Threshold analysis for a family of 2 × 2 operator matrices
https://doi.org/10.17586/2220-8054-2019-10-6-616-622
Аннотация
We consider a family of 2 × 2 operator matrices Aµ(k), k ∈ T3 := (−π, π]3, µ > 0, acting in the direct sum of zeroand one-particle subspaces of a Fock space. It is associated with the Hamiltonian of a system consisting of at most two particles on a three-dimensional lattice ℤ3, interacting via annihilation and creation operators. We find a set Λ := {k(1), ..., k(8)} ⊂ T3 and a critical value of the coupling constant µ to establish necessary and sufficient conditions for either z = 0 = min/ k∈T3 σess(Aµ(k)) ( or z = 27/2 = max/k∈T3 σess(Aµ(k)) is a threshold eigenvalue or a virtual level of Aµ(k(i)) for some k(i) ∈ Λ.
Ключевые слова
operator matrices,
Hamiltonian,
generalized Friedrichs model,
zeroand one-particle subspaces of a Fock space,
threshold eigenvalues,
virtual levels,
annihilation and creation operators
При поддержке: The authors thank the anonymous referee for reading the manuscript carefully and for making valuable suggestions
Об авторах
T. H. Rasulov
Bukhara State University
Узбекистан
Узбекистан
Е. В. Dilmurodov
Bukhara State University
Узбекистан
Узбекистан
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Рецензия
Для цитирования:
Rasulov T.H., Dilmurodov Е.В. Threshold analysis for a family of 2 × 2 operator matrices. Наносистемы: физика, химия, математика. 2019;10(6):616-622. https://doi.org/10.17586/2220-8054-2019-10-6-616-622
For citation:
Rasulov T.H., Dilmurodov E.B. Threshold analysis for a family of 2 × 2 operator matrices. Nanosystems: Physics, Chemistry, Mathematics. 2019;10(6):616-622. https://doi.org/10.17586/2220-8054-2019-10-6-616-622
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