From Classical to Semiclassical Non-trapping Behaviour: a New Proof
نویسنده
چکیده
For the semiclassical Schrr odinger operator with smooth long-range potential, it is well known that the boundary values of the resolvent at non-trapping energies exist and are bounded by O(h ?1) (h being the semiclassical parameter). We present here a new proof of this result, which avoids the semiclassical Mourre theory and makes use of semiclassical measures.
منابع مشابه
Semiclassical Estimates in Asymptotically Euclidean Scattering
The purpose of this note is to obtain semiclassical resolvent estimates for long range perturbations of the Laplacian on asymptotically Euclidean manifolds. For an estimate which is uniform in the Planck constant h we need to assume that the energy level is non-trapping. In the high energy limit (that is, when we consider ∆ − λ, as λ → ∞, which is equivalent to h∆ − 1, h → 0), this corresponds ...
متن کاملar X iv : m at h / 99 10 09 8 v 1 [ m at h . A P ] 1 9 O ct 1 99 9 SEMICLASSICAL ESTIMATES IN ASYMPTOTICALLY EUCLIDEAN SCATTERING
The purpose of this note is to obtain semiclassical resolvent estimates for long range perturbations of the Laplacian on asymptotically Euclidean manifolds. For an estimate which is uniform in the Planck constant h we need to assume that the energy level is non-trapping. In the high energy limit (that is, when we consider ∆ − λ, as λ → ∞, which is equivalent to h∆ − 1, h → 0), this corresponds ...
متن کاملA new security proof for FMNV continuous non-malleable encoding scheme
A non-malleable code is a variant of an encoding scheme which is resilient to tampering attacks. The main idea behind non-malleable coding is that the adversary should not be able to obtain any valuable information about the message. Non-malleable codes are used in tamper-resilient cryptography and protecting memories against tampering attacks. Many different types of non-malleability have alre...
متن کاملSemiclassical Analysis for Spectral Shift Functions in Magnetic Scattering by Two Solenoidal Fields
We study the semiclassical asymptotic behavior of the spectral shift function and of its derivative in magnetic scattering by two solenoidal fields in two dimensions under the assumption that the total magnetic flux vanishes. The system has a trajectory oscillating between the centers of two solenoidal fields. The emphasis is placed on analysing how the trapping effect is reflected in the semic...
متن کاملNon-trapping Estimates near Normally Hyperbolic Trapping
In this paper we prove semiclassical resolvent estimates for operators with normally hyperbolic trapping which are lossless relative to nontrapping estimates but take place in weaker function spaces. In particular, we obtain non-trapping estimates in standard L2 spaces for the resolvent sandwiched between operators which localize away from the trapped set Γ in a rather weak sense, namely whose ...
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 2002