NDLI: Wegner-type Bounds for a Two-particle Lattice Model with a Generic “Rough” Quasi-periodic Potential

Content Provider	Springer Nature Link
Author	Gaume, Martin
Copyright Year	2010
Abstract	In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice ℤ$^{d}$, d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodic and depending on auxiliary parameters. Such parametric families of ergodic deterministic potentials (“grands ensembles”) have been introduced earlier in Chulaevsky (2007), in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound holds true for a class of quasi-periodic grands ensembles. Using the approach proposed in Chulaevsky and Suhov (Commun Math Phys 283(2):479–489, 2008), we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random short-range interaction.
Ending Page	217
Page Count	13
Starting Page	205
File Format	PDF
ISSN	13850172
e-ISSN	15729656
Journal	Mathematical Physics, Analysis and Geometry
Issue Number	3
Volume Number	13
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-06-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs Theoretical, Mathematical and Computational Physics Quasi-periodic Geometry Two-particle Disordered systems (random Ising models, random SchrÃ¶dinger operators, etc.) Selfadjoint operator theory in quantum theory, including spectral analysis Random operators Analysis Schrödinger operator Wegner bounds Group Theory and Generalizations Applications of Mathematics Applications in the physical sciences
Content Type	Text
Resource Type	Article
Subject	Mathematical Physics Geometry and Topology

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