Nonlinear Adiabatic Evolution of Quantum Systems by Jie Liu & Sheng-Chang Li & Li-Bin Fu & Di-Fa Ye

Author:Jie Liu & Sheng-Chang Li & Li-Bin Fu & Di-Fa Ye
Language: eng
Format: epub
ISBN: 9789811326431
Publisher: Springer Singapore

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We now consider that the external field changes with time, and we use the dimensionless adiabatic parameter to measure its rate of change. Furthermore, we assume that is small enough that—according to the adiabatic evolution condition in mean-field models [5, 6]—the system, which is initially in an eigenstate of , can remain in this eigenstate and can thus evolve simultaneously with . When returns to its initial value, the system acquires a mean-field Berry phase . Here, we note that because includes and is thus state dependent, cannot be expressed in the conventional form, i.e., , where L is the evolution loop of the system in the parameter space. To obtain the expression for , we use the method introduced in [7] to separate the -related term from the expression for . To proceed, we first note that because the adiabatic parameter is small but finite, the system fluctuates around the eigenstate during the evolution, which implies that and , where . Then, from (4.4), (4.7), and (4.8), we obtain

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