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- W2996581008 abstract "We consider a family of $2 times 2$ operator matrices ${mathcal A}_mu(k),$ $k in {Bbb T}^3:=(-pi, pi]^3,$ $mu>0$, acting in the direct sum of zero- and 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 ${Bbb Z}^3,$ interacting via annihilation and creation operators. We find a set $Lambda:={k^{(1)},...,k^{(8)}} subset {Bbb T}^3$ and a critical value of the coupling constant $mu$ to establish necessary and sufficient conditions for either $z=0=minlimits_{kin {Bbb T}^3} sigma_{rm ess}({mathcal A}_mu(k))$ ( or $z=27/2=maxlimits_{kin {Bbb T}^3} sigma_{rm ess}({mathcal A}_mu(k))$ is a threshold eigenvalue or a virtual level of ${mathcal A}_mu(k^{(i)})$ for some $k^{(i)} in Lambda.$" @default.
- W2996581008 created "2019-12-26" @default.
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- W2996581008 date "2019-12-20" @default.
- W2996581008 modified "2023-09-27" @default.
- W2996581008 title "Threshold analysis for a family of $2 times 2$ operator matrices" @default.
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