Т. А. Суслина "Homogenization of the periodic Schrödinger-type equations"

Mathematical and Theoretical Physics, dedicated to Ludwig Faddeev
28-31 мая 2024 года
In L_2 (R^d;C^n ), we consider a selfadjoint strongly elliptic second-order differential operator A_ε. It is assumed that the coefficients of A_ε are periodic and depend on x/ε, where ε .. 0 is a small parameter. We study the behavior of the operator exponential e^(-iA_ε τ) for small ε and τ∈ R. The results are applied to study the behavior of the solution of the Cauchy problem for the Schrödinger-type equation i∂_τ u_ε (x,τ) = (A_ε u_ε )(x,τ) with the initial data from a special class.