PT-Symmetric Wave Chaos

Abstract

We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value γ_PT of the gain or loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γ_PT, and show that chaos assists the exact PT phase. Our results have applications to the design of optical elements with PT symmetry.

4 pages, 2 figures

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• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Localization transitions in non-Hermitian quantum mechanics
• PT-Symmetric Quantum Mechanics
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
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Cited by in corpus (76)

• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Non-Hermitian Physics
• The physics of exceptional points
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• Observation of Asymmetric Transport in Structures with Active Nonlinearities
• PT-Symmetric Electronics
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• Optical solitons in $\mathcal{P}\mathcal{T}$-symmetric nonlinear couplers with gain and loss
• PT-Symmetric Talbot Effects
• Observation of Fast Evolution in Parity-Time-Symmetric System
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Experimental realization of Floquet PT-symmetric systems
• Breathers in PT-symmetric optical couplers
• Bypassing the bandwidth theorem with PT symmetry
• Solitons supported by complex PT symmetric Gaussian potentials
• Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry
• Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
• PT Symmetric Aubry-Andre Model
• PT-symmetric quantum Liouvillian dynamics
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Defect Solitons in Parity-Time Symmetric Optical Lattices with Nonlocal Nonlinearity
• Geometric Phase in PT-Symmetric Quantum Mechanics
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Regularization of the spectral singularity in $\mathcal{P}\mathcal{T}$-symmetric systems by all order nonlinearities: Nonreciprocity and optical isolation
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Wave packet evolution in non-Hermitian quantum systems
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Perfect transmission scattering as a PT-symmetric spectral problem
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Statistical PT-symmetric lasing in an optical fiber network
• Quantum Zeno effect and nonclassicality in a PT symmetric system of coupled cavities
• Non-Hermitian quantum systems and their geometric phases
• Directed momentum current induced by the PT-symmetric driving
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Generic examples of PT-symmetric qubit (spin 1/2) Liouvillians
• Probability Density in the Complex Plane
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Defect solitons supported by nonlocal PT symmetric superlattices
• Deconfinement to Confinement as PT phase transition
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems
• Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Piecewise Adiabatic Following in Non-Hermitian Cycling
• PT phase transition in a (2+1)-d relativistic system
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Non-Hermitian noncommutative quantum mechanics
• Localization of Chaotic Resonance States due to a Partial Transport Barrier
• Chaotic diffusion of complex trajectory and its quantum signature
• Imaginary Potential Induced Quantum Coherence for Bose-Einstein Condensates
• Entangled Quantum State Discrimination using Pseudo-Hermitian System
• On regular and chaotic dynamics of a non-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
• Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
• Pseudo PT symmetric lattice
• Spin Josephson effects of spin-orbit-coupled Bose-Einstein condensates in a non-Hermitian double well
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
• PT-Symmetry Breaking Transitions in Polymeric Systems
• Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors
• Instantaneous modulations in time-varying complex optical potentials
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model
• Monopoles in non-Hermitian systems
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Synchronization in PT-symmetric optomechanical resonators
• A non-Hermitian PT-symmetric kicked top
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States