多极化子系统的稳定性和无束缚
Stability and Absence of Binding for Multi-Polaron Systems
摘要：
我们解决了几个长期存在的问题，有关的稳定性和N \geq 2极化子的多粒子结合的情况下。Fröhlich在1937年提出的极化子模型描述了非相对论性粒子与耦合为\sqrt α的标量量子化场相互作用，粒子之间通过库仑排斥相互作用。我们证明如下：（i）当U<2α时存在已知的热力学不稳定性，但当U>2α时，物质的稳定性确实成立，也就是说，每个粒子的基态能量有一个有限的极限，即N \to \infty。(ii)如果U超过一个取决于α而不取决于N的临界值，则不存在任何形式的束缚。Pekar-Tomasevich模型也得到了同样的结果。
英文摘要：
We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \sqrtα, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2α, stability of matter does hold for U>2α, that is, the ground state energy per particle has a finite limit as N\to\infty. (ii) There is no binding of any kind if U exceeds a critical value that depends on αbut not on N. The same results are shown to hold for the Pekar-Tomasevich model.
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