Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons

Chang Woo Lee, Paweł Kurzyński, Hyunchul Nha

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12 Citations (Scopus)


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.

Original languageEnglish
Article number052336
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
Publication statusPublished - 30 Nov 2015


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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