TY - JOUR

T1 - A variance formula related to a quantum conductance problem

AU - Jiang, Tiefeng

PY - 2009/6/1

Y1 - 2009/6/1

N2 - Let t be a block of an Haar-invariant orthogonal (β = 1), unitary (β = 2) or symplectic (β = 4) matrix from the classical compact groups O (n), U (n) or Sp (n), respectively. We obtain a close form for Var (tr (t* t)). The case for β = 2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit (8 β)-1 for β = 1, 2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.

AB - Let t be a block of an Haar-invariant orthogonal (β = 1), unitary (β = 2) or symplectic (β = 4) matrix from the classical compact groups O (n), U (n) or Sp (n), respectively. We obtain a close form for Var (tr (t* t)). The case for β = 2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit (8 β)-1 for β = 1, 2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.

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U2 - 10.1016/j.physleta.2009.04.035

DO - 10.1016/j.physleta.2009.04.035

M3 - Article

AN - SCOPUS:67349160474

VL - 373

SP - 2117

EP - 2121

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 25

ER -