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An example of physical systems where an electron moves along a closed path is cyclotron motion (details are given in the page of Berry phase). Berry phase must be considered to obtain the correct quantization condition.
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.
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 ...
It is the most widely accepted mechanism for pseudorotation and most commonly occurs in trigonal bipyramidal molecules such as PF 5, though it can also occur in molecules with a square pyramidal geometry. [1] The Berry mechanism is named after R. Stephen Berry, who first described this mechanism in 1960. [2] [3]
The superformula is a generalization of the superellipse and was proposed by Johan Gielis in 2003. [1] Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature.
Goal setting can be guided by goal-setting criteria (or rules) such as SMART criteria. [3] Goal setting is a major component of personal-development and management literature. Studies by Edwin A. Locke and his colleagues, most notably, Gary Latham [ 4 ] have shown that more specific and ambitious goals lead to more performance improvement than ...
In the November 1981 issue of Management Review (AMA Forum), George T. Doran's paper titled "There's a S.M.A.R.T. way to write management's goals and objectives" introduces a framework for setting management objectives, emphasizing the importance of clear goals. [1] [5] The S.M.A.R.T. criteria he proposes are as follows:
[1] [2] Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems ) exhibit a repellor that is the product of the Cantor set and a smooth manifold , and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift ...