论文标题
点源的狄拉克粒子的创建率
Creation Rate of Dirac Particles at a Point Source
论文作者
论文摘要
直到最近，才有可能构建一个自动伴侣的哈密顿量，该自动伴侣涉及在3D空间中的点源创建狄拉克粒子。它的定义利用了内部边界状况。在这里，我们为这种汉密尔顿式的bohmian配置的相应理论开发。也就是说，我们在配置空间中构建了一个马尔可夫跳跃过程$（q_t）_ {t \ in \ mathbb {r}} $，在可变数量的粒子的配置空间中，该粒子是$ |ψ_t|^t |^2 $ dission the $ t $ t $，并跟随跳跃之间的bohmian轨迹。跳跃对应于粒子的产生或歼灭事件，并发生在源位于源的粒子的配置中。该过程是贝尔跳跃过程的自然类似物，其构造中的一个中心部分是确定粒子创造速率。该结构需要对源附近的波哈米亚轨迹的渐近行为进行分析。我们发现粒子以径向速度0到达源，但是在吸收前（或发射后），在有限的时间内无限多次绕源轨道。
Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we construct a Markov jump process $(Q_t)_{t\in\mathbb{R}}$ in the configuration space of a variable number of particles that is $|ψ_t|^2$-distributed at every time $t$ and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).
