
165. Ventsel' A D and Freidlin M I 1970 Usp. Mat. Nauk. 25 3-55 (1970 Russian Math. Surveys 25 1-55)
166. Ventsel' A D and Freidlin M I 1970 Usp. Mat. Nauk. 25 3-55 (1970 Russian Math. Surveys 25 1-55)
167. Waldram J R, Pippard A B and Clarke J 1970 Phil. Trans. R. Soc. Lond. A 268 265-87
168. Waldram J R and Wu P H 1982 J. Low Temp. Phys. 47 363-74
169. Wang X H and Yao X X 1992 Phys. Lett. 167A 295-300
170. Wang Z D and Yau X X 1985 Acta Phys. Sin. 34 1149-55 (1986 Chin. Phys. 6 326-31)
171. Wang Z D and Yau X X 1985 Acta Phys. Sin. 34 1149-55 (1986 Chin. Phys. 6 326-31)
172. Werthamer N R 1966 Phys. Rev. 147 255-63
173. Wiesenfeld K 1985 Phys. Rev. B 32 1744-51
174. Wiesenfeld K and Pedersen N F 1987 Phys. Rev. A 36 1440-4
175. Xiao W and Yao X 1988 Acta Phys. Sin. 37 295-300 (1990 Chin. Phys. 10 1-7)
176. Xiao W and Yao X 1988 Acta Phys. Sin. 37 295-300 (1990 Chin. Phys. 10 1-7)
177. Xu H, Fan M, Yang S and Wu P 1995 J. Appl. Phys. 78 6664-9
178. Yang T H, Wang C S, Huang J C and Gou Y S 1995 Phys. Rev. E 51 5279-86
179. Yao X, Wu J Z and Ting C S 1990 Phys. Rev. B 42 244-50
180. Yeh W J and Kao Y H 1982 Phys. Rev. Lett. 49 1888-91
181. Yen W J and Kao Y H 1983 Appl. Phys. Lett. 42 299-301
182. Yoshida T and Tomita K 1987 Prog. Theor. Phys. 77 239-53