The crossover between orthogonal and unitary symmetry in small disordered systems: a supersymmetry approach

Universal correlations in vibrational spectra of complex crystals

“…It is apparent from this plot that the crossover between two distinct limits -from GOE to GUE -takes place at relatively small values of |Q| (which is the parameter responsible for the imaginary part of a dynamical matrix). A high sensitivity of correlations in the spectrum of optical phonons in a complex crystal to the rise of an imaginary part of D is in agreement with what is known about the crossover between GOE and GUE symmetry classes in chaotic electronic billiards [6], and it seems that it cannot be reduced to a trivial mixing of two typical (GOE and GUE) distribution functions [7][8][9].…”

Ergodicity of Unitary Random-Matrix Ensembles

“…(9) and (12). To simplify the following discussion, we explicitly display the fact that the integration over all the angles % : sj is done after the integration over all other variables have been performed and write the integrals I l 3 l 4 [ f ] in the form …”

“…A first substantial simplification arises when we adopt the procedure developed in Ref. [9]. We write the coset matrices T as the product of two matrices T C and T D ,…”

Asymptotic Expansion for the Magnetoconductance Autocorrelation Function

“…Motivated by the paper by Altland et al [18], we write our coset matrices T as products of matrices T I obtained by exponentiating the coset generators anticommuting with { 3 , and matrices T 0 obtained by exponentiating the coset generators commuting with { 3 ,…”