Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

Details Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

1998-05-13

arxiv.org/abs/quant-ph/9805038v1

Phys.Rev. E58 (1998) 2894-2901

Physics

Quantum Physics

22 pages, 4 figures

Scientific paper

10.1103/PhysRevE.58.2894

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.

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