论文标题
两分量玻色液滴的零能量模式
Zero-energy modes of two-component Bose-Bose droplets
论文作者
论文摘要
当对其相互作用进行适当调整时,玻色液液滴是从两个相互作用的玻色菌冷凝物的混合物中出现的自构物体。在液滴形成过程中,系统的哈密顿量的三个连续对称性被损坏:翻译对称性和两个U1对称性,可以任意选择描述这两个组件的平均场波函数的阶段。这些对称性的破坏必须伴随着在恢复断裂对称性的系统的能量谱中的零能激励的出现。与这些激发相对应的正常模式是零能量模式。在这里,我们找到了这些模式的分析表达式,并引入了Hamitonians产生时间演变 - 液滴的质量中心的动力学以及两个液滴波形的相位动态。当忽略激发的内部类型(准粒子)时,仅使用少量“全局”自由度来描述量子液滴的非常复杂的系统 - 液滴质量中心的位置和两个波动的两个阶段的位置,所有这些都是量子操作员。这提供了以相对简单的方式描述这些量子液滴的相互作用的过程,例如碰撞。
Bose-Bose droplets are self-bound objects emerging from a mixture of two interacting Bose-Einstein condensates when their interactions are appropriately tuned. During droplet formation three continuous symmetries of the system's Hamiltonian are broken: translational symmetry and two U1 symmetries, allowing for arbitrary choice of phases of the mean-field wavefunctions describing the two components. Breaking of these symmetries must be accompanied by appearance of zero-energy excitations in the energy spectrum of the system recovering the broken symmetries. Normal modes corresponding to these excitations are the zero-energy modes. Here we find analytic expressions for these modes and introduce Hamitonians generating their time evolution -- dynamics of the droplet's centers of mass as well as dynamics of the phases of the two droplet's wavefunctions. When internal types of excitations (quasiparticles) are neglected then the very complex system of a quantum droplet is described using only few "global" degrees of freedom - the position of the center of mass of the droplet and two phases of two wave-functions, all these being quantum operators. This gives the possibility of describing in a relatively easy way processes of interaction of these quantum droplets, such as collisions.