|
Singular continuous spectrum is generic
Author(s):
R.
del Rio;
S.
Jitomirskaya;
N.
Makarov;
B.
Simon
Journal:
Bull. Amer. Math. Soc.
31
(1994),
208-212.
MSC (1991):
Primary
MathSciNet review:
1260519
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [1]
- S.~Agmon, Spectral properties of Schr\"odinger operators and scattering theory, Ann. Scuola Norm. Sup.~Pisa Cl. Sci. (4) \textbf{2} (1975), 151--218. MR 397194
- [2]
- M.~Aizenman and S.~Molchanov, Localization at large disorders and at extreme energies\,\RM : An elementary derivation, Comm.~Math.~Phys. \textbf{157} (1993), 245--278. MR 1244867
- [3]
- E.~Balslev and J. M.~Combes, Spectral properties of many-body Schr\"odinger operators with dilation-analytic interactions, Comm.~Math.~Phys. \textbf{22} (1971), 280--294. MR 345552
- [4]
- R.~Carmona, Exponential localization in one-dimensional disordered systems, Duke Math.~J. \textbf{49} (1982), 191--213. MR 650377
- [5]
- R.~del Rio Castillo, A forbidden set for embedded eigenvalues, Proc.~Amer.~Math.~Soc. \textbf{121} (1994), 77--82. MR 1191867
- [6]
- R.~del Rio, N.~Makarov, and B.~Simon, Operators with singular continuous spectrum,~{\rm II}. Rank one operators, Comm.~Math.~Phys. MR 1298942
- [7]
- F.~Delyon, H.~Kunz, and B.~Souillard, One-dimensional wave equations in disordered media, J.~Phys.~ A \textbf{16} (1983), 25--42. MR 700179
- [8]
- F.~Delyon, Y.~L\'evy, and B.~Souillard, Anderson localization for multi-dimensional systems at large disorder or large energy, Comm.~Math.~Phys. \textbf{100} (1985), 463--470. MR 806247
- [9]
- J.~Fr\"ohlich and T.~Spencer, Absence of diffusion in the Anderson tight binding model for large disorder or low energy, Comm.~Math.~Phys. \textbf{88} (1983), 151--189. MR 696803
- [10]
- J.~Fr\"ohlich, T.~Spencer, and P.~Wittwer, Localization for a class of one dimensional quasi-periodic Schr\"odinger operators, Comm.~Math.~Phys. \textbf{132} (1990), 5--25. MR 1069198
- [11]
- I.~Goldsheid, Asymptotics of the product of random matrices depending on a parameter, Soviet Math.~Dokl. \textbf{16} (1975), 1375--1379. MR
- [12]
- I.~Goldsheid, S.~Molchanov, and L.~Pastur, A pure point spectrum of the stochastic one-dimensional Schr\"odinger equation, Funct.~Anal.~ Appl. \textbf{11} (1977), 1--10. MR 470515
- [13]
- A.~Gordon, On exceptional value of the boundary phase for the Schr\"odinger equation of a half-line, Russian Math.~Surveys \textbf{47} (1992), 260--261. MR
- [14]
- A.~Gordon, Pure point spectrum under \RM 1-parameter perturbations and instability of Anderson localization, Comm.~Math.~Phys. MR 1291242
- [15]
- P.~Halmos, In general a measure preserving transformation is mixing, Ann.~Math. \textbf{45} (1944), 786--792. MR 11173
- [16]
- S.~Jitomirskaya, Anderson localization for the almost Mathieu equation\,\RM : A nonperturbative proof, Comm.~Math.~Phys. MR 1298941
- [17]
- T.~Kato, Perturbation theory for linear operators (2nd, ed.), Springer-Verlag, Berlin, Heidelberg, and New York, 1980. MR
- [18]
- S.~Kotani and B.~Simon, Localization in general one-dimensional random systems, {\rm II}.~Continuum Schr\"odinger operators, Comm.~Math.~Phys. \textbf{112} (1987), 103--119. MR 904140
- [19]
- P.~Perry, I.~Sigal, and B.~Simon, Spectral analysis of $N$-body Schr\"odinger operators, Ann. of Math. (2) \textbf{114} (1981), 519-567. MR 634428
- [20]
- M.~Reed and B.~Simon, Methods of modern mathematical physics, {\rm IV}.~Analysis of operators, Academic Press, London, 1978. MR 493421
- [21]
- V.~Rohlin, A {\rm ``}general{\rm ''} measure-preserving transformation is not mixing, Dokl.~Akad.~Nauk SSSR (N.S.) \textbf{60} (1948), 349--351. MR 24503
- [22]
- B.~Simon, Operators with singular continuous spectrum, \RM I.~General operators, Ann. of Math. MR
- [23]
- B.~Simon and S.~Jitomirskaya, Operators with singular continuous spectrum, {\rm III}.~Almost periodic Schr\"odinger operators, Comm.~Math.~Phys. MR
- [24]
- B.~Simon and T.~Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Comm.~Pure Appl.~Math. \textbf{39} (1986), 75--90. MR 820340
- [25]
- Ya.~Sinai, Anderson localization for one-dimensional difference Schr\"odinger operator with quasi-periodic potential, J.~Stat.~Phys. \textbf{46} (1987), 861--909. MR 893122
- [26]
- J.~von Neumann, \emph{Charakterisierung des Spektrums eines Integraloperators}, Hermann, Paris, 1935. MR
- [27]
- H.~Weyl, \"Uber beschr\"ankte quadratische Formen, deren Differenz vollstetig ist, Rend.~Circ. Mat.~Palermo \textbf{27} (1909), 373--392. MR
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1991):
Retrieve articles in all Journals with MSC
(1991):
Additional Information:
DOI:
10.1090/S0273-0979-1994-00518-X
PII:
S 0273-0979(1994)00518-X
|
