Quantum geometrical effects in non-Hermitian systems
arXiv:2512.07264 · doi:10.1103/qb8s-9c6y
Abstract
We explore the relation between quantum geometry in non-Hermitian systems and physically measurable phenomena. We highlight various situations in which the behavior of a non-Hermitian system is best understood in terms of quantum geometry, namely the notion of adiabatic potentials in non-Hermitian systems and the localization of Wannier states in periodic non-Hermitian systems. Further, we show that the non-Hermitian quantum metric appears in the response of the system upon time-periodic modulation, which one can use to experimentally measure the non-Hermitian quantum metric. We validate our results by providing numerical simulations of concrete exemplary systems.
14 pages, 3 figures
References in corpus (55)
- Topological Insulators
- Topological insulators and superconductors
- Berry Phase Effects on Electronic Properties
- Maximally-localized generalized Wannier functions for composite energy bands
- Making Sense of Non-Hermitian Hamiltonians
- Artificial gauge potentials for neutral atoms
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Localization transitions in non-Hermitian quantum mechanics
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Synthetic magnetic fields for ultracold neutral atoms
- Topological Band Theory for Non-Hermitian Hamiltonians
- Vortex Pinning and Non-Hermitian Quantum Mechanics
- Superfluidity in topologically nontrivial flat bands
- Selective enhancement of topologically induced interface states in a dielectric resonator chain
- Fidelity, dynamic structure factor, and susceptibility in critical phenomena
- A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
- Biorthogonal Quantum Mechanics
- Quantum critical scaling of the geometric tensors
- Orbital magnetization in periodic insulators
- Non-Hermitian topological phenomena: A review
- The Insulating State of Matter: A Geometrical Theory
- Active topological photonics
- Topological invariance and global Berry phase in non-Hermitian systems
- Essay: Where Can Quantum Geometry Lead Us?
- Classifying and measuring the geometry of the quantum ground state manifold
- Non-Hermitian Linear Response Theory
- Geometry and response of Lindbladians
- Extracting the quantum metric tensor through periodic driving
- Topological and geometrical aspects of band theory
- How to Measure the Quantum Geometry of Bloch Bands
- Experimental measurement of the divergent quantum metric of an exceptional point
- Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
- Quantum Geometric Tensor in -Symmetric Quantum Mechanics
- Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
- Non-Hermitian waves in a continuous periodic model and application to photonic crystals
- Quantum metric and wavepackets at exceptional points in non-Hermitian systems
- Information Geometry of Complex Hamiltonians and Exceptional Points
- Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
- Information Geometry and Quantum Phase Transitions in the Dicke Model
- Steady-state Hall response and quantum geometry of driven-dissipative lattices
- Berry phase in atom optics
- From Non-Hermitian Linear Response to Dynamical Correlations and Fluctuation-Dissipation Relations in Quantum Many-Body Systems
- Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids
- Aspects of Berry phase in QFT
- Wave packet dynamics of Bogoliubov quasiparticles: quantum metric effects
- Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
- Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
- Berry-like phases in structured atoms and molecules
- Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
- Quantum metric dependent anomalous velocity in systems subject to complex electric fields
- Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
- Geometric contribution to adiabatic amplification in non-Hermitian systems
- Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models