### Abstract

Chapter 2 prepares the ground for the analysis of interacting particle systems carried out in Part II. The authors introduce here the principal technical tools of the single-particle multi-scale analysis (MSA), developed over the last thirty years by the mathematical community. The analytical tools of the so-called variable-energy MSA, developed in late 1980s, are streamlined and complemented by a simpler, fixed-energy approach. A simple and comprehensive derivation of the spectral and strong dynamical localization from the fixed-energy MSA, suitable for adaptations to interacting systems, is presented for the first time in mathematical literature.

Original language | English (US) |
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Title of host publication | Progress in Mathematical Physics |

Publisher | Birkhauser Boston |

Pages | 27-133 |

Number of pages | 107 |

DOIs | |

State | Published - Jan 1 2014 |

### Publication series

Name | Progress in Mathematical Physics |
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Volume | 65 |

ISSN (Print) | 1544-9998 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics

### Cite this

*Progress in Mathematical Physics*(pp. 27-133). (Progress in Mathematical Physics; Vol. 65). Birkhauser Boston. https://doi.org/10.1007/978-1-4614-8226-0_2

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*Progress in Mathematical Physics.*Progress in Mathematical Physics, vol. 65, Birkhauser Boston, pp. 27-133. https://doi.org/10.1007/978-1-4614-8226-0_2

**Single-particle MSA techniques.** / Chulaevsky, Victor; Suhov, Yuri.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Single-particle MSA techniques

AU - Chulaevsky, Victor

AU - Suhov, Yuri

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Chapter 2 prepares the ground for the analysis of interacting particle systems carried out in Part II. The authors introduce here the principal technical tools of the single-particle multi-scale analysis (MSA), developed over the last thirty years by the mathematical community. The analytical tools of the so-called variable-energy MSA, developed in late 1980s, are streamlined and complemented by a simpler, fixed-energy approach. A simple and comprehensive derivation of the spectral and strong dynamical localization from the fixed-energy MSA, suitable for adaptations to interacting systems, is presented for the first time in mathematical literature.

AB - Chapter 2 prepares the ground for the analysis of interacting particle systems carried out in Part II. The authors introduce here the principal technical tools of the single-particle multi-scale analysis (MSA), developed over the last thirty years by the mathematical community. The analytical tools of the so-called variable-energy MSA, developed in late 1980s, are streamlined and complemented by a simpler, fixed-energy approach. A simple and comprehensive derivation of the spectral and strong dynamical localization from the fixed-energy MSA, suitable for adaptations to interacting systems, is presented for the first time in mathematical literature.

UR - http://www.scopus.com/inward/record.url?scp=85019195817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019195817&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-8226-0_2

DO - 10.1007/978-1-4614-8226-0_2

M3 - Chapter

AN - SCOPUS:85019195817

T3 - Progress in Mathematical Physics

SP - 27

EP - 133

BT - Progress in Mathematical Physics

PB - Birkhauser Boston

ER -