ON THE WEAK COUPLING LIMIT FOR A FERMI GAS IN A RANDOM POTENTIAL
ON THE WEAK COUPLING LIMIT FOR A FERMI GAS IN A RANDOM POTENTIAL
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随机势下费米气体的弱耦合极限
DOI：
10.1142/s0129055x93000061
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
A. Wilkins
中科院分区：
文献类型：
--
作者：
T. Ho;L. J. Landau;A. Wilkins
本文给出了-ε + V的本质自伴性和微扰展开存在的一般条件，其中V是微扰不变的随机势。展示的一系列图违反了Dell'Antonio对骨架图的界。对费米气体的高斯随机势V和初始态S，当它们与随机势无关时，弱耦合极限（货车霍韦极限）产生熵的增加，混沌的传播，当参数τ足够小时状态收敛到规范不变和准自由的渐近状态，和描述两点函数演化的半群。渐近系统是伯努利。结果不仅得到了平均的随机势，但也与概率1。如果随机势V′关于V是绝对连续的，并且如果状态S′由S的GNS表示中的密度矩阵给出，则弱耦合极限与V和S的弱耦合极限相同。
General conditions are derived for the essential self-adjointness of –∆ + V, where V is a translation-invariant random potential, and for the existence of the perturbation expansion. A sequence of graphs is exhibited violating Dell'Antonio's bound for skeleton graphs. For a translation-invariant and clustering Gaussian random potential V, and a translation-invariant and clustering initial state S of the Fermi gas, uncorrelated with the random potential, the weak coupling limit (Van Hove limit) yields increase of entropy, propagation of chaos, convergence of the state for sufficiently small values of the parameter τ to a gauge-invariant and quasi-free asymptotic state, and the semigroup describing the evolution of the two-point function. The asymptotic system is Bernoulli. Results are obtained not only for the average over the random potential but also with probability one. If the random potential V′ is absolutely continuous with respect to V, and if the state S′ is given by a density matrix in the GNS representation for S, then the weak coupling limit is the same as for V and S.