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The concept was first introduced by S. Pancharatnam [1] as geometric phase and later elaborately explained and popularized by Michael Berry in a paper published in 1984 [2] emphasizing how geometric phases provide a powerful unifying concept in several branches of classical and quantum physics.
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.
Recently there was a generalization of this formula for arbitrary matrix Hamiltonians that involves a Berry phase-like term stemming from spin or other internal degrees of freedom. [9] The index distinguishes the primitive periodic orbits: the shortest period orbits of a given set of initial conditions.
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.
Phase retrieval is a key component of coherent diffraction imaging (CDI). In CDI, the intensity of the diffraction pattern scattered from a target is measured. The phase of the diffraction pattern is then obtained using phase retrieval algorithms and an image of the target is constructed.
A generalization was next introduced as the Fortuin–Kasteleyn random cluster model, which has many connections with the Ising model and other Potts models. Bernoulli (bond) percolation on complete graphs is an example of a random graph. The critical probability is p = 1 / N , where N is the number of vertices (sites) of the graph.
They became popular again at the end of the 19th century, perhaps the first example being the idea of enhanced viscosity of Osborne Reynolds, as a way to explain turbulence. The renormalization group was initially devised in particle physics, but nowadays its applications extend to solid-state physics , fluid mechanics , physical cosmology ...
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 .