Nonlinear Landau-Zener tunneling in Majorana’s stellar representation
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By representing the evolution of a quantum state with the trajectories of the stars on a Bloch sphere, the Majorana’s stellar representation provides an intuitive way to understand quantum motion in a high dimensional projective Hilbert space. In this work we show that the Majorana’s representation offers a very interesting and intuitive way to understand the nonlinear Landau-Zener tunneling. In particular, the breakdown of adiabaticity in this tunneling phenomenon can be understood as some of the stars never reaching the south pole. We also establish a connection between the Majorana stars in the second quantized model and the single star in the mean field model by using the reduced density matrix.
- 3.R. Penrose, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford University Press, Oxford, 1990)Google Scholar