D Hundertmark R Killip S Nakamura P Stollmann Veselic, I
COMMUNICATIONS IN MATHEMATICAL PHYSICS 262(2) 489-503 2006年3月 [査読有り]
We study spectra of Schrodinger operators on R-d. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values mu(n) of the...
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 29(1-2) 111-132 2004年 [査読有り]
We give a simple new proof of the exponential decay estimate in the adiabatic theory. The idea is to combine the stationary scattering theory for time-dependent Hamiltonian with tunneling estimates in the energy space.
JOURNAL OF FUNCTIONAL ANALYSIS 205(1) 180-205 2003年12月 [査読有り]
We show that the Schrodinger propagator can be expanded in terms of resonances at energy levels at which a barrier separates the interaction region from infinity. The expansions hold for all times with errors small in the semi-classical parameter....
JOURNAL OF MATHEMATICAL PHYSICS 44(11) 4975-4980 2003年11月 [査読有り]
This short note is devoted to the proof of Lifshitz tails and a Wegner estimate, and thus, band edge localization, for the random hopping model. (C) 2003 American Institute of Physics.
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