ar X iv : m at h - ph / 0 61 10 44 v 1 1 8 N ov 2 00 6 The Schrödinger operator in Newtonian space - time ∗

ar X iv : m at h - ph / 0 20 70 25 v 2 1 4 N ov 2 00 2 Bound states due to a strong δ interaction supported by a curved surface

We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion...

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h - ph / 0 30 30 72 v 1 3 1 M ar 2 00 3 Eigenvalue asymptotics for the Schrödinger operator with a δ - interaction on a punctured surface

Given n ≥ 2, we put r = min{ i ∈ N; i > n/2 }. Let Σ be a compact, Cr-smooth surface in Rn which contains the origin. Let further {Sǫ}0≤ǫ<η be a family of measurable subsets of Σ such that supx∈Sǫ |x| = O(ǫ) as ǫ → 0. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator −∆−βδ(·−Σ\Sǫ) in L2(Rn), where β is a positive constant, as ǫ → 0. An analogous result is g...

ar X iv : m at h - ph / 0 31 10 29 v 1 2 0 N ov 2 00 3 Group theoretical approach to the intertwined Hamiltonians

We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relati...

ar X iv : 1 61 1 . 00 87 9 v 1 [ m at h - ph ] 3 N ov 2 01 6 Stable laws for chaotic billiards with cusps at flat points ∗ PAUL

We consider billiards with a single cusp where the walls meeting at the vertex of the cusp have zero one-sided curvature, thus forming a flat point at the vertex. For Hölder continuous observables, we show that properly normalized Birkoff sums, with respect to the billiard map, converge in law to a totally skewed α-stable law.