Pseudo-Hermitian random matrix ensembles
Mauricio Pato (Universidade de São Paulo, Brazil)
In my talk, I will revise results obtained in an effort to construct ensemble of random matrices which are connected with their adjoint by a similarity transformation. Matrices satisfying this condition have eigenvalues real or complex conjugate and are called pseudo-Hermitian. This condition arose in studies of systems whose Hamiltonians are PT-symmetric invariant, that is, Hamiltonians which though not invariant under the time-reversl and the parity transformations performed isolatedly become invariant when these transformations are combined.