Clustering of exceptional points and dynamical phase transitions

Abstract

The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a non-analytical behavior at singular (exceptional) points (EPs). The eigenfunctions are biorthogonal, in contrast to the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure for the ratio between biorthogonality and orthogonality is the phase rigidity of the wavefunctions. At and near an EP, the phase rigidity takes its minimum value. The lifetimes of two nearby eigenstates of a quantum system bifurcate under the influence of an EP. When the parameters are tuned to the point of maximum width bifurcation, the phase rigidity suddenly increases up to its maximum value. This means that the eigenfunctions become almost orthogonal at this point. This unexpected result is very robust as shown by numerical results for different classes of systems. Physically, it causes an irreversible stabilization of the system by creating local structures that can be described well by a Hermitian Hamilton operator. Interesting non-trivial features of open quantum systems appear in the parameter range in which a clustering of EPs causes a dynamical phase transition.

A few improvements; 2 references added; 28 pages; 7 figures

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• High-order exceptional points in supersymmetric arrays
• Topological photonic states in one-dimensional dimerized ultracold atomic chains
• Topological phonon polaritons in one-dimensional non-Hermitian nanoparticle chains
• Hybrid exceptional point created from type III Dirac point
• Gain and loss in open quantum systems
• Exceptional points as signatures of dynamical magnetic phase transitions
• Nonclassical Attack on a Quantum KeyDistribution System
• Exceptional points in Fermi liquids with quadrupolar interactions
• Characterizing and Tuning Exceptional Points Using Newton Polygons
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Impact of non-Hermitian Mode interaction on Inter-cavity Light transfer
• Correlated Nonreciprocity around Conjugate Exceptional Points
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Critical points in two-channel quantum systems
• Emergent non-Hermitian conservation laws at exceptional points
• Three State Quantum System Exhibiting Third Order Exceptional Singularities and Flip-of-States