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andresB
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Are there theorems for sufficient and necessary conditions for the vanishing of Berry and/or Wilzeck-Zee phases for a given quantum mechanical system?
A geometrical phase in quantum mechanics is a phase shift that occurs when a quantum system undergoes a cyclic evolution. It is a purely quantum effect that arises due to the geometric properties of the system's state space.
The conditions for the vanishing of geometrical phases in quantum mechanics are a closed quantum system, a cyclic evolution, and a degenerate energy spectrum. Additionally, the system must not experience any external perturbations that break the cyclic symmetry.
Yes, geometrical phases can be experimentally observed through several techniques such as interferometry and nuclear magnetic resonance. These experiments have confirmed the existence of geometrical phases and their dependence on the system's geometric properties.
Yes, geometrical phases have practical applications in quantum computing and quantum information processing. They can also be used to study the geometric properties of materials and to control quantum systems through geometric manipulation.
Geometrical phases are purely quantum effects that arise due to the geometric properties of a system's state space, while dynamical phases arise due to the time evolution of a quantum system. Geometrical phases are independent of the system's energy, while dynamical phases are dependent on it.