arXiv subjects

Kentaro Kameoka

Publications and source records attributed to Kentaro Kameoka.

8 recordsLinked to original sources

arXiv2026

Semiclassical shape resonances for magnetic Stark Hamiltonians

We study shape resonances of two-dimensional magnetic Stark Hamiltonians in the semiclassical limit. The magnetic field is assumed to be constant and the scalar potential is a perturbation of a linear potential. Under the assumption that the scalar potential has potential wells, the existence of a one-to-one correspondence between shape resonances of the Hamiltonian and discrete eigenvalues of a certain reference operator is proved. This implies the Weyl law for the number of resonances and the asymptotic behavior of the real parts of resonances near the bottom of a potential well. Resonances are studied as complex eigenvalues of complex distorted Hamiltonians, which is defined by the complex translation outside a compact set.

math-ph↗

arXiv2024

Continuum limit of resonances for discrete Schrödinger operators

We consider complex resonances for discrete and continuous Schrödinger operators, and we show that the resonances of discrete models converge to resonances of continuous models in the continuum limit. The potential is supposed to be a sum of an exterior dilation analytic function and an exponentially decaying function, which may have local singularities. The proof employs a generalization of the norm resolvent convergence of discrete Schrödinger operators by Nakamura and Tadano (2021), combined with the complex distortion method in the Fourier space. Our results confirm that the complex resonances can be approximately computed using discrete Schrödinger operators. We also give a recipe for the construction of approximate discrete operators for Schrödinger operators with singular potentials.

math-ph↗

arXiv2024

Many-body Stark resonances by the complex absorbing potential method

The resonances of many-body Stark Hamiltonians are characterized by the complex absorbing potential method. Namely, the resonances are shown to be the limit points of complex discrete eigenvalues of many-body Stark Hamiltonians with quadratic complex potential when the coefficient of the complex potential tends to zero.

math-ph↗

arXiv2022

Semiclassical analysis and the Agmon-Finsler metric for discrete Schrödinger operators

The Agmon estimate for multi-dimensional discrete Schrödinger operators is studied with emphasis on the microlocal analysis on the torus. We first consider the semiclassical setting where semiclassical continuous Schrödinger operators are discretized with the mesh width proportional to the semiclassical parameter. Under this setting, the Agmon estimate for eigenfunctions is described by an Agmon metric, which is a Finsler metric rather than a Riemannian metric. Klein-Rosenberger (2008) proved this by a different argument in the case of a potential minimum. We also prove the Agmon estimate and the optimal anisotropic exponential decay of eigenfunctions for discrete Schrödinger operators in the non-semiclassical standard setting.

math.SP↗

arXiv2021

Complex absorbing potential method for Stark resonances

We characterize the resonances of Stark Hamiltonians by the complex absorbing potential method. Namely, we prove that the Stark resonances are the limit points of complex eigenvalues of the Stark Hamiltonian with a quadratic complex absorbing potential when the absorbing coefficient tends to zero. The proof employs the complex distortion outside a cone introduced in the previous work by the author. Potentials with local singularities such as the Coulomb potential are allowed as perturbations.

math-ph↗

arXiv2020

Semiclassical study of shape resonances in the Stark effect

Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent estimate is proved by the escape function method. The Weyl law and the resonance expansion of the propagator are proved in the shape resonance model. To prove the resonance expansion theorem, the functional pseudodifferential calculus in the Stark effect is established, which is also useful in the study of the spectral shift function.

math-ph↗

arXiv2020

Resonances and viscosity limit for the Wigner-von Neumann type Hamiltonian

The resonances for the Wigner-von Neumann type Hamiltonian are defined by the periodic complex distortion in the Fourier space. Also, following Zworski, we characterize resonances as the limit points of discrete eigenvalues of the Hamiltonian with a quadratic complex absorbing potential in the viscosity type limit.

math-ph↗

arXiv2019

Remarks on semiclassical wavefront set

The essential support of the symbol of a semiclassical pseudodifferentail operator is characterized by semiclassical wavefront sets of distributions. The proof employs a coherent state whose center in phase space is dependent on Planck's constant.

math.AP↗