Fredholm Determinants and the Statistics of Charge Transport
Fredholm Determinants and the Statistics of Charge Transport
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Fredholm 行列式和电荷传输统计
DOI：
10.1007/s00220-008-0449-x
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发表时间：
2007
影响因子：
2.4
通讯作者：
I. Klich
中科院分区：
文献类型：
--
作者：
J. Avron;S. Bachmann;G. M. Graf;I. Klich
利用算子代数方法，我们证明了具有无限多个非相互作用费米子的系统中电荷输运的矩母函数由单粒子希尔伯特空间中某个算子的行列式给出。该公式在有限维情形下等价于Levitov和Lesovik的一个公式，并且可以看作是它的一般正则化形式。我们的结果体现了介观物理学中经常实现的两个原则，即输运性质基本上与引线的长度和费米海的深度无关。
Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certain operator in the one-particle Hilbert space. The formula is equivalent to a formula of Levitov and Lesovik in the finite dimensional case and may be viewed as its regularized form in general. Our result embodies two tenets often realized in mesoscopic physics, namely, that the transport properties are essentially independent of the length of the leads and of the depth of the Fermi sea.