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In quantum mechanics, the Berry phase arises in a cyclic adiabatic evolution. The quantum adiabatic theorem applies to a system whose Hamiltonian H ( R ) {\displaystyle H(\mathbf {R} )} depends on a (vector) parameter R {\displaystyle \mathbf {R} } that varies with time t {\displaystyle t} .
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.
It is generally argued that the Aharonov–Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, in quantum mechanics.Classically it was possible to argue that only the electromagnetic fields are physical, while the electromagnetic potentials are purely mathematical constructs, that due to gauge freedom are not even unique for a given electromagnetic field.
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.
In classical mechanics, the Hannay angle is a mechanics analogue of the geometric phase (or Berry phase). It was named after John Hannay of the University of Bristol, UK. Hannay first described the angle in 1985, extending the ideas of the recently formalized Berry phase to classical mechanics. [1]
An example of a canonical quantum phase transition is the well-studied Superconductor Insulator Transition in disordered thin films which separates two quantum phases having different symmetries. Quantum magnets provide another example of QPT. The discovery of new quantum phases is a pursuit of many scientists.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
For states of sufficiently high energy, Berry's conjecture states that energy eigenfunctions in this many-body system of hard sphere particles will appear to behave as superpositions of plane waves, with the plane waves entering the superposition with random phases and Gaussian-distributed amplitudes [1] (the precise notion of this random ...