S. Kholmatov

activity

20162022

collaborators

8 papers

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-ph2021

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

Saidakhmat Lakaev, Shokhrukh Kholmatov, Shakhobiddin Khamidov

We study the discrete spectrum of the two-particle Schrödinger operator $H^_{μ λ} (K),$ $K \in T^{2},$ associated to the Bose-Hubbard Hamiltonian $H^_{μ λ}$ of…

math-ph2020

Bound states of discrete Schrödinger operators on one and two dimensional lattices

Shokhrukh Kholmatov, Saidakhmat Lakaev, Firdavs Almuratov

We study the spectral properties of discrete Schrödinger operator $H_{μ} = H_{0} + μ V, μ \geq 0,$ associated to a one-particle system in $d$ -dimensiona…

math.AP2020

Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities

Giovanni Bellettini, Antonin Chambolle, Shokhrukh Yu. Kholmatov

Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global $\frac{1}{n + 1}$ -Hölder continuous in time mean curvature flow with mobilities of a…

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

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…