Phase Under Generalized Uncertainty Principle

Since the discovery of geometric phase in 1984,it has exerted a great influence on the theory and application of physics.There are extensive theoretical researches,such as:the initial adiabatic and cyclic processes,then extended to non-adiabatic and non-cyclic,then studied mixed states,non-diagonal terms,geometric phases of open systems,and it is also closely related to differential geometry and gauge field theory.Its application also touches almost every aspect of physical research.Both molecular physics and condensed matter physics,as well as quantum information and computation,have geometric phases.Up to now,geometric phase has become a hot topic that has attracted much attention and many scholars are keen to study.At present,the research on geometric phase is based on common quantum theory.However,recent studies on quantum gravity,string theory and black hole physics show that under the high energy standard,the general The Uncertainty Principle should be replaced by the generalized The Uncertainty Principle.In double special relativity,in order to keep the characteristic energy based on the speed of light and Planck scale constant,the maximum momentum must exist.The introduction of minimum measurable length and maximum momentum naturally solves the divergence problem in quantum field theory.Under the generalized The Uncertainty Principle,in general,the Hamiltonian quantum mechanics of any quantum system will be modified accordingly.Therefore.,the generalized The Uncertainty Principle will affect the quantum behavior of the system.Quantum gravity under generalized The Uncertainty Principle has been extensively studied in various fields,including statistical physics,field theory,cosmology and black hole physics.However,there is still a lack of research on the phase problem under the generalized The Uncertainty Principle.In order to further expand the understanding of the phase under generalized The Uncertainty Principle and explore the influence of generalized The Uncertainty Principle on phase,I have carried out the research on the properties of phase under generalized The Uncertainty Principle and related issues in this work.My work mainly focuses on the following aspects.Firstly,considering the generalized Uncertainty Principle between the time and Hamiltonian,we studied the quantum behavior of dipole neutral particles with permanent electric moment and magnetic moment in magnetic and electric fields,and obtained the corresponding system wave function and probability current density.Based on this,we derived the corresponding Hall conductivity.The results show that the Hall conductivity of neutral particles with permanent electric moment and magnetic moment dipole depends on GUP parameter.Especially when GUP parameter is zero,the obtained results will return to the case of ordinary quantum mechanics.Secondly,based on the generalized The Uncertainty Principle between time and Hamiltonian,we studied the geometric phase formed by neutrinos propagating in adiabatic change’s magnetic field.The study found that the generalized theory would cause the system eigenvalue to change,but had no effect on the geometric phase.Thirdly,under the generalized The Uncertainty Principle between time and Hamiltonian,we studied the acyclic geometric phasesφveg(z)andφvμg(z)propagating in neutrino matter.In addition,considering the resonance between different neutrinos,φve-vμg(z)and φvμ-veg(z)phases in the mutual resonance process are also derived,and the influence of GUP parameters on them is analyzed.At the end of this article,I made a summary and outlook.