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
SN - 0375-9601
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
IS - 25
ER -