Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential
Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential
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具有维格纳-冯·诺依曼势的离散薛定谔算子的谱密度零点
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Simonov
中科院分区：
文献类型：
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作者：
S. Simonov
We consider a discrete Schrödinger operator $${mathcal{J}}$$ whose potential is the sum of a Wigner-von Neumann term $${frac{csin(2omega n+delta)}n}$$ and a summable term. The essential spectrum of the operator $${mathcal{J}}$$ is equal to the interval [−2, 2]. Inside this interval, there are two critical points $${pm2cosomega}$$ where eigenvalues may be situated. We prove that, generically, the spectral density of $${mathcal{J}}$$ has zeroes of the power $${frac{|c|}{2|sinomega|}}$$ at these points.
We consider a discrete Schrödinger operator $${mathcal{J}}$$ whose potential is the sum of a Wigner-von Neumann term $${frac{csin(2omega n+delta)}n}$$ and a summable term. The essential spectrum of the operator $${mathcal{J}}$$ is equal to the interval [−2, 2]. Inside this interval, there are two critical points $${pm2cosomega}$$ where eigenvalues may be situated. We prove that, generically, the spectral density of $${mathcal{J}}$$ has zeroes of the power $${frac{|c|}{2|sinomega|}}$$ at these points.