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  2. Berry connection and curvature - Wikipedia

    en.wikipedia.org/wiki/Berry_connection_and_curvature

    In this case, the Berry phase corresponding to any given path on the unit sphere in magnetic-field space is just half the solid angle subtended by the path. The integral of the Berry curvature over the whole sphere is therefore exactly 2 π {\displaystyle 2\pi } , so that the Chern number is unity, consistent with the Chern theorem.

  3. Geometric phase - Wikipedia

    en.wikipedia.org/wiki/Geometric_phase

    There are several important aspects of this generalization of Berry's phase: 1) Instead of the parameter space for the original Berry phase, this Ning-Haken generalization is defined in phase space; 2) Instead of the adiabatic evolution in quantum mechanical system, the evolution of the system in phase space needs not to be adiabatic.

  4. Hannay angle - Wikipedia

    en.wikipedia.org/wiki/Hannay_angle

    The Hannay angle is defined in the context of action-angle coordinates.In an initially time-invariant system, an action variable is a constant. After introducing a periodic perturbation (), the action variable becomes an adiabatic invariant, and the Hannay angle for its corresponding angle variable can be calculated according to the path integral that represents an evolution in which the ...

  5. Common integrals in quantum field theory - Wikipedia

    en.wikipedia.org/wiki/Common_integrals_in...

    4 Integrals that can be approximated by the method of stationary phase. ... Download as PDF; Printable version ... it is now easy to see the generalization to the ...

  6. Berry mechanism - Wikipedia

    en.wikipedia.org/wiki/Berry_mechanism

    Trigonal bipyramidal molecular shape ax = axial ligands (on unique axis) eq = equatorial ligand (in plane perpendicular to unique axis). The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerize by exchanging the two axial ligands (see the figure) for two of the equatorial ones.

  7. Phase retrieval - Wikipedia

    en.wikipedia.org/wiki/Phase_retrieval

    In this way, phase retrieval allows for the conversion of a diffraction pattern into an image without an optical lens. Using phase retrieval algorithms, it is possible to characterize complex optical systems and their aberrations. [6] For example, phase retrieval was used to diagnose and repair the flawed optics of the Hubble Space Telescope ...

  8. Berry phase - Wikipedia

    en.wikipedia.org/?title=Berry_phase&redirect=no

    What links here; Related changes; Upload file; Special pages; Permanent link; Page information; Cite this page; Get shortened URL; Download QR code

  9. Symplectic manifold - Wikipedia

    en.wikipedia.org/wiki/Symplectic_manifold

    Symplectic manifolds arise from classical mechanics; in particular, they are a generalization of the phase space of a closed system. [1] In the same way the Hamilton equations allow one to derive the time evolution of a system from a set of differential equations, the symplectic form should allow one to obtain a vector field describing the flow of the system from the differential of a ...