Stability and absence of binding for multi-polaron systems
Stability and absence of binding for multi-polaron systems
复制标题
多极化子系统的稳定性和无结合
DOI：
10.1007/s10240-011-0031-5
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
L. Thomas
中科院分区：
文献类型：
--
作者：
R. Frank;E. Lieb;R. Seiringer;L. Thomas
我们解决了几个长期存在的关于N≥2极化子的稳定性和不存在多粒子束缚的问题。Fröhlich在1937年提出的极化子模型描述了非相对论性粒子与标量量子化场的相互作用，场与场之间的耦合为$\sqrt{\alpha}$，相互之间的库仑排斥力为U。我们证明如下：（i）虽然U<2α时存在已知的热力学不稳定性，但U>2α时物质的稳定性确实成立，即每个粒子的基态能量在N→∞时有一个有限的极限。(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。
We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich’s 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling $\sqrt{\alpha}$, 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→∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model.