Zurek Wojciech H, Dorner Uwe
Theory Division, LANL, MS-B213, Los Alamos, NM 87545, USA.
Philos Trans A Math Phys Eng Sci. 2008 Aug 28;366(1877):2953-72. doi: 10.1098/rsta.2008.0069.
We extend the theory of symmetry-breaking dynamics in non-equilibrium second-order phase transitions known as the Kibble-Zurek mechanism (KZM) to transitions where the change of phase occurs not in time but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the 'scar' over which the order parameter adjusts as it 'bends' interpolating between the phases with different symmetries follows from a KZM-like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale--the size of the scar--is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.
我们将非平衡二阶相变中被称为基布尔-祖雷克机制（KZM）的对称性破缺动力学理论扩展到相变不是在时间上而是在空间上发生的情况。这可能是由于一个场的与时间无关的空间变化，该场在其达到临界值的位置左侧施加具有一种对称性的相，而在该临界边界右侧允许自发对称性破缺。在这种情况下拓扑缺陷不一定会形成。然而，我们表明，序参量在不同对称性的相之间“弯曲”插值时进行调整的“疤痕”在空间上的大小遵循一种类似KZM的方法。正如我们在横向量子伊辛模型的例子中所说明的，在量子相变中，这个空间尺度——疤痕的大小——直接反映在系统的能谱中：特别是，它决定了能隙的大小。
