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Two spin- 1/ 2 particle system and the fidelity of the geometric phase

Author: WangQi
Tutor: ZhangHongBiao
School: Northeast Normal University
Course: Theoretical Physics
Keywords: Spin Geometric phase Evolution operator SO (6) group Fidelity
CLC: O413.1
Type: Master's thesis
Year: 2009
Downloads: 80
Quote: 0
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Abstract


Throughout the quantum mechanical systems , the quantum geometric phase occupies a very important position . Since Berry in 1984 proposed quantum adiabatic evolution Hamiltion system for a cyclical process there are geometric phase since it caused widespread attention . It has been in nuclear physics , atomic and molecular physics, quantum computers , optics , condensed matter physics and other fields of gauge field theory on the geometric phase done a lot of experiments and theoretical analysis . Already proved that the geometric phase exist in any quantum system evolution , many physicists of the phase was further in-depth study and discussion. This paper studies the two spin particle system geometric phase and fidelity issues . The first part introduces the Berry geometric phase of development overview, basic principles , properties, applications and fidelity overview. The second part , through the so (5) group dynamics system, using tectonic evolution operator coherent state , a magnetic field exists for solving degenerate eigenstates of the system's two spin particle system geometric phase . We introduce a Hamiltonian evolution operator for solving the instantaneous eigenstates and the corresponding eigenvalues ??, use so (6) group and other mathematical tools to construct satisfy certain commutation relations spin-dependent operators. Commutation relations with the Hamiltonian deformation , structural unitary evolution operator , using the Taylor Theorem will deform the unitary evolution operator , then the operator will do the unitary transformation of the matrix elements with respect to time , and then calculating the geometric degenerate space liaison draw geometric phase system . The third part , the use of matrix solution of the system fidelity. The use of matrix direct product and Taylor Theorem and other mathematical means to deform the unitary evolution operator matrix form , so that we get D ~ (ρ), a / dt D ~ (ρ) and a / dt D (ρ) in matrix form , then we get the system by calculating the fidelity .

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory > Quantum mechanics ( wave mechanics,matrix mechanics )
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