Threshold effects in a two-fermion system on an optical lattice

Аннотация

For a wide class of two-particle Schrödinger operators H(k) = H0(k) + V, k ∈ $$\mathbb{T}^d$$, corresponding to a two-fermion system on a d-dimensional cubic integer lattice (d ≥ 1), we prove that for any value k ∈ $$\mathbb{T}^d$$ of the quasimomentum, the discrete spectrum of H(k) below the lower threshold of the essential spectrum is a nonempty set if the following two conditions are satisfied. First, the two-particle operator H(0) corresponding to a zero quasimomentum has either an eigenvalue or a virtual level on the lower threshold of the essential spectrum. Second, the one-particle free (nonperturbed) Schrödinger operator in the coordinate representation generates a semigroup that preserves positivity.

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DOI

10.1134/s0040577920050074

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