Resonances as viscosity limits for black box perturbations

作为粘度极限的散射共振

Scattering resonances as viscosity limits

利用复标度方法，我们证明了$ - Δ+ V $的散射共振，$ V \in L^\infty_{\rm{c}} ( \mathbb R^n ) $，是$ - Δ+ V - i εx^2 $作为$ ε\to 0+ $的本征值的极限.这证明了计算化学中提出的方法是正确的，并反映了其他环境中共振的一般原理。

Resonances as Viscosity Limits for Exterior Dilation Analytic Potentials

For exterior dilation analytic potential, $V$, we use the method of complex scaling to show that the resonances of $ - Δ+ V $, in a conic neighbourhood of the real axis, are limits of eigenvalues of $ - Δ+ V - i εx^2 $ as $ ε\to 0+ $, if $V$ can be analytically extended from $\mathbb{R}^n$ to a truncated cone in $\mathbb{C}^n$.

Resonances as Viscosity Limits for Exponentially Decaying Potentials

We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to the case of exponentially decaying potentials. That means that the eigenvalues of $-Δ+ V - iεx^2$, $|V(x)|\leq C e^{-2γ|x|}$ converge, as $ ε\to 0+ $, to the poles of the meromorphic continuation of $ ( -Δ+ V -λ^2 )^{-1} $ uniformly on compact subsets of $\textrm{Re}\,λ>0$, $\textrm{Im}\,λ>-γ$, $\argλ> -π/8$.

Wigner-von Neumann型哈密顿量的共振与粘性极限

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

该研究定义了Wigner-von Neumann型哈密顿量的共振，并借助Zworski方法将其表征为带二次复吸收势的哈密顿量在粘性型极限下离散本征值的极限点。

盒子里的共鸣

Resonances In a Box

研究了量子力学中共振态的数值计算方法。我们严格证明，这种方法产生精确的近似共振能量和宽度的形状共振的半经典极限。

A Quantitative Vainberg Method for Black Box Scattering

We give a quantitative version of Vainberg's method relating pole free regions to propagation of singularities for black box scatterers. In particular, we show that there is a logarithmic resonance free region near the real axis of size $τ$ with polynomial bounds on the resolvent if and only if the wave propagator gains derivatives at rate $τ$. Next we show that if there exist singularities in the wave trace at times tending to infinity which smooth at rate $τ$, then there are resonances in logarithmic strips whose width is given by $τ$. As our main application of these results, we give sharp …