Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons
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Overview
abstract
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© 2015 American Physical Society. Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of nonlinear QW and show that introducing nonlinearity to QW can lead to a wealth of remarkable possibilities, e.g., simulating nonlinear quantum dynamics, thus enhancing the applicability of QW above the existing level for a universal quantum simulator. As an illustration, we show that the dynamics of a nonlinear Dirac particle can be simulated on an optical nonlinear QW platform implemented with a measurement-based-feedforward scheme. The nonlinear evolution induced by the feed-forward introduces a self-coupling mechanism to (otherwise linear) Dirac particles, which accordingly behave as a soliton. We particularly consider two kinds of nonlinear Dirac equations, one with a scalar-type self-coupling (Gross-Neveu model) and the other with a vector-type one (Thirring model), respectively. Using their known stationary solutions, we confirm that our nonlinear QW framework is capable of exhibiting characteristic features of a soliton. Furthermore, we show that the nonlinear QW enables us to observe and control an enhancement and suppression of the ballistic diffusion.
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author list (cited authors)
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Lee, C., Kurzyński, P., & Nha, H.
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Lee, Chang-Woo||Kurzyński, Paweł||Nha, Hyunchul
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https://hdl.handle.net/1969.1/184576
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http://dx.doi.org/10.1103/PhysRevA.92.052336