A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

The relevance of the open quantum system formalism for the description of weakly bound
nuclei far from the valley of stability, small droplets of neutral atoms, gas of trapped atoms …

Assuming the validity of random matrices for describing the statistics of a closed chaotic
quantum system, we study analytically some statistical properties of the S-matrix …

The dynamical signatures of quantum chaos in an isolated system are captured by the
spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the …

The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is
reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by …

We review and further develop the Keldysh functional integral technique for the study of
Lindbladian evolution of many-body driven-dissipative quantum systems. A systematic and …

We consider random non-hermitian matrices in the large-N limit. The power of analytic
function theory cannot be brought to bear directly to analyze non-hermitian random matrices …

We analyse properties of non-Hermitian matrices of size Mconstructed as square
submatrices of unitary (orthogonal) random matrices of size N> M, distributed according to …

We study statistical properties of the eigenvectors of non-Hermitian random matrices,
concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary …

By using the method of orthogonal polynomials, we analyze the statistical properties of
complex eigenvalues of random matrices describing a crossover from Hermitian matrices …