论文标题
来自最小耦合量子同构的某些Euler-Bernoulli杆和环的动力学
Dynamics of certain Euler-Bernoulli rods and rings from a minimal coupling quantum isomorphism
论文作者
论文摘要
在某些参数和解决方案方案中，1D中的微小耦合的非递归量子粒子与3D的更重，振动，非常薄的Euler-Bernoulli杆同构，弯曲模量与线性密度$（\ HBAR/2M）^2 $，弯曲模量与线性密度$（^2 $）。对于$ m = m_e $，此数量可与微管的数量相媲美。施加到杆上的轴向力和扭矩分别发挥了标量和向量电势的作用，并且杆不可扩展性起着归一化的作用。 We show how an uncertainty principle $ΔxΔp_x\gtrsim\hbar$ governs transverse deformations propagating down the inextensible, force and torque-free rod, and how orbital angular momentum quantized in units of $\hbar$ or $\hbar/2$ (depending on calculation method) emerges when the force and torque-free inextensible rod is formed into a ring.对于带有大型波数的扭矩环，出现``扭曲量子''，它与磁通量量子有些类似。这些结果和其他结果是从纯粹的杆经典处理中获得的，即不量化任何经典磁场。
In some parameter and solution regimes, a minimally coupled nonrelativistic quantum particle in 1d is isomorphic to a much heavier, vibrating, very thin Euler-Bernoulli rod in 3d, with ratio of bending modulus to linear density $(\hbar/2m)^2$. For $m=m_e$, this quantity is comparable to that of a microtubule. Axial forces and torques applied to the rod play the role of scalar and vector potentials, respectively, and rod inextensibility plays the role of normalization. We show how an uncertainty principle $ΔxΔp_x\gtrsim\hbar$ governs transverse deformations propagating down the inextensible, force and torque-free rod, and how orbital angular momentum quantized in units of $\hbar$ or $\hbar/2$ (depending on calculation method) emerges when the force and torque-free inextensible rod is formed into a ring. For torqued rings with large wavenumbers, a ``twist quantum'' appears that is somewhat analogous to the magnetic flux quantum. These and other results are obtained from a purely classical treatment of the rod, i.e., without quantizing any classical fields.
