RESOLVENT EXPANSION AND TIME DECAY OF THE WAVE FUNCTIONS FOR TWO-DIMENSIONAL MAGNETIC SCHRÖDINGER OPERATORS

Abstract. We consider two-dimensional Schrödinger operators H(B, V) given by equation (1.1) below. We prove that, under certain regularity and decay assumptions on B and V, the character of the expansion for the resolvent (H(B, V)−λ)−1 as λ → 0 is determined by the flux of the magnetic field B through R2. Subsequently, we derive the leading term of the asymptotic expansion of the unitary group e−itH(B,V) as t→ ∞ and show how the magnetic field improves its decay in t with respect to the decay of the unitary group e−itH(0,V). 1