Non-Hermitian dynamics of slowly-varying Hamiltonians

Abstract

We develop a theoretical description of non-Hermitian time evolution that accounts for the break- down of the adiabatic theorem. We obtain closed-form expressions for the time-dependent state amplitudes, involving the complex eigen-energies as well as inter-band Berry connections calculated using basis sets from appropriately-chosen Schur decompositions. Using a two-level system as an example, we show that our theory accurately captures the phenomenon of "sudden transitions", where the system state abruptly jumps from one eigenstate to another.

arXiv comment12 pages, 4 figures

References in corpus (39)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Complex Extension of Quantum Mechanics
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Topological energy transfer in an optomechanical system with exceptional points
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-symmetric laser-absorber
• Visualization of Branch Points in PT-Symmetric Waveguides
• Pseudo-Hermitian Representation of Quantum Mechanics
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Robust light transport in non-Hermitian photonic lattices
• Topological invariance and global Berry phase in non-Hermitian systems
• General description of quasi-adiabatic dynamical phenomena near exceptional points
• High-order exceptional points in optomechanics
• Phases of Wave Functions and Level Repulsion
• Sufficiency Criterion for the Validity of the Adiabatic Approximation
• Time evolution of non-Hermitian Hamiltonian systems
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Adiabaticity condition for non-Hermitian Hamiltonians
• Experimental Observation of a Generalized Thouless Pump with a Single Spin
• Chiral state-conversion without encircling an exceptional point
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Geometric Phase in PT-Symmetric Quantum Mechanics
• Stabilizing Non-Hermitian Systems by Periodic Driving
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase
• Parametric instability of non-Hermitian systems near the exceptional point
• Interband Coherence Induced Correction to Adiabatic Pumping in Periodically Driven Systems
• Quantum trajectories for time-dependent adiabatic master equations
• Piecewise Adiabatic Following in Non-Hermitian Cycling
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
• Oscillating potential well in complex plane and the adiabatic theorem

Cited by in corpus (19)

• Topological Classification of Non-Hermitian Hamiltonians
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Non-Hermitian Photonic Lattices: tutorial
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Activity-induced phase transition in a quantum many-body system
• Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Unconventional steady states and topological phases in an open two-level non-Hermitian system
• Exact solutions for time-dependent complex symmetric potential well
• Nonadiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level systems
• Topological Operations Around Exceptional Points via Shortcuts to Adiabaticity
• State conversions around exceptional points
• Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops
• Non-Hermitian magnetic moment