Exceptional points, phase rigidity and nonlinear Schrodinger equation

Hichem Eleuch, Ingrid Rotter

The natural environment of a localized quantum system is the continuum of scattering wavefunctions into which the system is embedded. It can be changed by external fields, however never be deleted. The control of the system’s properties by varying a certain parameter provides us information on the system. It is, in many cases, counterintuitive and points to the same phenomena in different systems in spite of the specific differences between them. In our paper, we use a schematic model in order to simulate the main features of small open quantum systems. At low level density, the system is described well by standard Hermitian quantum physics while fundamental differences appear at high level density due to the non-Hermiticity of the Hamiltonian which cannot be neglected under this condition. The influence of exceptional points, the phase rigidity of the wavefunctions and the nonlinearities in the equations are discussed by means of different numerical and (when possible) analytical results. The transition from a closed system at low level density to an open one at high level density occurs smoothly.

Quantum Physics (quant-ph)

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