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

References in corpus (17)

• Making Sense of Non-Hermitian Hamiltonians
• A review of progress in the physics of open quantum systems: theory and experiment
• Twofold Transition in PT-Symmetric Coupled Oscillators
• Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Dynamics of quantum systems
• Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
• Phase transitions in open quantum systems
• Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift
• Nearby states in non-Hermitian quantum systems
• Non-Hermitian degeneracy of two unbound states
• Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations
• Phase rigidity and avoided level crossings in the complex energy plane
• Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
• Dynamical stabilization and time in open quantum systems
• Discussion of the adiabatic hypothesis in control schemes using exceptional points
• Clusters of Exceptional Points for a Laser Control of Selective Vibrational Transfer

Cited by in corpus (21)

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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