谐振势中隔墙上的量子力
Quantum Force Induced on a Partition Wall in a Harmonic Potential
摘要：
通过在谐振子系统中心插入一个隔墙，研究了量子力学中的边界效应。我们把相同数量的粒子放在不可穿透的墙的两侧，使系统保持在有限的温度下。当壁面两侧有不同的边界条件时，则在壁上产生净力。我们研究的温度行为的诱导力的分析和数值的Dirichlet和Neumann条件的组合下，并确定其标度性质的两个统计情况下的粒子：费米子和玻色子。我们发现，在零温度T = 0的力有一个非零的限制，并表现出缩放特性的粒子的统计。我们还看到，对于更高的温度，力根据1/sqrt{T}减小，与无限势阱的情况形成鲜明对比，在无限势阱中，力根据sqrt{T}发散。结果表明，如果这样一个非平凡的隔墙可以实现，它可以被用来作为一个探针，检查的电位和有关粒子的统计分布。
英文摘要：
Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under finite temperatures. When the wall admits distinct boundary conditions on the two sides, then a net force is induced on the wall. We study the temperature behaviour of the induced force both analytically and numerically under the combination of the Dirichlet and the Neumann conditions, and determine its scaling property for two statistical cases of the particles: fermions and bosons. We find that the force has a nonvanishing limit at zero temperature T = 0 and exhibits scalings characteristic to the statistics of the particles. We also see that for higher temperatures the force decreases according to 1/sqrt{T}, in sharp contrast to the case of the infinite potential well where it diverges according to sqrt{T}. The results suggest that, if such a nontrivial partition wall can be realized, it may be used as a probe to examine the profile of the potentials and the statistics of the particles involved.
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