Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Geometric_phase> ?p ?o }
- 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 a 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 geometric 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 geometric 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 geometric 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 geometric phase. This mechanics analogue of the geometric phase is known as the Hannay angle.".
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- Geometric_phase wikiPageWikiLink 2DEG.
- Geometric_phase wikiPageWikiLink Adiabatic.
- Geometric_phase wikiPageWikiLink Adiabatic_process.
- Geometric_phase wikiPageWikiLink Adiabatic_process_(quantum_mechanics).
- Geometric_phase wikiPageWikiLink Adiabatic_theorem.
- Geometric_phase wikiPageWikiLink Aharonov–Bohm_effect.
- Geometric_phase wikiPageWikiLink Amplitude.
- Geometric_phase wikiPageWikiLink Berry_connection_and_curvature.
- Geometric_phase wikiPageWikiLink Bohr-Sommerfeld_quantization.
- Geometric_phase wikiPageWikiLink Category:Classical_mechanics.
- Geometric_phase wikiPageWikiLink Category:Quantum_mechanics.
- Geometric_phase wikiPageWikiLink Category:Quantum_phases.
- Geometric_phase wikiPageWikiLink Chern_class.
- Geometric_phase wikiPageWikiLink Classical_mechanics.
- Geometric_phase wikiPageWikiLink Conical_intersection.
- Geometric_phase wikiPageWikiLink Experiment.
- Geometric_phase wikiPageWikiLink Foucault_pendulum.
- Geometric_phase wikiPageWikiLink Frequency.
- Geometric_phase wikiPageWikiLink Gauss_map.
- Geometric_phase wikiPageWikiLink Gauss–Bonnet_theorem.
- Geometric_phase wikiPageWikiLink Gennadi_Sardanashvily.
- Geometric_phase wikiPageWikiLink Geodesic.
- Geometric_phase wikiPageWikiLink Hamiltonian_(quantum_mechanics).
- Geometric_phase wikiPageWikiLink Hannay_angle.
- Geometric_phase wikiPageWikiLink Holonomy.
- Geometric_phase wikiPageWikiLink Interference_(wave_propagation).
- Geometric_phase wikiPageWikiLink Jahn–Teller_effect.
- Geometric_phase wikiPageWikiLink Landau_quantization.
- Geometric_phase wikiPageWikiLink Loop.
- Geometric_phase wikiPageWikiLink Magnetic_field.
- Geometric_phase wikiPageWikiLink Mathematical_singularity.
- Geometric_phase wikiPageWikiLink Measurement.
- Geometric_phase wikiPageWikiLink Michael_Berry_(physicist).
- Geometric_phase wikiPageWikiLink Molecular_geometry.
- Geometric_phase wikiPageWikiLink Momentum_space.
- Geometric_phase wikiPageWikiLink Old_quantum_theory.
- Geometric_phase wikiPageWikiLink Optical_rotation.
- Geometric_phase wikiPageWikiLink Optics.
- Geometric_phase wikiPageWikiLink Parallel_transport.
- Geometric_phase wikiPageWikiLink Parameter_space.
- Geometric_phase wikiPageWikiLink Period_(physics).
- Geometric_phase wikiPageWikiLink Phase_(waves).
- Geometric_phase wikiPageWikiLink Position_and_momentum_space.
- Geometric_phase wikiPageWikiLink Potential_energy_surface.
- Geometric_phase wikiPageWikiLink Quantum_mechanics.
- Geometric_phase wikiPageWikiLink Riemann_curvature_tensor.
- Geometric_phase wikiPageWikiLink S._Pancharatnam.
- Geometric_phase wikiPageWikiLink Sardanashvily.
- Geometric_phase wikiPageWikiLink Simply_connected.
- Geometric_phase wikiPageWikiLink Simply_connected_space.
- Geometric_phase wikiPageWikiLink Single-mode_optical_fiber.
- Geometric_phase wikiPageWikiLink Singularity_(mathematics).
- Geometric_phase wikiPageWikiLink Solid_angle.
- Geometric_phase wikiPageWikiLink Spherical_excess.
- Geometric_phase wikiPageWikiLink Spherical_trigonometry.
- Geometric_phase wikiPageWikiLink Wave.
- Geometric_phase wikiPageWikiLink Waveguide.
- Geometric_phase wikiPageWikiLink Wilson_loop.
- Geometric_phase wikiPageWikiLink Winding_number.
- Geometric_phase wikiPageWikiLinkText "Berry phase".
- Geometric_phase wikiPageWikiLinkText "Berry phases".
- Geometric_phase wikiPageWikiLinkText "Berry's phase".
- Geometric_phase wikiPageWikiLinkText "Berry’s phase".
- Geometric_phase wikiPageWikiLinkText "Geometric phase".
- Geometric_phase wikiPageWikiLinkText "Pancharatnam phase".
- Geometric_phase wikiPageWikiLinkText "geometric phase".
- Geometric_phase date "May 2015".
- Geometric_phase hasPhotoCollection Geometric_phase.
- Geometric_phase reason "Abend status Interlaced parenthesis fault.".
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- Geometric_phase subject Category:Classical_mechanics.
- Geometric_phase subject Category:Quantum_mechanics.
- Geometric_phase subject Category:Quantum_phases.
- Geometric_phase hypernym Difference.
- Geometric_phase type Disease.
- Geometric_phase type Mechanic.
- Geometric_phase type Physic.