Abstract
In this chapter, we discuss the physical origins of the nonlinearity in quantum many-body systems. Based on the nonlinear Schrödinger equation, we introduce the adiabatic evolution of the quantum states, including both eigenstates and noneigenstates, and we introduce the nonlinear geometric phase acquired by an eigenstate during the adiabatic evolution. A nonlinear two-mode model for Bose-Einstein condensates (BECs) is used to demonstrate the nonlinear adiabatic theory.
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Liu, J., Li, SC., Fu, LB., Ye, DF. (2018). Nonlinear Adiabatic Evolution of Quantum Systems. In: Nonlinear Adiabatic Evolution of Quantum Systems. Springer, Singapore. https://doi.org/10.1007/978-981-13-2643-1_2
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DOI: https://doi.org/10.1007/978-981-13-2643-1_2
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