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Discrete spectrum of a model operator in Fock space

“…Let E min and E max be the greatest lower and least upper bounds of the set σ ∩ −∞; max p∈T 3 m(p) . The following theorem [7], [8] describes the structure of the part of the essential spectrum of H located in (−∞; M w ].…”

“…We note that some spectral properties of the model operator H were studied in [6]- [8]. In particular, it was established (without proof) in [7] that the discrete spectrum to the left of the "three-particle" branch of the essential spectrum of the model operator H is finite. The present paper is devoted to completely proving this result in a more general case.…”

Spectrum of a Model Operator in the Perturbation Theory of the Essential Spectrum

“…In [2], a spin-bosonic Hamiltonian was considered that is analogous to the standard three-particle Hamiltonian, and the absolutely continuous spectrum and bound states were investigated. A certain model operator H 0 (a lattice analogue of the spin-bosonic Hamiltonian [2]) corresponding to the energy operator with a nonconserved bounded number of particles and acting in a subspace of the Fock space was considered in [3], [4]. Under some natural conditions on the parameters specifying this model operator, the position and structure of the essential spectrum were described, and the number of eigenvalues was found to be finite or infinity (Efimov's effect).…”

“…In this paper, we consider a certain model operator H = H(ϕ 1 , ϕ 2 ) (see (2)) as a noncompact perturbation of the operator H 0 = H(0, 0) considered in [3], [4]; it corresponds to the energy operator with a nonconserved bounded number of particles and acts in a subspace of the Fock space. We describe the positions and structure of the essential spectrum.…”

Описание Местоположения И Структуры Существенного Спектра Одного Модельного Оператора В Подпространстве Фоковского Пространства

“…В настоящей работе рассматривается модельный оператор, действующий в трехчастичном обрезанном подпространстве фермионного пространства Фока F a (L 2 (T 3 )) над L 2 (T 3 ) как некомпактное возмущение оператора H 0 = H(0, 0), рассмотренного в [9], [10], соответствующий оператору энергии с несохраняющимся ограниченным числом частиц, действующему в подпространстве фоковского пространства. Описываются "двухчастичные" и "трехчастичные" ветви существенного спектра, а также получен аналог уравнения Фаддеева для собственных векторов рассматриваемого оператора.…”