References

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8 Index A Assumption A, 28 Assumption B, 28 Assumption C, 169 Assumption U, 143 C Carmona s argument, 155 center of localization, 123 Combes Thomas estimate, 62 combined multi-particle induction, 171 completely non-resonant (E-CNR) multiparticle cube, 177 completely non-resonant (E-CNR) singleparticle cube, 48 conditional Wegner bound, 156 D density of states, DoS, 50 diagonally monotone function, 45 distant n-particle cubes; 11nL-distant n-particle cubes, 198 double singularity for multi-particle systems (DS.N; n; m; p k ;L k ), 146 double singularity for multi-particle systems, modified.f DS:N;n;m;p0 ;L 0 /, 196 double singularity.ds:i;m;p k ;L k / for single-particle systems, 111 dynamical localization, 15, 18, 20, 41, 121, 148 E eigenfunction (EF) correlator, 41 eigenvalue concentration (EVC) bounds, 43 external random potential, 28 F finite range of interaction, 174 fixed-energy analysis, 33, 34 fixed-energy analysis, multi-particle, 176 Fractional moment method, FMM, 18 fully interactive (FI) cube, 174 G geometric resolvent equation, 55, 56 geometric resolvent inequality (GRI), 55 geometric resolvent inequality (GRI) for eigenfunctions, 57 I independent identically distributed (IID) potential, 27 integrated density of states (IDoS), 214, interaction, 139, 143, 174 J jump Markov process, 153 L lattice Schrödinger operator (LSO), 7 localization center, 123 M mass, 34 Minami bound, 52 Molchanov s path integral formula, 152 MPMSA induction: the inductive step, fixed energy, 185 V. Chulaevsky and Y. Suhov, Multi-scale Analysis for Random Quantum Systems with Interaction, Progress in Mathematical Physics 65, DOI / , Springer Science+Business Media New York

9 238 Index MPMSA induction: the inductive step, variable energy, 197 MPMSA induction: the initial step, fixed energy, 177 MPMSA induction: the initial step, variable energy, 196 multi-particle MSA (MPMSA), 137 Multi-scale analysis (MSA), 8 N non-partially singular cube,.m;i;k/-nonpartially singular (.m;i;k/-nps), 108 non-resonant (E-NR) multi-particle cube, 177 non-resonant (E-NR) single-particle cube, 48 non-singular (.E; m/-ns) multi-particle cube, 143 non-singular (.E; m/-ns) single-particle cube, 33 O one-volume Stollmann bound for multi-particle systems, 162 P pair of distant FI cubes, 182 pair of FI cubes, 175, 197 pair of multi-particle cubes (mixed), 197 pair of PI cubes, 197 partially interactive (PI) cube, 174 partially resonant (E-PR) multi-particle cube, 177 partially resonant (E-PR) single-particle cube, 48 partially singular cube,.m;i;k/-partially singular (.m;i;k/-ps), 108 Q quantum graphs, 5, 19, 226 R radial descent bounds, 102 resonant (E-R) single-particle cube, 48 resonant (E-R) multi-particle cube, 177 S separability of cubes, 144 singular (.E; m/-s) multi-particle cube, 143 singular (.E; m/-s) single-particle cube, 33 singularity for multi-particle systems (SS.N; E; m; p k ;L k ), 145 spectral localization, 18 Stollmann s bound, 47 Stollmann s lemma, 45 strong dynamical localization, 19 subharmonic (.l; q/-subharmonic), 75 T two-volume Stollmann bound for multi-particle systems, 163 V variable-energy analysis, 37 variable-energy analysis, multi-particle, 195 W weak separability of cubes, 167 Wegner s bound, 43, 156, 164