Loss, Gain, and Singular Points in Open Quantum Systems

Abstract

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 E ≡ + Γ /2 of the non-Hermitian Hamiltonian H coalesce (where is the energy and Γ is the inverse lifetime of the state ). We show that also the eigenfunctions Φ 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 = cr in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

Non-Hermitian flat-band generator in one dimension

“…[45][46][47][48][49][50] Moreover non-Hermitian Hamiltonians can account for coupling with environment in open quantum systems and simplify the analysis reducing the large number of degrees of freedom associated with the environment. [51][52][53] After the discovery that parity-time (PT )-symmetric non-Hermitian Hamiltonians have real eigenvalues, [54][55][56] PT symmetry has been realized in optical systems with gain/loss, 57 leading to an explosion of studies in PT -symmetric non-Hermitian photonics. [58][59][60][61][62][63][64][65][66][67][68] Recently non-Hermitian systems with nontrivial topological properties started to attract attention.…”