Phase transition-like behavior in a low-pass filter

American Journal of Physics

Volumn 71, Issue 1, 2003, Pages 31-33

  Krivine, H ^a   Lesne, A ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037243466     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1514233     Document Type: Article

References (14)

1. J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1940), Chap. 13.
2. C. N. Yang and T. D. Lee, "Statistical theory of equations of state and phase transitions," Phys. Rev. 87, 404-409 (1952).
3. An observable signature of this discontinuity is critical opalescence.
4. R. P. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1964), Vol. II, p. 22-12.
5. The additional condition, not discussed here, requires that the sequence actually reaches the neighborhood of z*, where |f′(z)|<1. In other words, the initial condition should belong to the basin of attraction (with respect to the transformation f) of the stable fixed-point z*.
6. R. J. Rubin, "Statistical dynamics of simple cubic lattices. Model for the study of Brownian motion," J. Math. Phys. 1, 309-318 (1960); 2, 373-386 (1961).
7. R. J. Rubin, "Statistical dynamics of simple cubic lattices. Model for the study of Brownian motion," J. Math. Phys. 1, 309-318 (1960); 2, 373-386 (1961).
8. E. Ising, "Beitrag zur Theorie des Ferromagnetismus," Z. Phys. 31, 252-258 (1925).
9. A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973).
10. A. Lesne, Renormalization Methods (Wiley, New York, 1998).
11. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Reading, MA, 1992).
12. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, Berlin, 1983).
13. R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, MA, 1975).
14. M. Berry, "Some quantum-to-classical asymptotics," in Les Houches 1989, Session LII, Chaos and Quantum Physics, edited by M. J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam, 1990), pp. 251-304.