Floquet exponents of underdamped Josephson ladders: A comparison with predictions of the discrete sine-Gordon equation

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 6, 2000, Pages 6415-6425

  Trees, B R ^a   Hussain, N ^a  

^a OHIO WESLEYAN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CAPACITANCE; LADDERS; LOCKS (FASTENERS); PHASE STABILITY; PHONONS; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; DYNAMICS; ELECTRIC CURRENTS; MATHEMATICAL MODELS; NUMERICAL METHODS; OSCILLATIONS; PERTURBATION TECHNIQUES;

CROSSOVER BEHAVIOR; DISCRETE SINE-GORDON EQUATIONS; FLOQUET EXPONENTS; HARMONIC OSCILLATORS; JUNCTION CAPACITANCES; OPTIMIZE THE STABILITIES; RESISTIVELY AND CAPACITIVELY SHUNTED JUNCTIONS; VERTICAL JUNCTIONS;

SINE-GORDON EQUATION; JOSEPHSON JUNCTION DEVICES;

CRITICAL CURRENT ANISOTROPY; DISCRETE SINE GORDON EQUATION; FLOQUET EXPONENTS; JOSEPHSON LADDERS; PHASE LOCKED SOLUTIONS; RESISTIVELY AND CAPACITIVELY SHUNTED JUNCTION MODEL;

EID: 0034205557     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.6415     Document Type: Article

References (35)

1. P. Caputo, M. V. Fistul, A. V. Ustinov, B. A. Malomed, and S. Flach, Phys. Rev. B 59, 14 050 (1999).
2. M. Barahona, S. H. Strogatz, and T. P. Orlando, Phys. Rev. B 57, 1181 (1998).
3. J. J. Mazo and J. C. Ciria, Phys. Rev. B 54, 16 068 (1996).
4. S. Ryu, W. Yu, and D. Stroud, Phys. Rev. E 53, 2190 (1996).
5. I. Hwang, S. Ryu, and D. Stroud, Phys. Rev. B 53, R506 (1996).
6. L. M. Floría, J. L. Marín, P. J. Martínez, F. Falo, and S. Aubry, Europhys. Lett. 36, 539 (1996).
7. C. Denniston and C. Tang, Phys. Rev. Lett. 75, 3930 (1995).
8. B. J. Kim, S. Kim, and S. J. Lee, Phys. Rev. B 51, 8462 (1995).
9. J. M. Kim and S. J. Lee, Phys. Rev. B 50, 13 829 (1994).
10. J. Kim, W. G. Chee, S. Kim, and H. J. Lee, Phys. Rev. B 49, 459 (1994).
11. A. V. Ustinov, M. Cirillo, and B. A. Malomed, Phys. Rev. B 47, 8357 (1993).
12. M. Kardar, Phys. Rev. B 33, 3125 (1986).
13. H. S. J. van der Zant, T. P. Orlando, S. Watanabe, and S. H. Strogatz, Phys. Rev. Lett. 74, 174 (1995).
14. S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett. 74, 379 (1995).
15. A. V. Ustinov, M. Cirillo, B. H. Larsen, V. A. Oboznov, P. Carellí, and G. Rotolí, Phys. Rev. B 51, 3081 (1995).
16. P. J. Martínez, L. M. Floría, J. L. Marín, S. Aubry, and J. J. Mazo, Physica D 119, 175 (1998).
17. L. M. Florí, J. L. Marín, S. Aubry, P. J. Martínez, F. Falo, and J. J. Mazo, Physica D 113, 387 (1998).
18. J. J. Mazo, F. Falo, and L. M. Floría, Phys. Rev. B 52, 10 433 (1995).
19. J. F. Currie, S. E. Trullinger, A. R. Bishop, and J. A. Krumhansl, Phys. Rev. B 15, 5567 (1977).
20. S. Watanabe, H. S. J. van der Zant, S. H. Strogatz, and T. P. Orlando, Physica D 97, 429 (1996).
21. H. S. J. van der Zant, M. Barahona, A. E. Duwel, E. Trías, T. P. Orlando, S. Watanabe, and S. H. Strogatz, Physica D 119, 219 (1998).
22. L. M. Floría and J. J. Mazo, Adv. Phys. 45, 505 (1996).
23. S. N. Coppersmith and D. S. Fisher, Phys. Rev. B 28, 2566 (1983), and references therein.
24. Z. Zheng, B. Hu, and G. Hu, Phys. Rev. E 57, 1139 (1998), and references therein.
25. Y. Frenkel and T. K. Kontorova, Zh. Eksp. Teor. Fiz. 8, 1340 (1938).
26. This is for the classical limit, where the charging energy of the junction is much less than the Josephson tunneling energy.
27. Z. Q. Wang and D. Stroud, Phys. Rev. B 44, 9643 (1991).
28. D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations (Clarendon, Oxford, 1977).
29. If any exponents are positive, then phase locking in the ladder, for the given values of bias current, capacitance, and critical current anisotropy, is not stable because perturbations grow with time. We do not find any evidence for such an instability for the values of these parameters that we have used.
30. See, for example, J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems (Saunders, Fort Worth, 1995), pp. 116–123.
31. B. R. Trees and D. Stroud, Phys. Rev. B 59, 7108 (1999).
32. These arrays are similar to that of Fig. 11, except that there are no vertical junctions, just superconducting shorts connecting the horizontal junctions.
33. These “phonons” can be thought of as small-angle oscilla-tions, or normal modes, of the pendulum system. They have also been described as phasons or spin-wave-like modes of the junction arrays.
34. See Ref. 4 for the derivation of the DSG equation from the RCSJ model.
35. As will be seen in Sec. IV, the long-wavelength normal modes seem to play an important role in determining the Floquet exponent for the longest-lived mode of the ladder.