S. Kholmatov

activity

20142025

most citedBose-Hubbard models with on-site and nearest-neighbor interactions: Exactly solvable case

28 citations · 41 across the 17 of their papers we have counts for

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4 papers · 1 filter

math.SP2025

Bound states of 2+1 fermionic trimers on lattice at strong couplings

Janikul Abdullaev, Ahmad Khalkhuzhaev, Shokhrukh Yu. Kholmatov

In this paper, we investigate the bound states of $2 + 1$ fermionic trimers on a three-dimensional lattice at strong coupling. Specifically, we analyze the discrete spectrum of the a…

math.SP2022

On the spectrum of Schrödinger-type operators on two dimensional lattices

Shokhrukh Yu. Kholmatov, Saidakhmat N. Lakaev, Firdavsjon M. Almuratov

We consider a family $H_{a, b} (μ) = H_{0} + μ V_{a, b} μ > 0,$ of Schrödinger-type operators on the two dimensional lattice $Z^{2},$ where $\wideha…

math.SP2019

Expansion of eigenvalues of rank-one perturbations of the discrete bilaplacian

Ahmad Khalkhuzhaev, Shokhrukh Yu. Kholmatov, Mardon Pardabaev

We consider the family $h^_{μ} := Δ^Δ^- μ v^,$ $μ \in R,$ of discrete Schrödinger-type operators in $d$ -dimensional lattice $Z^{d}$ , where…

math.SP2019★ 1 cited

Asymptotics of eigenvalues of the zero-range perturbation of the discrete bilaplacian

Shokhrukh Yu. Kholmatov, Mardon Pardabaev

We consider the family $h^_{μ} := Δ^Δ^- μ v^, μ \in R,$ of discrete Schrödinger-type operators in one-dimensional lattice $\m…