Bounds on the Minimal Energy of Translation Invariant N-Polaron Systems
Bounds on the Minimal Energy of Translation Invariant N-Polaron Systems
复制标题
平移不变N极化子系统的最小能量界限
DOI：
10.1007/s00220-010-1013-z
复制
发表时间：
2009
影响因子：
2.4
通讯作者：
J. S. Møller
中科院分区：
文献类型：
--
作者：
M. Griesemer;J. S. Møller
对于N带电费米子（如电子）与极性晶体的纵向光学量子化晶格振动相互作用的系统，我们推导了H. Fröhlich模型内最小能量的上界和下界。在去掉紫外截止后，该模型的唯一参数是测量电子-电子和电子-声子耦合强度的常数U > 0和α > 0。它们受到条件$${\sqrt{2}\alpha < U}$$的约束，这是由U和α对晶体电学性质的依赖所引起的。我们证明了最小能量EN的大N渐近行为在$${\sqrt{2}\alpha=U}$$发生变化，并且$${\sqrt{2}\alpha\leq U}$$对于热力学稳定性是必要的：对于$${\sqrt{2}\alpha > U}$$，声子介导的电子-电子吸引克服了库仑排斥，EN的行为类似于- N7/3。
For systems of N charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fröhlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U > 0 and α > 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition $${\sqrt{2}\alpha < U}$$, which follows from the dependence of U and α on electrical properties of the crystal. We show that the large N asymptotic behavior of the minimal energy EN changes at $${\sqrt{2}\alpha=U}$$ and that $${\sqrt{2}\alpha\leq U}$$ is necessary for thermodynamic stability: for $${\sqrt{2}\alpha > U}$$ the phonon-mediated electron-electron attraction overcomes the Coulomb repulsion and EN behaves like −N7/3.