Loss, gain, and singular points in open quantum systems
Summary: Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues \(\mathcal{E}_i \equiv E_i + i \Gamma_i / 2\) of the non-Hermitian Hamiltonian \(\mathcal{H}\) coalesce (where \(E_i\) is the energy and \(\Gamma_i\) is the inverse lifetime of the state \(i\)). We show that also the eigenfunctions \(\Phi_i\) of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points \(a = a^{\text{cr}}\) in the parameter space, the biorthogonal eigenfunctions of \(\mathcal{H}\) become orthogonal. For illustration, we show characteristic numerical results.
scientific article; zbMATH DE number 6991952