论文标题
$ \ sqrt {t \ bar {t}} $ - 由modmax启发的变形振荡器
$\sqrt{T\bar{T}}$-deformed oscillator inspired by ModMax
论文作者
论文摘要
受麦克斯韦理论（ModMax）的最近提出的二元性和保形不变修改的启发，我们在经典力学中构建了一个二维动力学系统的单参数家族，该家族与Modmax理论共享许多特征。它由几个$ \ sqrt {t \ bar {t}} $ - 变形的振荡器，这些振荡器仍然保留duality $（q \ rightarrow p，p \ rightarrow -q）$，取决于连续的参数$γ$，如在ModMax情况下。尽管具有非线性功能，但该系统还是可集成的。可以明显地将其解释为一对两个耦合振荡器，其频率取决于与二元性对称和旋转对称性相对应的一些基本不变性。基于模型的属性，我们可以构造基于$γ$的非线性地图，该$γ$将振荡器以2D映射到非线性，但具有参数$2γ$。动力学还显示了能量转移的现象，我们计算了与几何阶段和载体相关的汉奈角。
Inspired by a recently proposed Duality and Conformal invariant modification of Maxwell theory (ModMax), we construct a one-parameter family of two-dimensional dynamical system in classical mechanics that share many features with the ModMax theory. It consists of a couple of $\sqrt{T\bar{T}}$-deformed oscillators that nevertheless preserves duality $(q \rightarrow p,p \rightarrow -q)$ and depends on a continuous parameter $γ$, as in the ModMax case. Despite its non-linear features, the system is integrable. Remarkably can be interpreted as a pair of two coupled oscillators whose frequencies depend on some basic invariants that correspond to the duality symmetry and rotational symmetry. Based on the properties of the model, we can construct a non-linear map dependent on $γ$ that maps the oscillator in 2D to the nonlinear one, but with parameter $2γ$. The dynamics also shows the phenomenon of energy transfer and we calculate a Hannay angle associated to geometric phases and holonomies.
