THE SEMI-CIRCLE DIAGRAMS IN THE STOCHASTIC LIMIT OF THE ANDERSON MODEL
THE SEMI-CIRCLE DIAGRAMS IN THE STOCHASTIC LIMIT OF THE ANDERSON MODEL
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ANDERSON模型随机极限下的半圆图
DOI：
10.1142/s0219025798000259
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
V. Mastropietro
中科院分区：
文献类型：
--
作者：
L. Accardi;Y. Lu;V. Mastropietro
我们证明了在Anderson模型的随机极限下，从自由哈密顿量的第一激发态到相互作用哈密顿量的第一激发态的过渡幅值只有非交叉图存在。这证实了Migdal（1958）和Abrikosov， Gorkov, Dzyaloshinski（1975）的一个猜想。由此推导出极限跃迁振幅的一个闭合（非线性）Schwinger-Dyson型方程，并给出了该振幅与激发态动量的显式关系。
We prove that, in the stochastic limit of the Anderson model only the non-crossing diagrams survive for the transition amplitude from the first excited state of the free Hamiltonian to the first excited state of the interacting Hamiltonian. This confirms a conjecture of Migdal (1958) and Abrikosov, Gorkov, Dzyaloshinski (1975). From this we deduce a closed (nonlinear) Schwinger–Dyson type equation for the limit transition amplitude whose solution can be found and gives the explicit dependence of this amplitude on the momentum of the excited state.