Khalkhuzhaev Akhmad Miyassarovich

Professor | Doctor of Physical and Mathematical Sciences, Professor

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Probability theory and Mathematical Statistics, Mathematics

 

 

He is a participant in the fundamental project No. FZ-20200929224 - “Important and discrete spectra of Schrödinger operators suitable for models of finite particle systems in a lattice” for the period 2022-2026. Under the leadership of A. Khalkhuzhaev, 2 master's, 22 master's and 43 master's theses were defended.
Currently, under his leadership, 1 candidate's dissertation is being prepared for defense, in addition, he supervises 3 basic doctoral students and 3 master's students.
A. Khalkhuzhaev published 2 teaching aids for students.

 

 

1991-1996 - Student of the Faculty of Mechanics and Mathematics of Samarkand State University
1996-1999 - Postgraduate student at Samarkand State University
1999-2003 - Junior researcher at the Samarkand branch of the Academy of Sciences of Uzbekistan
2003-2004 - Assistant at the Department of Mathematical Physics and Theory of Functions, Samarkand State University
2004-2007 - Doctoral student of the Samarkand branch of the Academy of Sciences of Uzbekistan
2007-2013 - Associate Professor of the Department of Mathematical Physics and Functional Analysis, Samarkand State University
2013-2016 - Head of the Department of Mathematical Physics and Functional Analysis, Samarkand State University
2016-2017 - Associate Professor of the Department of Mathematical Physics and Functional Analysis, Samarkand State University
2017-2019 - Head of the educational and methodological department of Samarkand State University
2019-2019 - Head of the Department of Probability Theory and Mathematical Statistics, Samarkand State University
2019-2020 - Director of the School of Exact and Natural Sciences of Samarkand State University
2019 - present - Professor, Department of Probability Theory and Mathematical Statistics, Samarkand State University

 

 

We consider the two-particle discrete Schrödinger operator hµ(k), k ∈ Td, corresponding to the Hamiltonian of a system with two fermions acting on neighboring sites in a multidimensional (d ≥ 3) lattice.
To the left of the critical spectrum, the values of the operator hµ(k) that have an eigenvalue or do not have an eigenvalue are highlighted; quasimomentum of the system k ∈ Td for some k
If ∗ε Td tends to a value, then the eigenvalue z (µ, k), µ >0, k ∈ Td, is determined by the asymptotic behavior of tending to the left edge of the critical spectrum.

 

 

"1. A.M. Khalkhuzhaev, M. Pardabaev, Asymptotics of eigenvalues of perturbed bilaplacian in the 1D lattice. Uzbek Mathematical Journal. - Tashkent, 2021. -№4. -P. 62-78.
2. J.I. Abdullaev, A.M. A.M. Khalkhuzhaev, L.S. Usmonov, Monotonicity of the eigenvalues of the two-particle Schrödinger operatoron a lattice. Nanosystems: Phys. Chem. Math.12:6 (2021), 657-663.
3. J.I. Abdullaev, A.M. A.M. Khalkhuzhaev, The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum, Journal of Physics: Conference Series, 2021, 2070(1), 012017.
4. Sh. Kholmatov, A.M. Khalkhuzhaev, M. Pardabaev, Expansion of eigenvalues of the perturbed discrete bilaplacian, Monatshefte für Mathematik, 2022. Vol. 197, -№ 4. -P. 607-633. (3.Scopus, IF= 1.127).
5. A.M. Khalkhuzhaev, J.I. Abdullaev, J.Kh. Boymurodov, The Number of Eigenvalues of the Three-Particle Schredinger Operator on Three Dimensional Lattice, Lobachevskii Journal of Mathematics, 2022, Vol. 43, №12, pp. 3486-3495.
6. J.I. Abdullaev, A.M. Khalkhuzhaev, K.D. Kuliev, The existence of eigenvalues of Schrodinger operator on three dimensional lattice, Methods of Functional Analysis and Topology, Vol. 28 (2022), №3, pp. 189–208.
7. KhalkhuzhaevA.M., Khujamiyorov I.A. On the discrete spectrum of the Schrödinger operator using the 2+1 fermionic trimer on the lattice. Nanosystems: Phys. Chem. Math. 2023. Vol. 14 №5 pp. 518-529.
8. J. I. Abdullaev, A. M. Khalkhuzhaev and I. A. Khujamiyorov Existence Condition for the Eigenvalue of a Three-Particle Schrödinger Operator on a Lattice. Russian Mathematics, 2023, Vol. 67, No. 2, pp. 1–22.
9. Zh. I. Abdullaev, J. Kh. Boymurodov, A. M. Khalkhuzhaev, “On the Existence of Eigenvalues of the Three-Particle Discrete Schrödinger Operator”, Math. Notes, 114:5 (2023), 645–658
10.Zh. I. Abdullaev, A. M. Khalkhuzhaev, I. A. Khujamiyorov, “Existence condition of an eigenvalue of the three particle Schrödinger operator on a lattice”, Russian Math. (Iz. VUZ), 67:2 (2023), 1–22
11. Ahmad Khalkhuzhaev, Shakhobiddin Khamidov, Habibullo Mahmudov On the existence of eigenvalues of the one particle discrete Schrödinger operators. AIP Conf. Proc.3004, 020007 (2024) https://doi.org/10.1063/5.0200550

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