TY - JOUR

T1 - Multi-particle anderson localisation

T2 - Induction on the number of particles

AU - Chulaevsky, Victor

AU - Suhov, Yuri

N1 - Funding Information:
Acknowledgements VC thanks The Isaac Newton Institute (INI) and Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, for hospitality during visits in 2003, 2004, 2007 and 2008. YS thanks the Département de Mathématiques, Université de Reims for hospitality during visits in 2003 and 2006–2008, in particular, for a Visiting Professorship in the Spring of 2003. YS thanks IHES, Bures-sur-Yvette, and STP, Dublin Institute for Advanced Studies, for hospitality during visits in 2003–2007. YS thanks the Departments of Mathematics of Penn State University and of UC Davis, for hospitality during Visiting Professorships in the Spring of 2004, Fall of 2005 and Winter of 2008. YS thanks the Department of Physics, Princeton University and the Department of Mathematics of UC Irvine, for hospitality during visits in the Spring of 2008. YS acknowledges the support provided by the ESF Research Programme RDSES towards research trips in 2003–2006.

PY - 2009/5

Y1 - 2009/5

N2 - This paper is a follow-up of our recent papers Chulaevsky and Suhov (Commun Math Phys 283:479-489, 2008) and Chulaevsky and Suhov (Commun Math Phys in press, 2009) covering the two-particle Anderson model. Here we establish the phenomenon of Anderson localisation for a quantum N-particle system on a lattice Zd with short-range interaction and in presence of an IID external potential with sufficiently regular marginal cumulative distribution function (CDF). Our main method is an adaptation of the multi-scale analysis (MSA; cf. Fröhlich and Spencer, Commun Math Phys 88:151-184, 1983; Fröhlich et al., Commun Math Phys 101:21-46, 1985; von Dreifus and Klein, Commun Math Phys 124:285-299, 1989) to multi-particle systems, in combination with an induction on the number of particles, as was proposed in our earlier manuscript (Chulaevsky and Suhov 2007). Recently, Aizenman and Warzel (2008) proved spectral and dynamical localisation for N-particle lattice systems with a short-range interaction, using an extension of the Fractional-Moment Method (FMM) developed earlier for single-particle models in Aizenman and Molchanov (Commun Math Phys 157:245-278, 1993) and Aizenman et al. (Commun Math Phys 224:219-253, 2001) (see also references therein) which is also combined with an induction on the number of particles.

AB - This paper is a follow-up of our recent papers Chulaevsky and Suhov (Commun Math Phys 283:479-489, 2008) and Chulaevsky and Suhov (Commun Math Phys in press, 2009) covering the two-particle Anderson model. Here we establish the phenomenon of Anderson localisation for a quantum N-particle system on a lattice Zd with short-range interaction and in presence of an IID external potential with sufficiently regular marginal cumulative distribution function (CDF). Our main method is an adaptation of the multi-scale analysis (MSA; cf. Fröhlich and Spencer, Commun Math Phys 88:151-184, 1983; Fröhlich et al., Commun Math Phys 101:21-46, 1985; von Dreifus and Klein, Commun Math Phys 124:285-299, 1989) to multi-particle systems, in combination with an induction on the number of particles, as was proposed in our earlier manuscript (Chulaevsky and Suhov 2007). Recently, Aizenman and Warzel (2008) proved spectral and dynamical localisation for N-particle lattice systems with a short-range interaction, using an extension of the Fractional-Moment Method (FMM) developed earlier for single-particle models in Aizenman and Molchanov (Commun Math Phys 157:245-278, 1993) and Aizenman et al. (Commun Math Phys 224:219-253, 2001) (see also references therein) which is also combined with an induction on the number of particles.

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U2 - 10.1007/s11040-008-9055-6

DO - 10.1007/s11040-008-9055-6

M3 - Article

AN - SCOPUS:67349149120

VL - 12

SP - 117

EP - 139

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

SN - 1385-0172

IS - 2

ER -