Spontaneous Decoherence Of Quantum Systems With High Symmetry

Symmetry is a very important concept in physics.Noether’s theorem tells us that if a physical system has a symmetry,then that symmetry corresponds to a conservation law.Mathematically,all the symmetries of the system actually form a symmetric group,and the Hamiltonian of the system does not change under the operation of that group.However,the symmetry of the system is often broken,for example when some additional fields or phase transitions occur,then we need something to measure the symmetry,which we call the degree of symmetry.Previous articles have studied degrees of symmetry based on the definition of the Frobenius norm.We propose an definition of a vector form of the symmetry degree base on this definition.Using this vector form of the symmetry degree,we can distinguish not only the magnitude of the symmetry of the scale that we used before,the frobenius norm,a.nd how the symmetry breaks,but also the different,ways in which it breaks.Not only can we use this definition of a vector form of the symmetry degree for a discrete group of points,but we can do the same for a continuous group.Also related to symmetry is the coherence of the quantum system,which indicates the degree of quantum coherence of the quantum system.Ordinary quantum systems are very unstable,so the coherence will quickly disappear in the external environment.Previous studies have also shown that quantum systems with high symmetry protect coherence to some extent.Our study finds that in some special quantum systems with high symmetry,the degree of coherence destruction is intensified.The reason is that the high symmetry of the boundary introduces a gauge field that cannot be ignored,and this gauge field will make the originally uncoupled part of the center of mass recoupled with the relative moving part,thus intensifying the quantum decoherence.