标题： 新物理在狄拉克材料上的影子，类GUP及其他娱乐 显示英文标题

标题： Shadows of new physics on Dirac materials, analog GUPs and other amusements

摘要： 我们在这里讨论的是，当考虑与晶格间距$\ell$相关的参数$\frac{\ell}{\hbar} |\vec{p}|$的高阶效应时，纯石墨烯和其他狄拉克材料可以作为实验桌面上的系统，其中广义对易关系自然实现。 这些导致广义海森堡不确定性原理版本的广义量子化代数，目前正受到密切关注，因为它们可能表现出时空的基本长度尺度。 尽管做出了努力并取得了许多引人注目的结果，但还没有任何广义不确定性原理（GUP）的实验迹象。 因此，我们在这里的结果，即如何使用实验桌面上的物理系统在类似实验中测试某些GUP，应该会引起量子引力实践者的兴趣。 我们识别了三个不同的能量区域，我们称之为“层”，其中物理性质仍然是狄拉克类型的，但处于精确描述的限制内。 能量越高，狄拉克系统对晶格效应就越敏感。 在这里，这样的晶格扮演着离散空间的角色，狄拉克准粒子就生活在这个空间中。 为了实现上述目标，我们必须确定高能坐标$X^i$与低能坐标$x^i$之间的映射，即实验室中测量的那些坐标。 然后我们得到了三个广义海森堡代数。 其中两个代数有一个显著的结果，即$X^i = x^i$，而对于第三个代数，我们相对于早期的工作获得了改进：广义坐标用标准相空间变量$X^i(x,p)$和高阶项来表示。 显示英文摘要

摘要： We discuss here how, when higher-order effects in the parameter $\frac{\ell}{\hbar} |\vec{p}|$, related to the lattice spacing $\ell$, are considered, pristine graphene, and other Dirac materials, can be used as tabletop systems where generalized commutation relations are naturally realized. Such generalized algebras of quantization, which lead to generalized versions of the Heisenberg uncertainty principle, are under intense scrutiny these days, as they could manifest a fundamental length scale of spacetime. Despite the efforts and the many intriguing results, there are no experimental signatures of any generalized uncertainty principle (GUP). Therefore, our results here, which tell how to use tabletop physical systems to test certain GUPs in analog experiments, should be of interest to practitioners of quantum gravity. We identify three different energy regimes that we call ``layers'', where the physics is still of a Dirac type but within precisely described limits. The higher the energy, the more sensitive the Dirac system becomes to the effects of the lattice. Here such lattice plays the role of a discrete space where the Dirac quasi-particles live. With the goals just illustrated, we had to identify the mapping between the high-energy coordinates, $X^i$, and the low-energy ones, $x^i$, i.e., those measured in the lab. We then obtained three generalized Heisenberg algebras. For two of them we have the noticeable result that $X^i = x^i$, and for the third one we obtained an improvement with respect to an earlier work: the generalized coordinates expressed in terms of the standard phase space variables, $X^i(x,p)$, and higher order terms.