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- Geometric_phase abstract "In classical and quantum mechanics, the geometric phase, Pancharatnam–Berry phase (named after S. Pancharatnam and Sir Michael Berry), Pancharatnam phase or most commonly Berry phase, is a phase difference acquired overthe course of a cycle, when the system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Hamiltonian. The phenomenon was first discovered in 1956, and rediscovered in 1984. It can be seen in the Aharonov–Bohm effect and in the conical intersection of potential energy surfaces. In the case of the Aharonov–Bohm effect, the adiabatic parameter is the magnetic field enclosed by two interference paths, and it is cyclic in the sense that these two paths form a loop. In the case of the conical intersection, the adiabatic parameters are the molecular coordinates. Apart from quantum mechanics, it arises in a variety of other wave systems, such as classical optics. As a rule of thumb, it can occur whenever there are at least two parameters characterizing a wave in the vicinity of some sort of singularity or hole in the topology; two parameters are required because either the set of nonsingular states will not be simply connected, or there will be nonzero holonomy.Waves are characterized by amplitude and phase, and both may vary as a function of those parameters. The Berry phase occurs when both parameters are changed simultaneously but very slowly (adiabatically), and eventually brought back to the initial configuration. In quantum mechanics, this could involve rotations but also translations of particles, which are apparently undone at the end. One might expect that the waves in the system return to the initial state, as characterized by the amplitudes and phases (and accounting for the passage of time). However, if the parameter excursions correspond to a loop instead of a self-retracing back-and-forth variation, then it is possible that the initial and final states differ in their phases. This phase difference is the Berry phase, and its occurrence typically indicates that the system's parameter dependence is singular (its state is undefined) for some combination of parameters.To measure the Berry phase in a wave system, an interference experiment is required. The Foucault pendulum is an example from classical mechanics that is sometimes used to illustrate the Berry phase. This mechanics analogue of the Berry phase is known as the Hannay angle.".
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- Geometric_phase wikiPageExternalLink 2.pdf.
- Geometric_phase wikiPageExternalLink PreprintRflash.pdf.
- Geometric_phase wikiPageExternalLink 794.
- Geometric_phase wikiPageExternalLink cats.ps.
- Geometric_phase wikiPageExternalLink molphys40,1011.pdf.
- Geometric_phase wikiPageExternalLink berryphase.html.
- Geometric_phase wikiPageID "323137".
- Geometric_phase wikiPageRevisionID "602976886".
- Geometric_phase hasPhotoCollection Geometric_phase.
- Geometric_phase subject Category:Classical_mechanics.
- Geometric_phase subject Category:Quantum_mechanics.
- Geometric_phase subject Category:Quantum_phases.
- Geometric_phase comment "In classical and quantum mechanics, the geometric phase, Pancharatnam–Berry phase (named after S. Pancharatnam and Sir Michael Berry), Pancharatnam phase or most commonly Berry phase, is a phase difference acquired overthe course of a cycle, when the system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Hamiltonian. The phenomenon was first discovered in 1956, and rediscovered in 1984.".
- Geometric_phase label "Berry-Phase".
- Geometric_phase label "Fase di Berry".
- Geometric_phase label "Fase geométrica".
- Geometric_phase label "Geometric phase".
- Geometric_phase label "Geometrische fase".
- Geometric_phase label "Phase géométrique".
- Geometric_phase label "Фаза Берри".
- Geometric_phase sameAs Berry-Phase.
- Geometric_phase sameAs Fase_geométrica.
- Geometric_phase sameAs Phase_géométrique.
- Geometric_phase sameAs Fase_di_Berry.
- Geometric_phase sameAs 기하학적_위상.
- Geometric_phase sameAs Geometrische_fase.
- Geometric_phase sameAs m.01vsl3.
- Geometric_phase sameAs Q3283.
- Geometric_phase sameAs Q3283.
- Geometric_phase wasDerivedFrom Geometric_phase?oldid=602976886.
- Geometric_phase isPrimaryTopicOf Geometric_phase.