有限距排斥对势下二维正方形和非正方形Bravais格点的调和稳定性分析。二维超冷复合玻色子系统的结果
Harmonic Stability Analysis of the 2D Square and Hexagonal Bravais Lattices for a Finite--Ranged Repulsive Pair Potential. Consequence for a 2D System of Ultracold Composite Bosons
摘要：
我们考虑一个经典的，二维系统的全同粒子相互作用，通过一个有限范围，排斥对潜力。我们假设系统处于结晶相。我们计算的正常振动模式的二维正方形布拉维晶格，第一次解析内的最近邻近似，然后在数值上，放松前面的假设。我们表明，在谐波近似下，横向振动模式的激发导致崩溃的正方形晶格。我们接下来研究的情况下，六角布拉维晶格，我们表明，它可以是稳定的晶格振动。我们给出了一个判断它在最近邻近似下是否稳定的判据。最后，我们将我们的结果应用到一个二维系统的复合玻色子和推断，这样一个系统的晶相，如果它存在，对应于一个六方晶格。
英文摘要：
We consider a classical, two-dimensional system of identical particles which interact via a finite-ranged, repulsive pair potential. We assume that the system is in a crystalline phase. We calculate the normal vibrational modes of a two-dimensional square Bravais lattice, first analytically within the nearest-neighbour approximation, and then numerically, relaxing the preceding hypothesis. We show that, in the harmonic approximation, the excitation of a transverse vibrational mode leads to the breakdown of the square lattice. We next study the case of the hexagonal Bravais lattice and we show that it can be stable with respect to lattice vibrations. We give a criterion determining whether or not it is stable in the nearest-neighbour approximation. Finally, we apply our results to a two-dimensional system of composite bosons and infer that the crystalline phase of such a system, if it exists, corresponds to a hexagonal lattice.
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。
