Resonances for magnetic Stark Hamiltonians in two-dimensional case
Resonances for magnetic Stark Hamiltonians in two-dimensional case
复制标题
二维情况下磁斯塔克哈密顿量的共振
DOI：
10.1155/s1073792804141044
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发表时间：
2004
影响因子：
1
通讯作者：
V. Petkov
中科院分区：
文献类型：
--
作者：
M. Dimassi;V. Petkov
我们研究二维薛定谔算子 P1(B;β)=(Dx−By)2+Dy2+βx+V(x,y), B > 0, β > 0 在恒定磁场和电场下的共振。我们定义了 P 1 (B; β) 的共振以及与 P 1 (B; β) 和 P 0 (B; β) = P 1 (B; β) − V(x, y) 相关的谱位移函数 ψ(λ)，对 B 和 β 没有任何限制。对于强磁场 (B → ∞)，我们得到 ψ(λ) 导数的表示、tr(f(P1(B;β))−f(P0(B;β))) 的迹公式以及位于 {zε3/8:|ℜz−(2n−1)B|≤αB, Imz≥μImθ} 中的共振数量的上限，0 0 是独立于 B 和 n ε 的常数ℕ* = ℕ \ {0}。
We study the resonances of the two-dimensional Schrodinger operator P1(B;β)=(Dx−By)2+Dy2+βx+V(x,y), B > 0, β > 0, with constant magnetic and electric fields. We define the resonances of P 1 (B; β) and the spectral shift function ξ(λ) related to P 1 (B; β) and P 0 (B; β) = P 1 (B; β) − V(x, y) without any restriction on B and β. For strong magnetic fields (B → ∞) we obtain a representation of the derivative of ξ(λ), a trace formula for tr(f(P1(B;β))−f(P0(B;β))) and an upper bound for the number of the resonances lying in {z∈3/8:|ℜz−(2n−1)B|≤αB, Imz≥μImθ}, 0 0 is a constant independent of B and n ∈ ℕ* = ℕ \ {0}.