 
Summary: Enhanced mesoscopic fluctuations in the crossover between randommatrix ensembles
Shaffique Adam, Piet W. Brouwer, James P. Sethna, and Xavier Waintal*
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 148532501
Received 28 February 2002; revised manuscript received 12 August 2002; published 9 October 2002
In randommatrix ensembles that interpolate between the three basic ensembles orthogonal, unitary, and
symplectic , there exist correlations between elements of the same eigenvector and between different eigen
vectors. We study such correlations, using a remarkable correspondence between the interpolating ensembles
late in the crossover and a basic ensemble of finite size. In small metal grains or semiconductor quantum dots,
the correlations between different eigenvectors lead to enhanced fluctuations of the electronelectron interac
tion matrix elements which become parametrically larger than the nonuniversal fluctuations.
DOI: 10.1103/PhysRevB.66.165310 PACS number s : 73.23. b, 24.60.Ky, 42.25.Dd, 73.21.La
Randommatrix theory has focused on the study of three
ensembles of Hamiltonians: the Gaussian Unitary Ensemble
GUE , the Gaussian Orthogonal Ensemble GOE , and the
Gaussian Symplectic Ensemble GSE . These describe the
statistics of singleparticle energy levels and wave functions
of disordered metal grains or chaotic quantum dots with the
corresponding symmetries; GUE if timereversal symmetry
is broken, and GOE or GSE if timereversal symmetry is
present and spinrotation symmetry is present or absent, re
