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Abstract <p>In this work we investigate a one-dimensional quantum-mechanical model with a complicated kinetic term which is similar to a dispersion relation for electrons in graphene. External potential is chosen to be harmonic. For this system we develop a path integral formalism in the space of wavenumbers and obtain a relation similar to Feynman–Kac formula. We performed a numerical simulation via a Hybrid Monte Carlo method. Ground state energy was obtained. We demonstrate that in wavenumber space instantons between Dirac cones are present. To supplement these results, we numerically solve Shrodinger equation in <i>k</i>-representation, which allowed us to determine energy spectra and wavefunctions for coordinate traps of different strength. It is shown that because of non-trivial dispersion relation the system exhibits ground state splitting, despite the coordinate trap being harmonic.</p>

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Two-Level Quantum System Based on Electronic Excitations in Graphene in a Harmonic Trap

  • 期刊论文

  • 发表日期：

    2025年12月21日

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  • A. M. Ulianov,
  • O. V. Pavlovsky

摘要

Abstract

In this work we investigate a one-dimensional quantum-mechanical model with a complicated kinetic term which is similar to a dispersion relation for electrons in graphene. External potential is chosen to be harmonic. For this system we develop a path integral formalism in the space of wavenumbers and obtain a relation similar to Feynman–Kac formula. We performed a numerical simulation via a Hybrid Monte Carlo method. Ground state energy was obtained. We demonstrate that in wavenumber space instantons between Dirac cones are present. To supplement these results, we numerically solve Shrodinger equation in k-representation, which allowed us to determine energy spectra and wavefunctions for coordinate traps of different strength. It is shown that because of non-trivial dispersion relation the system exhibits ground state splitting, despite the coordinate trap being harmonic.