Adiabatic Geometric Phase for a General Quantum States

Abstract

A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems. Furthermore, this new phase is related to Hannay's angles as we find that these angles, a classical concept, can arise naturally in quantum systems. The results are demonstrated with a two-level model.

4 pages, 2 figures

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• Adiabaticity in nonreciprocal Landau-Zener tunneling
• Geometric phase with full-wedge and half-wedge rotation in nonlinear frequency conversion
• Berry Phase and Hannay's Angle in a Quantum-Classical Hybrid System
• Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation
• Thomas Precession for Dressed Particles
• Loschmidt echo and Berry phase around degeneracies in nonlinear systems
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• Anomalous Monopole In an Interacting Boson System
• Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators
• Probing Wigner Rotations for Any Group
• Dynamical fluctuations in classical adiabatic processes: General description and their implications
• Phase space hybrid theory of quantum measurement with nonlinear and stochastic dynamics
• Orbits of hybrid systems as qualitative indicators of quantum dynamics
• Cosmology emerging as the gauge structure of a nonlinear quantum system
• Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection
• On adiabatic evolution for a general time-dependent quantum system