2010

Anderson model on Bethe lattices: density of states, localization properties and isolated eigenvalue

Biroli, Giulio, Semerjian, Guilhem, Tarzia, Marco

Understand

We revisit the Anderson localization problem on Bethe lattices, putting in contact various aspects which have been previously only discussed separately.

For the case of connectivity 3 we compute by the cavity method the density of states and the evolution of the mobility edge with disorder.
Furthermore, we show that below a certain critical value of the disorder the smallest eigenvalue remains delocalized and separated by all the others (localized) ones by a gap.
We also study the evolution of the mobility edge at the center of the band with the connectivity, and discuss the large connectivity limit.

Built on

P.W. Anderson, Phys. Rev. 109
1958
Earlier work this paper cites.
I.M. Lifshits, Adv. Phys. 13
1964
Earlier work this paper cites.
D.J. Thouless, J. Phys. C 3
1970
Earlier work this paper cites.
E.N. Economou and M.H. Cohen, Phys. Rev. B 5
1972
Earlier work this paper cites.
R. Abou-Chacra, P.W. Anderson and D.J. Thouless, J. Phys. C 6
1973
Earlier work this paper cites.
R. Abou-Chacra and D.J. Thouless, J. Phys. C 7
1974
Earlier work this paper cites.
F.J. Wegner, Z. Phys. B 44
1981
Earlier work this paper cites.
H. Kunz and B. Souillard, J. Physique Lettres 44
1983
Earlier work this paper cites.
Y. Kim and A.B. Harris, Phys. Rev. B 31
1985
Earlier work this paper cites.
I.M. Lifshits, S.A. Gredeskul and L.A. Pastur, Introduction to the theory of disordered systems , Wiley Interscience (1988)
1988
Earlier work this paper cites.
M.P.A. Fisher, P.B. Weichman, G. Grinstein and D.S. Fisher, Phys. Rev. B 40
1989
Earlier work this paper cites.

Similar

R. Carmona and J. Lacroix, Spectral Theory of Random Schrödinger Operators , Birkhaüser (1990)
1990
Cited alongside, same era.
A.D. Mirlin and Y.V. Fyodorov, Nucl. Phys. B 366
1991
Cited alongside, same era.
J.-M. Luck, Systèmes désordonnés unidimensionnels , CEA, collection Aléa Saclay, Saclay (1992)
1992
Cited alongside, same era.
L.A. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators , Springer-Verlag (1992)
1992
Cited alongside, same era.
V. Acosta and A. Klein, J. Stat. Phys. 69
1992
Cited alongside, same era.
J.D. Miller and B. Derrida, J. Stat. Phys. 75
1994
Cited alongside, same era.
B.L. Altshuler, Y. Gefen, A. Kamenev and L.S. Levitov, Phys. Rev. Lett. 78
1997
Cited alongside, same era.
A. Klein, Advances in Mathematics 133
1998
Cited alongside, same era.
N. C. Wormald, Models of random regular graphs, in Surveys in Combinatorics, J.D. Lamb and D.A. Preece, eds, London Mathematical Society Lecture Note Series 276
1999
Cited alongside, same era.
M. Mézard and G. Parisi, Eur. Phys. J. B 20
2001
Cited alongside, same era.
Y. Weiss and W.T. Freeman, Neural Computation 13
2001
Cited alongside, same era.
G. Biroli, G. Semerjian, M. Tarzia, work in progress
Cited in the paper.

Then

F.X. Bronold, A. Alvermann and H. Fehske, Phil. Mag. 84
2005
Later among the works it cites.
M. Aizenman, R. Sims and S. Warzel, Probab. Theory Relat. Fields 136
2006
Later among the works it cites.
J. Friedman, A Proof of Alon’s Second Eigenvalue Conjecture and Related Problems
2008
Later among the works it cites.
C. Bordenave and M. Lelarge, arXiv
2008
Later among the works it cites.
A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Physics Today 62
2009
Later among the works it cites.
C. Monthus and T. Garel, J. Phys. A 42
2009
Later among the works it cites.
C.R. Laumann, S.A. Parameswaran and S.L. Sondhi, arXiv
2009
Later among the works it cites.
L. Pollet, N. V. Prokof’ev, B. V. Svistunov, and M. Troyer Phys. Rev. Lett. 103
2009
Later among the works it cites.
P. Müller and P. Stollmann, arXiv
2010
Closest in time.
Y. Kabashima, H. Takahashi and O. Watanabe, arXiv
2010
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…