论文标题
复杂的博学系统中的混沌轨迹
Chaotic trajectories in complex Bohmian systems
论文作者
论文摘要
我们在2-D量子谐波振荡器中考虑了Bohmian轨迹，其波函数的波函数为$ψ=aψ_{m_1，n_1，n_1}（x，y）+bin_2，m_2，n_2，n_2，n_2，n_2}（x，y）+cin_）我们首先找到了量子数$ m，n $不同组合的节点点的轨迹。然后，我们详细研究了一个相对较大的量子数和两个相等$ m的$的情况。我们发现％我们首先找到$ψ= 0 $的节点点。只有在$ m $和$ n $很小的情况下，才能在分析上找到节点。如果两个$ m的$（或两个$ n的$相等），我们可以明确地找到淋巴结点，这些点有两种类型（1）固定节点独立于时间和（2）移动节点，这些节点不时与固定节点相撞，并且在特定时间碰撞。 最后，我们研究了靠近节点点的量子颗粒的轨迹，并首次观察如何在复杂系统中产生混乱，该系统在配置空间上散布了多个节点。
We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $Ψ=aΨ_{m_1,n_1}(x,y)+bΨ_{m_2,n_2}(x,y)+cΨ_{m_3,n_3}(x,y)$. We first find the trajectories of the nodal points for different combinations of the quantum numbers $m,n$. Then we study, in detail, a case with relatively large quantum numbers and two equal $m's$. We find %We find first the nodal points where $Ψ=0$. The nodes can be found analytically only if $m$ and $n$ are small. If two $m's$ (or two $n's$ are equal we can find explicitly the nodal points , which are of two types (1) fixed nodes independent of time and (2) moving nodes which from time to time collide with the fixed nodes and at particular times they go to infinity. Finally, we study the trajectories of quantum particles close to the nodal points and observe, for the first time, how chaos is generated in a complex system with multiple nodes scattered on the configuration space.
