Ionization of Coulomb Systems in $${mathbb{R}^3}$$ by Time Periodic Forcings of Arbitrary Size
Ionization of Coulomb Systems in $${mathbb{R}^3}$$ by Time Periodic Forcings of Arbitrary Size
复制标题
$${mathbb{R}^3}$$ 中任意大小的时间周期强迫的库仑系统电离
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发表时间：
2010
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影响因子：
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通讯作者：
S. Tanveer
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作者：
O. Costin;J. Lebowitz;S. Tanveer
我们分析了一个库仑系统在空间紧支撑时间周期电位V(t, x) = V（t + 2π/ω, x）作用下解的长时间行为（$${ipsi_t=(-Delta-b/r+V(t,x))psi}$$, $${xinmathbb{R}^3}$$, r = |x|）。我们证明，对于任何形式为$${2Omega(r) sin (omega t- heta)}$$的V(t, x)，其支持Ω(r)非零，不存在Floquet束缚态。这意味着系统电离，即$${P(t, K) = int_K|psi(t,x)|^2dx o 0}$$为t→∞对于任何紧集$${Ksubsetmathbb{R}^3}$$。更进一步，如果初始状态是紧支撑且只有有限多个球谐模态，则P（t， K）在t→∞时像$${t^{-5/3}}$$一样衰减。为了证明这些命题，我们对无穷常微分方程组建立了一个严格的WKB理论。
We analyze the long time behavior of solutions of the Schrödinger equation $${ipsi_t=(-Delta-b/r+V(t,x))psi}$$, $${xinmathbb{R}^3}$$, r = |x|, describing a Coulomb system subjected to a spatially compactly supported time periodic potential V(t, x) = V(t + 2π/ω, x) with zero time average.We show that, for any V(t, x) of the form $${2Omega(r) sin (omega t- heta)}$$, with Ω(r) nonzero on its support, Floquet bound states do not exist. This implies that the system ionizes, i.e. $${P(t, K) = int_K|psi(t,x)|^2dx o 0}$$ as t → ∞ for any compact set $${Ksubsetmathbb{R}^3}$$. Furthermore, if the initial state is compactly supported and has only finitely many spherical harmonic modes, then P(t, K) decays like $${t^{-5/3}}$$ as t → ∞.To prove these statements, we develop a rigorous WKB theory for infinite systems of ordinary differential equations.