Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation

DOI10.1063/1.2968344zbMath1152.81556arXiv0807.3405OpenAlexW2089005763MaRDI QIDQ5505011

Hossein Mehri-Dehnavi, Ali Mostafazadeh

Publication date: 23 January 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.3405

Mathematics Subject Classification ID

Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (12)

Information geometry of complex Hamiltonians and exceptional points ⋮ Bloch vector, disclination and exotic quantum holonomy ⋮ Classical correspondence of the exceptional points in the finite non-Hermitian system ⋮ A Unifying E2-Quasi Exactly Solvable Model ⋮ Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions ⋮ Topological adiabatic dynamics in classical mass-spring chains with clamps ⋮ Geometric Criterion of Topological Phase Transition for Non‐Hermitian Systems ⋮ Floquet exceptional points and chirality in non-Hermitian Hamiltonians ⋮ The need for a flat higher gauge structure to describe a Berry phase associated with some resonance phenomena ⋮ A unified view on geometric phases and exceptional points in adiabatic quantum mechanics ⋮ Thermodynamic geometry of Kaniadakis statistics ⋮ Adiabatic theorem and generalized geometrical phase in the case of pseudo-Hermitian systems

Cites Work

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• Generalized adiabatic product expansion: A nonperturbative method of solving the time-dependent Schrödinger equation
• Berry phase of a resonant state
• Unfolding a diabolic point: a generalized crossing scenario
• Exceptional points of non-Hermitian operators
• Introduction to Topological Manifolds
• Observation of exceptional points in electronic circuits
• Noncyclic geometric phase and its non-Abelian generalization
• Projective Hilbert space structures at exceptional points

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