0 M ay 2 00 7 On the dense point and absolutely continuous spectrum for Hamiltonians with concentric δ shells
نویسنده
چکیده
Abstract. We consider Schrödinger operator in dimension d ≥ 2 with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum covers a halfline determined by the appropriate one-dimensional comparison operator; it is dense pure point in the gaps of the latter. If the interaction is radially periodic, there are absolutely continuous bands; in contrast to the regular case the measure of the p.p. segments does not vanish in the high-energy limit.
منابع مشابه
Interlaced Dense Point and Absolutely Continuous Spectra for Hamiltonians with Concentric-shell Singular Interactions
We analyze the spectrum of the generalized Schrödinger operator in L2(Rν), ν ≥ 2, with a general local, rotationally invariant singular interaction supported by an infinite family of concentric, equidistantly spaced spheres. It is shown that the essential spectrum consists of interlaced segments of the dense point and absolutely continuous character, and that the relation of their lengths at hi...
متن کامل0 M ay 2 00 6 The L p boundedness of wave operators for Schrödinger operators with threshold singularities II . Even dimensional case
Let H = −∆ + V (x) be a Schrödinger operator on R, m ≥ 1, with real potential V (x) such that |V (x)| ≤ C〈x〉, 〈x〉 = (1+ |x|2) 1 2 , for some δ > 2. Then, H with domain D(H) = H(R), the Sobolev space of order 2, is selfadjoint in the Hilbert space H = L(R) and C 0 (R) is a core. The spectrum σ(H) ofH consists of absolutely continuous part [0,∞) and a finite number of non-positive eigenvalues {λj...
متن کاملAbsolutely continuous spectrum and spectral transition for some continuous random operators
In this paper we consider two classes of random Hamiltonians on L 2(Rd) one that imitates the lattice case and the other a Schrödinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also know the existence of dense pure point spectrum for some disorder thus exhibiting spectral transition valid for the Bethe lattice and expected for th...
متن کاملar X iv : 0 90 5 . 09 74 v 1 [ m at h - ph ] 7 M ay 2 00 9 Symmetries and resonance sets for δ ′ - interactions July 20 , 2009
The symmetry properties of the family of δ ′-interactions with a resonant non-zero transparency resulting in non-separated states are discussed. It is shown that the connection matrix for these physically motivated interactions and the corresponding family of self-adjoint extensions can be constructed in a self-consistent way if the product δ ′ (x)ψ(x), where ψ(x) is a discontinuous wavefunctio...
متن کاملar X iv : 0 80 3 . 31 77 v 2 [ m at h . SP ] 1 5 M ay 2 00 8 LOCAL SPECTRAL PROPERTIES OF REFLECTIONLESS JACOBI , CMV , AND SCHRÖDINGER OPERATORS
We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008