Existence of bound states of N-body problem in an optical lattice

2014/08/19 by Shokhrukh Yu. Kholmatov, Kholmatov, Shokhrukh, Zahriddin Muminov +1
Physics and Astronomy · #81Q10 #81Q15 #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Laser-Matter Interactions and Applications #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1408.4280

openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide sufficient conditions to have at least one N-particle bound state below the essential spectrum of a large class of N-particle discrete Schrödinger operators H(K), K∈ \mathbbT^d, d≥1, associated to the Hamiltonian of (not necessarily identical) N particles, moving on a lattice ℤ^d and interacting via short-range pair potentials. We also describe the essential spectrum of H(K).

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