标题： 相空间工程中的Gromov基态用于聚变能源 显示英文标题

标题： Gromov ground state in phase space engineering for fusion energy

摘要： 通过射频波进行相空间工程在热D-T聚变和非热先进燃料聚变中都起着重要作用。 但并非所有的相空间操作都是允许的，某些基本限制存在。 除了要求操作保持体积不变的Liouville定理外，Gromov的不可压缩定理也施加了另一个约束。 Gardner基态被定义为可通过平滑体积不变映射达到的基态。 然而，额外的Gromov约束应产生更高能量的基态。 给出了一个因Gromov不可压缩定理而被禁止的Gardner基态示例。 挑战性问题是：什么是Gromov基态，即可通过平滑辛映射达到的最低能量状态？ 这是一个困难的问题。 作为简化，我们猜想线性Gromov基态问题是可以解决的。 显示英文摘要

摘要： Phase space engineering by RF waves plays important roles in both thermal D-T fusion and non-thermal advanced fuel fusion. But not all phase space manipulation is allowed, certain fundamental limits exist. In addition to Liouville's theorem, which requires the manipulation to be volume-preserving, Gromov's non-squeezing theorem imposes another constraint. The Gardner ground state is defined as the ground state accessible by smooth volume-preserving maps. However, the extra Gromov constraint should produce a higher-energy ground state. An example of a Gardner ground state forbidden by Gromov's non-squeezing theorem is given. The challenge question is: What is the Gromov ground state, i.e., the lowest energy state accessible by smooth symplectic maps? This is a difficult problem. As a simplification, we conjecture that the linear Gromov ground state problem is solvable.