论文标题
陀螺系统和暗能量的经典和量子动力学
Classical and Quantum Dynamics of Gyroscopic Systems and Dark Energy
论文作者
论文摘要
古典和量子场理论中的陀螺仪系统的特征是至少存在两个标量的自由度，并以二次拉格朗日语中的术语及其时间衍生物混合。在Minkowski时空中，它们自然出现在具有时间依赖的真空期望值和具有空间依赖真空期望值的字段之间的耦合中，从而自发地破坏了Lorentz的对称性。 Supersolid就是这种情况。在宇宙学背景下，陀螺仪系统也可能是由于非对抗动力学和质量矩阵的时间依赖性而产生的。我们研究了计算最小化能量的真空状态上相关函数的经典和量子动力学。发现了参数空间中的两个稳定区域：在一个被称为正常的区域中，哈密顿量为正定义，而在第二个区域则被称为异常，它没有确定的符号。有趣的是，在异常区域中，2点相关函数在某个参数空间的某个区域中表现出共鸣的行为。我们表明，动态的暗能量模型（具有状态$ W = -1 $的精确方程）可以实现为陀螺系统。
Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees of freedom and by terms that mix fields and their time derivatives in the quadratic Lagrangian. In Minkowski spacetime, they naturally appear in the presence of a coupling among fields with time-dependent vacuum expectation values and fields with space-dependent vacuum expectation values, breaking spontaneously Lorentz symmetry; this is the case for a supersolid. In a cosmological background a gyroscopic system can also arise from the time dependence of non-diagonal kinetic and mass matrices. We study the classical and quantum dynamics computing the correlation functions on the vacuum state that minimizes the energy. Two regions of stability in parameter space are found: in one region, dubbed normal, the Hamiltonian is positive defined, while in the second region, dubbed anomalous, it has no definite sign. Interestingly, in the anomalous region the 2-point correlation function exhibits a resonant behaviour in a certain region of parameter space. We show that dynamical dark energy models (with exact equation of state $w=-1$) can be realised as a gyroscopic system.
