We give a semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity and obtain a general family of hypoelliptic, but not analytic hypoelliptic operators.
In this article, we prove the finiteness of the number of eigenvalues for a class of Schrödinger operators H = −∆ + V (x) with a complex-valued potential V (x) on R n , n ≥ 2. If ℑV is sufficiently small, ℑV ≤ 0 and ℑV = 0, we show that N (V) = N (ℜV) + k, where k is the multiplicity of the zero resonance of the selfadjoint operator −∆+ℜV and N (W) the… (More)
Recent theoretical and experimental findings suggest the long-known but not well understood low temperature resistance plateau of SmB6 may originate from protected surface states arising from a topologically non-trivial bulk band structure having strong Kondo hybridization. Yet others have ascribed this feature to impurities, vacancies, and surface… (More)
For a class of dissipative Schrödinger operators H = −∆ + V (x) with a complex-valued potential V = V 1 −iV 2 with V 2 ≥ 0 and |V (x)| = O(|x| −2) as |x| tends to infinity, we prove that the complex eigenvalues of H can not accumulate to zero. In the perturbation regime where V 2 is sufficiently small, we show under some conditions that N (V) = N (V 1) + k,… (More)
In this paper, we study the inverse scattering related to channel scattering operator S in many-body problems. If the incoming and outgoing channels are associated with a same, but arbitary cluster decomposition, a, of the N-particle system, we prove that all eeective interactions between the mass-centers of the clusters in a can be recovered from the high… (More)