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Abstract <p> We consider the Cauchy problem for the two-dimensional massless Dirac equation in graphene with a constant electric field. It is assumed that at the initial time, a localized wave function describes quasi-electrons with momenta lying in the right half-plane. We describe the effect based on the phenomenon of changing the multiplicity of terms (characteristics), which leads to Klein tunneling and consists in the fact that, after some time, a hole component appears in addition to the wave function for the electron component. The components move in opposite directions, and the hole component localizes near a moving point. </p>

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Effects of changing the multiplicity of terms in the Cauchy problem for the Dirac equation in graphene with a constant electric field and a localized initial condition

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • I. A. Bogaevskii,
  • S. Yu. Dobrokhotov,
  • A. A. Tolchennikov

摘要

Abstract

We consider the Cauchy problem for the two-dimensional massless Dirac equation in graphene with a constant electric field. It is assumed that at the initial time, a localized wave function describes quasi-electrons with momenta lying in the right half-plane. We describe the effect based on the phenomenon of changing the multiplicity of terms (characteristics), which leads to Klein tunneling and consists in the fact that, after some time, a hole component appears in addition to the wave function for the electron component. The components move in opposite directions, and the hole component localizes near a moving point.