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| Lang R. — Spectral Theory of Random Schrodinger Operators: A Genetic Introduction |
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| Предметный указатель |
And generalized Floquet exponent 84 95
Bloch waves 9
Brownian motion 22ff 32ff 43ff 64ff
Brownian motion, large deviations for Brownian motion 23 34 64ff
Brownian motion, survival of Brownian motion 23 24 32ff
Cauchy — Riemann differential equations 83 109
Complex plane 78 82 86 90f 106 114
Conserved quantities 10 27 74 111 117
Convexity 61 62 68
Crystal 2
Crystal, quasi-crystal 117
Dirichlet integral 48ff 68
Discriminant 13 14
Disorder 2 21 30 31 37
Disorder, parameter of 30
Divergence form 81 97 102
Eigenfunction, eigenvalue 1 5 7 27 28 39
Eigenfunction, lowest eigenvalue 8 20 32 34 35 49 50 66 68 69
Eigenvalue and positivity of the Ljapunov exponent 27 28 39
entropy 45 49 55ff 113 114
Ergodic theorem, multiplicative 27
Ergodic theorem, subadditive 28 106
Ergodicity 5
Extended states 2 21 31
Floquet, exponent 11 15 82
Floquet, generalized Floquet exponent 74 95ff 101 113 114
Floquet, solution 11
Floquet, theory 80 86
Gibbs, measure 61 65
Gibbs, variational principle 61 68 114
Green's function 13 78
Green's function and generalized Floquet exponent 100 101
Green's function and spectral measure 79
Green's function and Weyl solutions 84
Hadamard's factorization theorem 86 98ff
Herglotz function 84 112
Herglotz function, holomorphic 81 83 84 91 99f 105f 109 112
Integrated density of states 7 27ff 32 35 73
Integrated density of states and Brownian motion 23ff 73
Integrated density of states and Ljapunov exponent 101
Integrated density of states and spectral measure 73
Integrated density of states, inverse problem 110
Korteweg de Vries equation 116
Large deviations for Brownian motion 23 34 47 64ff
Legendre transform 62 68
Lifschitz tails 4 22 32
Limit point case 91
Ljapunov exponent 26ff 37ff 77 82 101
| localization 2 7 19ff 28 40 42
Localization length 21
Localization length, multidimensional localization 19ff 30f
Mobility edge 21
Occupation number 48 49 55ff
Penrose tiling 117
Periodic 9ff
Phase 11 15 16 74 82
Poisson point process 2 6 20 22 33f
Potential of Poisson type 2 6ff 20ff 32
Potential, almost periodic 18 41 114
Potential, deterministic 37 110
Potential, ergodic 5 25 37 71ff
Potential, non-deterministic 37
Potential, non-periodic 18 36 78
Potential, one-dimensional 9ff 36ff 71ff
Random 1
Rayleigh — Ritz principle 50 68 114
Resolution of the identity 71
Resonance 21 40 42 47
Riccati equation 81
Rotation number 76 115
Rotation number and generalized Floquet exponent 82 101
Schrodinger operator 1
Schrodinger operator, one-dimensional 36ff 71ff
Shift 5
Singularly continuous 36 37 41f 72
Singularly continuous and stability lOff 26f 39f
Singularly continuous gaps in the spectrum 9 15 16 26
Spectral measure 72
Spectral measure and Green's function 78 79
Spectral measure and integrated density of states 73
Spectrum, absolutely continuous 36 38 41f 72
Spectrum, Cantor like 18
Spectrum, continuous 1 5 27 36 72
Stability, instability lOff 19 26f 39f 113
Statistical mechanics 21 31 49 61f 114 116
Stieltjes transform 78
Sturm's oscillation theory 77 86f
Thouless formula 101
Titchmarsh - Weyl functions 81ff 85 114
Variational Principle 45 50 61 68 114
Vibrating string 7 98 115
Weak topology 51 57
Weyl's theory of singular Sturm - Liouville operators 80f 88ff
Wiener, measure 23
Wiener, sausage 44ff
Wronski determinant 10 12 26ff 74 84 95
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