The interaction between flexural modes due to nonlinear potentials is critical to heat conductivity and mechanical vibration of two dimensional materials such as graphene. Much effort has been devoted to understanding the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during the equipartition process. In particular, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes, forming symmetry blockades. As a result, the energy first flows to the modes in the same symmetry class. Breakdown of the symmetry blockade, i.e., inter-class energy flow, starts when the displacement profile becomes complex and the inter-class couplings bear nonneglectable values. The equipartition time follows the stretched exponential law and survives in the thermodynamic limit. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two dimensional systems with complex potentials and reveal clearly the physical picture of dynamical interactions between the flexural modes, which will be crucial to the understanding of their contribution in high thermal conductivity and mechanism of energy dissipation that may intrinsically limit the quality factor of the resonator.The interaction between flexural modes due to nonlinear potentials is critical to heat conductivity and mechanical vibration of two dimensional materials such as graphene. Much effort has been devoted to understanding the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during the equipartition process. In particular, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes, forming symmetry blockades. As a result, the energy first flows to the modes in the same symmetry class. Breakdown of the symmetry blockade, i.e., inter-class energy flow, starts when the displacement profile becomes complex and the inter-class couplings bear nonneglectable values. The equipartition time follows the stretched exponential law and survives in the thermodynamic limit. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two dimens...

中文翻译：

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方形石墨烯谐振器能量均分中的对称性阻塞及其破坏

由于非线性电位引起的弯曲模式之间的相互作用对于二维材料（如石墨烯）的热导率和机械振动至关重要。已经付出了很多努力来理解潜在的机制。在本文中，我们仅检查面外弯曲模式并确定它们在均分过程中的能量流动路径。特别是，这些模式根据其不同的对称性分为四类。类内的耦合明显大于类之间的耦合，形成对称阻塞。结果，能量首先流向相同对称类的模式。当位移剖面变得复杂并且类间耦合具有不可忽略的值时，对称性阻塞（即类间能量流）的分解开始。均分时间遵循拉伸指数定律并在热力学极限内存活。这些结果为具有复杂势能的二维系统中的 Fermi-Pasta-Ulam 问题带来了基本的理解，并清楚地揭示了弯曲模式之间动态相互作用的物理图，这对于理解它们在高热导率和机理中的贡献至关重要能量耗散可能从本质上限制谐振器的品质因数。由于非线性电位引起的弯曲模式之间的相互作用对于二维材料（例如石墨烯）的热导率和机械振动至关重要。已经付出了很多努力来理解潜在的机制。在本文中，我们仅检查面外弯曲模式并确定它们在均分过程中的能量流动路径。特别是，这些模式根据其不同的对称性分为四类。类内的耦合明显大于类之间的耦合，形成对称阻塞。结果，能量首先流向相同对称类的模式。当位移剖面变得复杂并且类间耦合具有不可忽略的值时，对称性阻塞（即类间能量流）的分解开始。均分时间遵循拉伸指数定律并在热力学极限内存活。这些结果从两个维度为 Fermi-Pasta-Ulam 问题带来了基本的理解...... 这些模式根据其独特的对称性分为四类。类内的耦合明显大于类之间的耦合，形成对称阻塞。结果，能量首先流向相同对称类的模式。当位移剖面变得复杂并且类间耦合具有不可忽略的值时，对称性阻塞（即类间能量流）的分解开始。均分时间遵循拉伸指数定律并在热力学极限内存活。这些结果从两个维度为 Fermi-Pasta-Ulam 问题带来了基本的理解...... 这些模式根据其独特的对称性分为四类。类内的耦合明显大于类之间的耦合，形成对称阻塞。结果，能量首先流向相同对称类的模式。当位移剖面变得复杂并且类间耦合具有不可忽略的值时，对称性阻塞（即类间能量流）的分解开始。均分时间遵循拉伸指数定律并在热力学极限内存活。这些结果从两个维度为 Fermi-Pasta-Ulam 问题带来了基本的理解...... 当位移剖面变得复杂并且类间耦合具有不可忽略的值时，对称性阻塞（即类间能量流）的分解开始。均分时间遵循拉伸指数定律并在热力学极限内存活。这些结果从两个维度为 Fermi-Pasta-Ulam 问题带来了基本的理解...... 当位移剖面变得复杂并且类间耦合具有不可忽略的值时，对称性阻塞（即类间能量流）的分解开始。均分时间遵循拉伸指数定律并在热力学极限内存活。这些结果从两个维度为 Fermi-Pasta-Ulam 问题带来了基本的理解......