Frédéric Klopp Michael Loss Shu Nakamura Günter Stolz
Duke Mathematical Journal 161(4) 2012年3月 [査読有り]
We prove spectral and dynamical localization for the multi-dimensional random
displacement model near the bottom of its spectrum by showing that the approach
through multiscale analysis is applicable. In particular, we show that a
previously known...
Frédéric Klopp Michael Loss Shu Nakamura Günter Stolz
Spectral Analysis of Quantum Hamiltonians: Spectral Days 2010 224 183-219 2012年1月 [査読有り][招待有り]
We give a detailed survey of results obtained in the most recent half-decade which led to a deeper understanding of the random displacement model, a model of a random Schrödinger operator which describes the quantum mechanics of an electron in a s...
Annales de l'Institut Fourier 62(3) 1091-1121 2012年 [査読有り]
We consider Schrödinger operators H on ℝ n with variable coefficients. Let H o = -1/2δ be the free Schrödinger operator and we suppose H is a "short-range" perturbation of H o. Then, under the nontrapping condition, we show that the time evolution...
Journal of the London Mathematical Society 81(3) 774-792 2010年6月 [査読有り]
We construct a time-dependent scattering theory for Schrödinger operators
on a manifold with asymptotically conic structure. We use the two-space
scattering theory formalism, and a reference operator on a space of the form
$R\times \partial ...
Let be the spacetime, where is a closed manifold
equipped with a Riemannian metric , and we consider a symmetric Klein-Gordon
type operator on , which is asymptotically converges to a...
Here we discuss a new simplified proof of the essential self-adjointness for
formally self-adjoint differential operators of real principal type, previously
proved by Vasy (2020) and Nakamura-Taira (2021). For simplicity, here we
discuss the secon...
We consider the quantum graph Hamiltonian on the square lattice in Euclidean
space, and we show that the spectrum of the Hamiltonian converges to the
corresponding Schrödinger operator on the Euclidean space in the continuum
limit, and that the ...
We propose a method of data quantization of finite discrete-time signals
which optimizes the error estimate of low frequency Haar coefficients. We also
discuss the error/noise bounds of this quantization in the Fourier space. Our
result shows one ...
We consider scattering matrix for Schr\"odinger-type operators on with<br />
perturbation as . We show that<br />
the scattering matrix (with time-independent modifiers) is a pseudodifferent...
人文科学研究科
理学部