量子阱中分区的边界效应
Boundary effect of a partition in a quantum well
摘要：
本文希望证明，在具有边界的量子系统中，不同的边界条件可以导致显着不同的物理行为。我们看似无辜的设置是一个一维势阱，被一个薄的隔离墙分成两半。两个半孔填充有相同类型和数量的颗粒，并保持在相同的温度下。唯一的区别是在分隔壁两侧施加的边界条件，从左边是狄利克雷条件，从右边是诺依曼条件。由此产生的不同能谱导致两侧量子统计出现压力的差异。作用在分隔壁上的净力证明在任何温度下都是非零的，并且在低温域中弱下降之后，在高温下以温度的平方根渐近性增加并发散。这些观测结果对玻色子和费米子类型的粒子都成立，但有数量上的差异。我们制定了几个解析近似来解释这些差异和发现意外复杂的图片的各个方面。
英文摘要：
The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. The only difference is in the boundary condition imposed at the two sides of the separating wall, which is the Dirichlet condition from the left and the Neumann condition from the right. The resulting different energy spectra cause a difference in the quantum statistically emerging pressure on the two sides. The net force acting on the separating wall proves to be nonzero at any temperature and, after a weak decrease in the low temperature domain, to increase and diverge with a square-root-of-temperature asymptotics for high temperatures. These observations hold for both bosonic and fermionic type particles, but with quantitative differences. We work out several analytic approximations to explain these differences and the various aspects of the found unexpectedly complex picture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
