Home Home Home Home Home

My publications

Daniel Osadchy and Joseph Avron, Hofstadter butterfly as a quantum phase diagram (pdf), Journal of Mathematical Physics, Vol. 42, 5665 (2001), (earchive)
Shlomo A. Ben-Haim, Daniel Osadchy, Israel Schuster, Lior Gepstein, Gal Hayam & Mark Josephson, Nonfluoroscopic, in vivo navigation and mapping technology, Nature Medicine, Vol. 2, 1393 (1996)

Bibliography on the Hofstadter Butterfly

D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)
M. Ya. Azbel, Sov. Phys. JETP 19, 634, (1964)
D. Hofstadter, Phys. Rev. B 14, 2239, (1976)
J. Bellissard, A. van Elst, H. Schultz-Baldes, The noncommutative geometry of the quantum Hall effect, J. Math. Phys. 35, 5373 (1994)
A. I. Bobenko and R. Seiler, Discrete integrable geometry and physics, Oxford University Press, Oxfrod, (1999)
B. Helffer and J. Sjõstrand, Mémoires de la société mathématique de France (nouvelle série), 39, 1 (1989)
Y. Last, Comm. Math. Phys., 164, 421, (1994)
D. Thouless, Phys. Rev. B 28, 4272, (1983)
P. Wiegmann and A.V. Zabrodin, Nuc. Phys. B 422, 495, (1994); Nuc. Phys. 451, 699, (1995)
M. Wilkinson, J. Phys. A 17, 3459, (1984)
K. von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)
R. B. Laughlin, Phys. Rev. B 23, 5632 (1981)
D. Springsguth, R. Ketzmerick, T. Geisel, Phys. Rev. B 56, 2036, (1997)
J. Avron and L. Sadun, J. Math. Phys. 42, 1, (2001)
P. Bak and R. Bruinsma, Phys. Rev. Lett. 49, 249 (1982)
H. E. Nusse, E. Ott and J.A. Yorke, Phys. Rev. Lett. 75, 2482 (1995)
W. G. Chambers, Phys. Rev. A 140, 135 (1965)
S. Ya. Jitomirskaya and Y. Last, XIth International Congress of Mathematical Physics, 366-372 (1995)
H. L. Cycon, R. G. Froese, W. Kirsch, B. Simon, Schrõdinger operators, Berlin, Heidelberg, New York: Springer (1987)
S. Aubry, G. Andre, Ann. Israel Phys. Soc. 3, 133 (1980)
J. Avron, B. Simon, Duke Math. J. 50, 369 (1983)
P. M. H. van Mouche, Comm. Math. Phys. 122, 23 (1989)
M. D. Choi, G. A. Elliot, N. Yui, Invent. Math. 99, 225 (1990)
J. Avron, P. H. M. van Mouche, B. Simon, Comm. Math. Phys. 132, 103 (1990)
Y. Last and M. Wilkinson, J. Phys. A. 25, 6123 (1992)
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4-th edition, Oxford University Press, Oxford (1960)
I. Dana, Y. Avron, J. Zak, J. Phys. C, 18, L679 (1985)
D. J. Thouless, Topological quantum numbers in nonrelativistic physics, World Scientific, Singapore, 1998; J. Math. Phys. 35, 1 (1994)
P. Streda, J. Phys. C, 15, L717 (1982)
T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms, The MIT Press (1994)