论文标题
部分可观测时空混沌系统的无模型预测
Force balance in thermal quantum many-body systems from Noether's theorem
论文作者
论文摘要
我们解决了空间不均匀量子多体系统的自由能不变特性的后果。我们考虑系统的特定位置依赖性转换，该转换由空间变形和相应的局部解决方案变化组成。该操作员的转换是规范的，因此等效于系统的基础希尔伯特空间上的统一转换。结果，自由能是转化下的不变。 Noether的不变变化定理允许得出确切的总和规则，我们表明该规则是局部分辨的平衡一体力平衡。对于均匀转移的特殊情况，总和规则指出，平均全球外力在热平衡中消失。
We address the consequences of invariance properties of the free energy of spatially inhomogeneous quantum many-body systems. We consider a specific position-dependent transformation of the system that consists of a spatial deformation and a corresponding locally resolved change of momenta. This operator transformation is canonical and hence equivalent to a unitary transformation on the underlying Hilbert space of the system. As a consequence, the free energy is an invariant under the transformation. Noether's theorem for invariant variations then allows to derive an exact sum rule, which we show to be the locally resolved equilibrium one-body force balance. For the special case of homogeneous shifting, the sum rule states that the average global external force vanishes in thermal equilibrium.
