arXiv subjects

Zahriddin Muminov

Publications and source records attributed to Zahriddin Muminov.

2 recordsLinked to original sources

arXiv2018

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

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 $H(K),$ $K\in \mathbb{T}^d,$ $d\ge1,$ associated to the Hamiltonian of (not necessarily identical) $N$ particles, moving on a lattice $\mathbb{Z}^d$ and interacting via short-range pair potentials. We also describe the essential spectrum of $H(K).$

math-ph↗

arXiv2018

Threshold of discrete Schrödinger operators with delta potentials on $n$-dimensional lattice

Eigenvalue behaviors of Schrödinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$, and lower super-threshold resonance appeared for $n=1$.

math.SP↗