We study quantum adiabatic dynamics, where the slowly moving field is influenced by the system's state (feedback). The feedback is achieved either via mean-field quantum-classical interaction, or, alternatively, via non-disturbing measurements done on an ensemble of identical non-interacting systems. The situation without feedback is governed by the adiabatic theorem: adiabatic energy level populations stay constant, while the adiabatic eigenvectors get a specific phase contribution (Berry phase). However, under feedback the adiabatic theorem does not hold: the adiabatic populations satisfy a closed equation of motion that coincides with the replicator dynamics known by its numerous applications in evolutionary game theory. The feedback generates a new gauge-invariant adiabatic phase, which is free of the constraints on the Berry phase ( e.g. , the new phase is non-zero even for real adiabatic eigenfunctions). In a particular case the adiabatic theorem can still hold, but the new phases are non-trivial.We study quantum adiabatic dynamics, where the slowly moving field is influenced by the system's state (feedback). The feedback is achieved either via mean-field quantum-classical interaction, or, alternatively, via non-disturbing measurements done on an ensemble of identical non-interacting systems. The situation without feedback is governed by the adiabatic theorem: adiabatic energy level populations stay constant, while the adiabatic eigenvectors get a specific phase contribution (Berry phase). However, under feedback the adiabatic theorem does not hold: the adiabatic populations satisfy a closed equation of motion that coincides with the replicator dynamics known by its numerous applications in evolutionary game theory. The feedback generates a new gauge-invariant adiabatic phase, which is free of the constraints on the Berry phase ( e.g. , the new phase is non-zero even for real adiabatic eigenfunctions). In a particular case the adiabatic theorem can still hold, but the new phases are non-trivial.

arXiv:0804.1643Europhysics Letters (EPL)Nov 1, 20085 citations

The stability of Berry's phases

Stefan Giller, Cezary Gonera, Piotr Kosiński +1 more

Physics Letters ADec 1, 19940 citations

Berry Phases and Curvatures

David H. Vanderbilt

Cambridge University Press eBooksOct 26, 20182 citations

Berry Phases of Classical Trajectories in the Presence of Hard-Wall Boundaries

Hsiu‐Hau Lin, Tzay-Ming Hong

We study the quantum propagator in the semiclassical limit with hard-wall potentials. We show that, upon each reflection by the hard wall, a Berry phase $π$ is accumulated and leads to interferences between different classical trajectories. Including the Berry phase caused by the hard walls, the modified Van Vleck's formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a new quantization rule that applies to {\it both} smooth and sharp boundary potentials. It provides an easy way to compute quantized energies in the semiclassical limit and is extremely useful for many physical systems.We study the quantum propagator in the semiclassical limit with hard-wall potentials. We show that, upon each reflection by the hard wall, a Berry phase $π$ is accumulated and leads to interferences between different classical trajectories. Including the Berry phase caused by the hard walls, the modified Van Vleck's formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a new quantization rule that applies to {\it both} smooth and sharp boundary potentials. It provides an easy way to compute quantized energies in the semiclassical limit and is extremely useful for many physical systems.

arXiv:cond-mat/0106393Jun 20, 20010 citations

Berry's Phase and Some of its Consequences

Brian K. Kendrick

Jan 1, 19920 citations

We study the quantum propagator in the semiclassical limit with hard-wall potentials. We show that, upon each reflection by the hard wall, a Berry phase

π

is accumulated and leads to interferences between different classical trajectories. Including the Berry phase caused by the hard walls, the modified Van Vleck's formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a new quantization rule that applies to {\it both} smooth and sharp boundary potentials. It provides an easy way to compute quantized energies in the semiclassical limit and is extremely useful for many physical systems.