保持对称性：通过退相干实现自发对称性破缺
Preserving Symmetry: Spontaneous Symmetry Breaking through Decoherence
AI总结：
本文针对有限量子系统的局域化问题，通过量子化环境，利用退相干分支实现局域化，复合系统态矢量仍保持平移对称，可恢复半经典描述并预测实验可区分修正。
AI中文摘要：
固体看似具有局域化的质心，但多体量子理论用平移对称模型描述固体，这与局域化相矛盾。传统上，通过引入与半经典环境的相互作用来解决该矛盾，该相互作用会破坏对称性。在热力学极限下，可移除该相互作用而使态保持局域化，但这引发了有限量子系统（非热力学极限下）如何产生局域化的问题（Wallace，2018）。本文表明，通过对环境进行量子化，有限系统的局域化发生在退相干分支中，而复合系统的态矢量仍保持平移对称。本文方法类似于Page-Wootters构造（Page & Wootters，1983）和量子参考框架，还可将半经典描述作为极限情况恢复，并预测偏离该极限时实验可区分的修正。
英文摘要：
Solids appear to have localised centres of mass, yet many-body quantum theory describes them using translationally symmetric models that preclude localisation. Conventionally, this is resolved through spontaneous symmetry breaking by introducing an interaction with a semiclassical environment that breaks the symmetry. In the thermodynamic limit, the interaction can be removed while leaving the state localised. This, however, raises the question of how localisation arises outside the thermodynamic limit, i.e., in finite quantum systems (Wallace, 2018). Here, we show that, by quantising the environment, the localisation of finite systems occurs within decoherent branches, while the state vector of the composite system remains translationally symmetric. Our approach is analogous to the Page-Wootters construction (Page & Wootters, 1983) and quantum reference frames; moreover, we recover the semiclassical description as a limiting case while predicting experimentally distinguishable corrections away from this limit.
