How to Geometric phase?

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In classical and quantum mechanics, the geometric phase is a phase difference acquired over the 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 independently discovered by S. Pancharatnam (1956) and by H. C. Longuet-Higgins (1958) and later generalized by Sir M. Berry (1984). It is also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase. 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.

Phase arrays exploiting geometry phase and methods of creating such arrays

InactiveUS20070285315A1Reduce couplingMulti-channel direction-finding systems using radio wavesBeacon systemsEngineeringArray element

In the context of array sensors such as radar, sonar, and communications receiver arrays, the present invention exploits the geometry phase components of radiated wavefronts associated with the signals of interest in order to reduce the bandwidth requirements for DOA and beamforming processing. Additionally, geometry phase is exploited in order to effectively increase the resolution of an array without changing the size of its physical footprint or the number of array elements. Other embodiments of the invention include the use of virtual array elements for increase in effective array size.

41 results about "Geometric phase" patented technology

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