The anisotropy of a trap potential can impact the density and variance of a Bose-Einstein condensate (BEC) in an opposite manner. We exemplify this effect for both the ground state and out-of-equilibrium dynamics of structureless bosons interacting by a long-range inter-particle interaction and trapped in a two-dimensional single-well potential. We demonstrate that even when the density of the BEC is, say, wider along the y direction and narrower along the x direction, its position variance can actually be smaller and momentum variance larger in the y direction than in the x direction. This behavior of the variance in a many-particle system is counterintuitive. It suggests using the variance as a tool to characterize the strength of correlations along the y and x directions in a trapped BEC.

阱势的各向异性会以相反的方式影响玻色-爱因斯坦凝聚物（BEC）的密度和方差。我们举例说明了无结构玻色子的基态和不平衡动力学的这种效应，该玻色子通过长程粒子间相互作用而相互作用，并被困在二维单阱势中。我们表明，即使当BEC的密度是，比方说，沿宽ÿ方向和更窄的沿X方向，其位置方差实际上可以在较小的和动量方差较大ý方向上比在X方向。在多粒子系统中这种方差的行为是违反直觉的。它建议使用方差作为一种工具来描述捕获的BEC中沿y和x方向的相关强度。