Study On The Quantum System Of Berry Phase, A-A Phase And PM Phase

For a long time, the phase problem in quantum mechanics has been widespread concernby theoretical physicists. Geometric phase since found have had a significant impact on thetheoretical and applied aspects of physics. Physical theory includes promotion of opensystems and recycling adiabatic process, the non-adiabatic and non-cycling system, mixedstates, differential collections and gauge field theory, etc., what’s more quantum precisetheoretical calculations and quasi-exact solvability problem for physics experiments directcomparison result is significant. Application areas include molecular physics, condensedmatter and quantum information and computing, etc. In this paper, the use of mathematicalmethods in quantum theory and the theory of generalized linear transformation, to calculatedthe phase of two-level quantum systems and time-dependent multimode coupled quadraticpolynomial Bose system, then analysised the theoretical results, all in all, the theoreticalresults and conclusions have a certain reference value for studies of quantum phase.This thesis contents three aspects, they are as follows,The first aspect is the solving and comparision about quantum phase of half-spin particlesin a rotating magnetic field system. The results are as follows, the three quantum phase andtheir cycling conditions of half-spin particles in a rotating magnetic field system are achieved.When the cycling conditions are reached, PM quantum phase is just the same as the A-Aquantum phase, what’s more Berry phase is the adiabatic approximation of A-A quantumphase or PM quantum phase.The second aspect is the comparison between the tradition conditions of adiabaticapproximation and the new condition of that. The result is that the tradition condition ofadiabatic approximation is the full of unnecessary conditions of adiabatic approximation forthe half-spin particles in a rotating magnetic field system. Also the necessary and sufficientconditions of systematic adiabatic approximation should be confirmed by the strict solution ofthe system itself.The third aspect is about the PM quantum phase and A-A quantum phase abouttime-dependent multimode coupled quadratic polynomial Bose system and the relationshipsbetween both the result reveals that the PM quantum phase also applies to the Non-adiabaticand circulatory system. But only at the condition of t KT, can the PM quantum phase be equal to the A-A quantum phase. This means A-A quantum phase is only meaningful at thecondition of t KTin the cycling system. While at the condition of t KT, the meaningof A-A quantum phase can not be certained.The thesis includes five chapters. Chapter one is introduction of geometric phase, whichcontains the discovery, development and research status of it. It also includes the background,content and significance of this thesis. Chapter two is the basic theory of Berry phase and anexample given to introduce the conception of Berry phase. Chapter three mainly solving andresearch of the half-spin quantum spin magnetic particle’s three kinds of quantum phase, thenthere is comparison between the tradition conditions of adiabatic approximation and the newcondition of that. Chapter four is introduction of the theory of generalized lineartransformation, the only strict solution is calculated by using the method for solving thetime-dependent multimode coupled quadratic polynomial Bose system evolution operator, andcalculate the system’s PM quantum phase, A-A quantum phase, and to study the relationshipbetween these two phases. Chapter five is the main research contents and conclusions of thisthesis...