高级检索

时空克莱因瓶上的热力学——从二维生物的奇妙旅行到共形量子态的路径积分

Thermodynamics on the space-time Klein bottle——from the wonder trip in the flatland to the path integral of conformal quantum states

  • 摘要: 在克莱因瓶和莫比乌斯带上环游世界的二维生物会经历有趣的手征变换,这可归因于这些不可定向曲面的独特拓扑性质。作者最近在研究中发现,让共形场论中的量子态在这些曲面上做“时空旅行”(路径积分),也会得到新奇而普适的热力学性质。例如,克莱因瓶上的二维共形场论的自由能中包含一项普适的克莱因瓶熵。它仅依赖于共形场论的一些基本特征。利用克莱因瓶熵,可以精确地找到量子相变点,并刻画其普适类。更一般地,不可定向曲面上的普适热力学数据不仅对于研究凝聚态和统计物理中的临界现象有意义,对于其他领域,比如全息黑洞热力学等也有启发。

     

    Abstract: Due to the distinct topology of non-orientable surfaces (such as the Klein bottle and Möbius band), a 2D chiral creature changes its parity after travelling around the manifold. When we consider a space-time journey of quantum states in conformal field theory (CFT) on non-orientable world sheets, we find that the Euclidean path integral of CFT on non-orientable surfaces gives rise to intriguing universal thermal properties. For instance, on the Klein bottle there exists a universal entropy in the free energy which can be exploited to locate phase transition points and identify their corresponding CFTs. Universal thermal data of the Klein bottle, as well as other non-orientable surfaces, can play an important role in studying critical phenomena in condensed matter and statistical physics. We also anticipate their potential applications and far-reaching implications in other areas, such as holographic blackhole thermodynamics, and so forth.

     

/

返回文章
返回