Superradiance in finite quantum systems randomly coupled to continuum

Stránský, Pavel; Cejnar, Pavel

doi:10.1103/physreve.100.042119

Cited by 3 publications

(1 citation statement)

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“…Moreover, relevance of EPs in the context of quantum chaos and quantum phase transitions has been demonstrated theoretically [12,[38][39][40][41][42][43][44][45][46][47][48]. The role of EPs in the superradiance phenomenon has also been recognized [49,50]. Higher order EPs have been explored e.g.…”

Section: Introductionmentioning

confidence: 99%

Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians

Šindelka

Stránský

Cejnar

2023

J. Phys. A: Math. Theor.

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We study exceptional points (EPs) of a nonhermitian Hamiltonian $\hat{H}\n(\lambda,\delta)$ whose parameters $\lambda \in {\mathbb C}$and $\delta \in {\mathbb R}$. As the real control parameter $\delta$ is varied, the $k$-th EP (or $k$-th cluster of simultaneously existing EPs)of $\hat{H}\n(\lambda,\delta)$ moves in the complex plane of $\lambda$ along a continuous trajectory, $\lambda_k(\delta)$.Using an appropriate non-hermitian formalism (based upon the $c$-product and not upon the conventional Dirac product), wederive a self contained set of equations of motion (EOM) for the trajectory $\lambda_k(\delta)$, while interpreting $\delta$ as the propagationtime. Such EOM become of interest whenever one wishes to study the response of EPs to external perturbations or continuous parametric changes ofthe pertinent Hamiltonian. This is e.g.~the case of EPs emanating from hermitian curve crossings/degeneracies (which turn into avoidedcrossings/near-degeneracies when the Hamiltonian parameters are continuously varied). The presented EOM for EPs have not only their theoreticalmerits, they possess also a substantial practical relevance. Namely, the just presented approach can be regarded even as an efficient numericalmethod, useful for generating EPs for a broad class of complex quantum systems encountered in atomic, nuclear and condensed matter physics. Performance of such a method is tested here numerically on a simple yet nontrivial toy model.

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