PANJARADAGI CHEKLI SONDAGI ZARRACHALAR SISTEMALARI MODELLARIGA MOS SHREDINGER OPERATORLARINING MUHIM VA DISKRET SPEKTRLARI ILMIY YO'NALISHI BO‘YICHA YETAKCHI MUTAXASSIS

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BOG'LANISH

YUTUQLAR, MUKOFOTLAR

ilmiy maqollarining 62 tasi SCOPUS va Web of Sciencs bazalariga kiritilgan, h-index - 16.

LAQAYEV SAIDAHMAT NORJIGITOVICH

Fizika-matematika fanlari doktori, professor, akademik Matematik fizika va funksional analiz kafedrasi mudiri

Ilmiy tadqiqot yo‘nalishi:

Panjaradagi ko‘p zarrachali sistemaga mos Shredinger operatorlarining qat’iy matematik nazaryasini yaratish.

Ilmiy tadqiqotlarining asosiy natijalari:

Chiziqli operatorlarning spektral nazariyasi va matematik fizikaga umumlashgan Fridrixs modeli deb ataluvchi chiziqli operatorlar sinfini kiritdi va bu model hamda ikki va uch zarrachali sistemalar bog‘langan holatlari va rezonanslarini o‘rganishga Fredgolm determinantini qo‘llash kabi yangi usulni ishlab chiqdi. Pajaradagi ikki zarrachali sistemaga mos effektiv bir zarrachali Shredinger operatori uchun sistema kvaziimpulsiga bog‘lik bo‘lgan yangi bo‘sag‘a effekti (hodisasi) aniqlandi va bu hodisa keng sinf zarrachalar sistemalari uchun isbotlandi. Uch o‘lchamli panjaradagi uchta bir xil zarrachali sistema uchun Efimov effekti (hodisasi) mavjudligini isbotladi va Efimov effekti mavjud bo‘ladigan sistema kvaziimpulslari sirtini ajratdi. Uch o‘lchamli panjarada uchta ixtiyoriy zarrachalar sistemasi uchun uzluksiz holda uchramaydigan, ammo Efimov effektiga o‘xshash yangi effektni (hodisani) topdi. Uch o‘lchamli panjaradagi uchta tortishuvchi zarrachalar sistemalari uchun Efimov effekti uch zarrachali sistema kvaziimpulsining faqat nol qiymatida mavjud bo‘lishi kabi bo‘sag‘a effekti ochildi. Bir va ikki o‘lchamli panjaradagi o‘zaro kontakt tortishuvchi uch zarrachali sistemalar uchun bog‘langan holatlarning mavjud bo‘lishini ko‘rsatdi (bu natija uzluksiz holda hozirgacha ham isbotlanmagan). Yangi L-juft va L-toq funksiyalar tushunchalari kiritildi va ulardan panjaradagi ikki va uch zarrachali sistemalarni o‘rganishda keng foydalanilmoqda.

Asosiy ilmiy nashrlari:

1.Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions, Journal of Physics A: Mathematical and Theoretical 56 (31), 315202, 2023.
2.The Number and Location of Eigenvalues for the Two-Particle Schredinger Operators on Lattices, Complex Analysis and Operator Theory 17 (6), 92 2023.
3.On the Number and Locations of Eigenvalues of the Discrete Schredinger Operator on a Lattice, Lobachevskii Journal of Mathematics 44 (3), 1091-1099, 2023.
4.On the spectrum of Schredinger-type operators on two-dimensional lattices, Journal of Mathematical Analysis and Applications 2022. V. 514. N2. 126363.
5.On the Existence of Bound States of a System of Two Fermions on the Two-Dimensional Cubic Lattice, Lobachevskii Journal of Mathematics 44 (4), 1241-1250, 2023.
6.The Essential Spectrum of a Three Particle Schredinger Operator on Lattices, Lobachevskii Journal of Mathematics 44 (3), 1176-1187, 2023.
7.On the number and location of eigenvalues of the two particle Schredinger operator on a lattice. Lobachevskii Journal of Mathematics, 2022, Vol.42, No. 12, pp.135-145.
8.The Number and Location of Eigenvalues of the Two Particle Discrete Schredinger Operators. Lobachevskii Journal of Mathematics, 2022, Vol. 43, No. 11, pp. 47-58.
9.On the discrete spectra of the Schrodinger-type operators on one-dimensional lattices, Lobachevskii Journal of Mathematics, 2022, Vol.43, No. 3, pp.1523-1536.
10.Convergent Expansions of Eigenvalues of the Generalized Friedrichs Model with a Rank-One Perturbation, Complex Analysis and Operator Theory (2021) 15:121.
11.Bose-Hubbard model with on-site and nearest-neighbor interactions; exactly solvable case, Journal of Physics A: Mathematical and Theoretical. 54, (2021), 245201, (22pp).
12.Bound states of Schredinger-type operators on one and two dimensional lattices; Journal of Mathematical Analysis and Applications, 2021. 503, 125280.
The exact number of eigenvalues of the discrete Schrodinger operators in one-dimensional case; Lobachevskii Journal Of Mathematics, 2021.