Absolute continuity of the spectra of two-dimensional periodic magnetic Schrödinger and Dirac operators with potentials in Zygmund class (Q2773601)

The aim of the article is to prove absolute continuity of the spectrum of the Schrödinger operator NEWLINE\[NEWLINE (\mathbf D - \mathbf A (\mathbf x))^2 + V(\mathbf x),\quad \mathbf x \in\mathbb R^d, NEWLINE\]NEWLINE and the Dirac operator NEWLINE\[NEWLINE \sum_{j = 1}^d\bigl(D_j - A_j(\mathbf x)\bigr)\alpha_j + V_0(\mathbf x)\alpha_{d+1} + V(\mathbf x)\mathbf 1,\quad \mathbf x \in \mathbb R^d. NEWLINE\]NEWLINE Here \(\mathbf D = -i\nabla\), \(V_0(\mathbf x)\), \(V(\mathbf x)\) are the scalar electric potentials, \(\mathbf A (\mathbf x)\) is the vector magnetic potential, \(\alpha_j\), \(1 \leq j \leq d + 1\), are the Dirac matrices; \(V\) and \(\mathbf A(\mathbf x)\) are supposed to be periodic with respect to a lattice \(\Gamma\).NEWLINENEWLINENEWLINEThe main results of the article assert that, under certain conditions, the spectra of the Schrödinger and Dirac operators are absolutely continuous.