论文标题
Holomorthic Hamiltonian $ξ$ - 流和Riemann Zeros
Holomorphic Hamiltonian $ξ$-Flow and Riemann Zeros
论文作者
论文摘要
With a view on the formal analogy between Riemann-von-Mangoldts explicit formula and semiclassical quantum mechanics in terms of the Gutzwiller trace formula we construct a complex-valued Hamiltonian $H(q,p)=ξ(q)p$ from the holomorphic flow $\dot{q}=ξ(q)$ and its variational differential equation.汉密尔顿相肖像$ q（p）$是一个riemann的表面，等同于在复杂时间中重新聚集$ξ$ -Newton流量解决方案，其流量图差异是由所有Riemann Zeros确定的，并让人联想到痕量公式中的“光谱总和”。圆圈上粒子量子力学的规范量化导致Dirac-type动量运算符，其频谱由衍生物$ξ'（ρ_n）$在Riemann Zeros上确定的经典封闭轨道周期给出。
With a view on the formal analogy between Riemann-von-Mangoldts explicit formula and semiclassical quantum mechanics in terms of the Gutzwiller trace formula we construct a complex-valued Hamiltonian $H(q,p)=ξ(q)p$ from the holomorphic flow $\dot{q}=ξ(q)$ and its variational differential equation. The Hamiltonian phase portrait $q(p)$ is a Riemann surface equivalent to reparameterized $ξ$-Newton flow solutions in complex-time, its flow map differential is determined by all Riemann zeros and reminiscent of a 'spectral sum' in trace formulas. Canonical quantization for particle quantum mechanics on a circle leads to a Dirac-type momentum operator with discrete spectrum given by classical closed orbit periods determined by derivatives $ξ'(ρ_n)$ at Riemann zeros.
