经典不稳定哈密顿动力学的量子场论
Quantum Field Theory of Classically Unstable Hamiltonian Dynamics
摘要：
我们研究了一类动力系统，其运动可以用流形上的测地线来描述（普通的势模型可以通过保角映射转换成这种形式）。严格证明了由二阶协变导数构造的Jacobi测地偏差方程与参量谐振子的测地偏差方程是酉等价的，并研究了该谐振子的第二重化. Fock空间模式的激发对应于量子的发射和吸收到动力学介质中，从而将动力学系统的不稳定行为与具有可能的热力学后果的系综中的可计算波动相关联。
英文摘要：
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic deviation equation of Jacobi, constructed with a second covariant derivative, is unitarily equivalent to that of a parametric harmonic oscillator, and we study the second quatization of this oscillator. The excitations of the Fock space modes correspond to the emission and absorption of quanta into the dynamical medium, thus associating unstable behavior of the dynamical system with calculable fluctuations in an ensamble with possible thermodynamic consequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
