论文标题
三个相同的玻色子：非整数维度和外部磁场中的属性
Three identical bosons: Properties in non-integer dimensions and in external fields
论文作者
论文摘要
研究了从三维（3D）空间不断挤压到二维（2D）空间的三体系统。可以通过沿单个轴作用的外部限制电势来获得这种挤压。但是，此过程在数字上可能是要求的，甚至可能是不可能的，尤其是对于大型挤压场景。使用尺寸$ d $作为参数提供替代方案，该参数在$ 2 \ leq d \ leq 3 $范围内连续更改。利用$ d $ - 估计的简单性来调查渐进式限制后三体状态的演变。考虑了三个相同的无旋转玻色子的情况，具有3D相对$ s $ - 波和谐波振荡器挤压电位的情况。我们比较了两种方法的结果，并提供了它们之间的翻译，将两种方法的维度，挤压长度和波函数相关联。然后，所有计算都可以在更简单的$ d $ -Method中完全进行，但同时提供了具有外部电位的等效几何形状。
Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated. Such a squeezing can be obtained by means of an external confining potential acting along a single axis. However, this procedure can be numerically demanding, or even undoable, especially for large squeezed scenarios. An alternative is provided by use of the dimension $d$ as a parameter that changes continuously within the range $2\leq d \leq 3$. The simplicity of the $d$-calculations is exploited to investigate the evolution of three-body states after progressive confinement. The case of three identical spinless bosons with relative $s$-waves in 3D, and a harmonic oscillator squeezing potential is considered. We compare results from the two methods and provide a translation between them, relating dimension, squeezing length, and wave functions from both methods. All calculations are then possible entirely within the simpler $d$-method, but simultaneously providing the equivalent geometry with the external potential.
