QUANTUM LORENTZ GAS - EFFECTIVE EQUATIONS AND SPECTRAL-ANALYSIS

We consider the quantum Lorentz gas (QLG) in the plane. We show that t he spectral properties of the quantum Lorentz gas can be obtained from the study of a homogeneous system of one-dimensional integral equatio ns. The qualitative spectral analysis is performed, and the spectrum i s shown to have a band structure. The wave functions in the complete c onfiguration space can be constructed in terms of the solutions of the obtained effective equations. We apply the obtained result to a simpl er Lorentz gas model including additional symmetry.