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In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions in the parameter space, and has proven to be an essential physical ingredient for understanding a variety of electronic properties.
In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. [1] It was devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger in 1979, to describe the increase of electrical conductivity of polyacetylene polymer chain when doped, based on the existence of solitonic defects.
Sir Michael Victor Berry (born 14 March 1941) is a British theoretical physicist.He is the Melville Wills Professor of Physics (Emeritus) at the University of Bristol.. He is known for the Berry phase, a phenomenon observed in both quantum mechanics and classical optics, as well as Berry connection and curvature.
The phenomenon was independently discovered by S. Pancharatnam (1956), [2] in classical optics and by H. C. Longuet-Higgins (1958) [3] in molecular physics; it was generalized by Michael Berry in (1984). [4] It is also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase.
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 ...
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.
Subsequent work has strongly borne out the connection between the distribution of the zeros of the Riemann zeta function and the eigenvalues of a random Hermitian matrix drawn from the Gaussian unitary ensemble, and both are now believed to obey the same statistics. Thus the Hilbert–Pólya conjecture now has a more solid basis, though it has ...
The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel.Levi-Civita, [1] along with Gregorio Ricci-Curbastro, used Christoffel's symbols [2] to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the modern notion of holonomy.