code for Physical Review A publication 2025

This dataset contains Python and SageMath source code used to compute the Liouvillian spectrum in the Scully–Lamb quantum laser model. The Python code numerically diagonalizes a truncated, symmetrized rate matrix to obtain eigenvalues in a fixed off-diagonal sector of the density matrix using efficient tridiagonal routines. The SageMath code solves the two-point connection problem for the confluent Heun equation governing the generating function of density matrix elements. The connection coefficient vanishes at eigenvalues of the rate matrix, enabling independent verification of the spectrum. Both codes accept arbitrary off-diagonal sectors k, and eigenvalues are expressed in units of the decay rate C.