GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NONIDEAL LEADS

被引：149
作者：
BROUWER, PW
机构：
[1] Instituut-Lorentz, University of Leiden, 2300 RA Leiden
来源：
PHYSICAL REVIEW B | 1995年 / 51卷 / 23期
关键词：
D O I：
10.1103/PhysRevB.51.16878
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We consider the problem of the statistics of the scattering matrix S of a chaotic cavity (quantum dot), which is coupled to the outside world by nonideal leads containing N scattering channels. The Hamiltonian H of the quantum dot is assumed to be an M×M Hermitian matrix with probability distribution P(H)det[λ2+(H-)2]-(βM+2-β)/2, where λ and are arbitrary coefficients and β=1,2,4 depending on the presence or absence of time-reversal and spin-rotation symmetry. We show that this ''Lorentzian ensemble'' agrees with microscopic theory for an ensemble of disordered metal particles in the limit M→, and that for any MN it implies P(S)det(1-S̄°S)-(βM+2-β), where S̄ is the ensemble average of S. This ''Poisson kernel'' generalizes Dyson's circular ensemble to the case S̄0 and was previously obtained from a maximum entropy approach. The present work gives a microscopic justification for the case that chaotic motion in the quantum dot is due to impurity scattering. © 1995 The American Physical Society.
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页码：16878 / 16884
页数：7
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共 36 条
  • [21] Verbaarschot J.J.M., Weidenmuller H.A., Zirnbauer M.R., Phys. Rep., 129, (1985)
  • [22] Iida S., Weidenmuller H.A., Zuk J., Phys. Rev. Lett., 64, (1990)
  • [23] Iida S., Weidenmuller H.A., Zuk J., Ann. Phys. (N.Y.), 200, (1990)
  • [24] Altland A., Z. Phys. B., 82, (1991)
  • [25] Lewenkopf C.H., Weidenmuller H.A., Ann. Phys. (N.Y.), 212, (1991)
  • [26] Blumel R., Smilansky U., Phys. Rev. Lett., 60, (1988)
  • [27] Blumel R., Smilansky U., Random-matrix description of chaotic scattering: Semiclassical approach, Physical Review Letters, 64, (1990)
  • [28] Smilansky U., Chaos and Quantum Physics, (1991)
  • [29] Dyson F.J., J. Math. Phys., 3, (1962)
  • [30] Mello P.A., Pereyra P., Seligman T.H., Ann. Phys. (N.Y.), 161, (1985)
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