Boundary effect of a partition in a quantum well
Boundary effect of a partition in a quantum well
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DOI：
10.1088/1751-8113/40/17/013
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发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
T. Fülöp;I. Tsutsui
中科院分区：
文献类型：
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作者：
T. Fülöp;I. Tsutsui
本文希望证明，在有边界的量子系统中，不同的边界条件可以导致显著不同的物理行为。我们看似无辜的场景是一个一维势阱，它被一层薄薄的隔离墙分成两半。两个半阱中填充了相同类型和数量的粒子，并保持在相同的温度下。唯一的区别是在分离壁两侧施加的边界条件，左边是狄利克雷条件，右边是诺伊曼条件。由此产生的不同能谱导致双方在量子统计上出现的压力不同。作用在分离壁上的净力在任何温度下都是非零的，在低温域中弱减小后，在高温域中以温度的平方根渐近增加并发散。这些观察结果对玻色子和费米子类型的粒子都成立，但在数量上有所不同。我们制定了几个解析近似来解释这些差异和发现的意想不到的复杂画面的各个方面。
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.