Fermion Doubling in Dirac Quantum Walks

• URL: http://arxiv.org/abs/2601.15885v1
• Date: Thu, 22 Jan 2026 12:01:04 GMT
• Title: Fermion Doubling in Dirac Quantum Walks
• Abstract summary: We consider discrete spacetime models known as quantum walks, which can be used to simulate Dirac particles.<n>We consider fermion doubling in these models, in which high momentum states yield additional low energy solutions which behave like Dirac particles.<n>We also consider pseudo-doublers, which have high energy but behave like low energy Dirac particles, and cause potential problems regarding the stability of the vacuum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider discrete spacetime models known as quantum walks, which can be used to simulate Dirac particles. In particular we look at fermion doubling in these models, in which high momentum states yield additional low energy solutions which behave like Dirac particles. The presence of doublers carries over to the `second quantised' version of the walks represented by quantum cellular automata, which may lead to spurious solutions when introducing interactions. Moreover, we also consider pseudo-doublers, which have high energy but behave like low energy Dirac particles, and cause potential problems regarding the stability of the vacuum. To address these issues, we propose a family of quantum walks, that are free of these doublers and pseudo-doublers, but still simulate the Dirac equation in the continuum limit. However, there remain a small number of additional low energy solutions which do not directly correspond to Dirac particles. While the conventional Dirac walk always has a zero probability for the walker staying at the same point, we obtain the family of walks by allowing this probability to be non-zero.

Related papers

• Tangent fermions can restore vacuum stability of discrete-time Dirac models [0.0]
  We show that an alternative discretization scheme, with a tangent rather than a sine dispersion relation, offers stability while retaining a single Dirac cone.<n>The key step is the Cayley transformation from the unit circle of Floquet eigenvalues $e-ivarepsilon$ to the real line of energies $E=2tan(varepsilon/2)$.<n>We compute the Schwinger effect (particle-hole pair creation in a uniform electric field) for tangent fermions and show that the pair-production rate agrees with the continuum result for a single Dirac cone
  arXiv  Detail & Related papers  (2026-09-01T10:27:21Z)
• Fragile single-cone Dirac quantum walks in two dimensions [0.0]
  We show that the analogous 2D construction is fundamentally more fragile.<n>We demonstrate that the 2D Dirac quantum walk based on the Ho-Chalker network model can be gapped by potential scattering.
  arXiv  Detail & Related papers  (2026-07-06T14:04:57Z)
• The Dirac Vacuum in Discrete Spacetime [0.0]
  We consider introducing the Dirac sea in a quantum cellular automata model of fermions in discrete spacetime.<n>A new boundary is created between positive and negative energy states, at which pair creation seems energetically favourable.<n>This happens because of the modular nature of energy in discrete time models.
  arXiv  Detail & Related papers  (2024-12-04T16:55:50Z)
• Dirac quantum walk on tetrahedra [0.0]
  We show how to recover the Dirac equation in (3+1)-dimensions with a QW evolving in a tetrahedral space. This paves the way to simulate the Dirac equation on a curved spacetime.
  arXiv  Detail & Related papers  (2024-04-15T14:46:28Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• One-dimensional scattering of fermions in double Dirac delta potentials [0.0]
  The spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background is studied. A distinction will be made between mass-spike and electrostatic Dirac delta-potentials.
  arXiv  Detail & Related papers  (2023-05-03T17:20:34Z)
• Bound state of distant photons in waveguide quantum electrodynamics [137.6408511310322]
  Quantum correlations between distant particles remain enigmatic since the birth of quantum mechanics. We predict a novel kind of bound quantum state in the simplest one-dimensional setup of two interacting particles in a box. Such states could be realized in the waveguide quantum electrodynamics platform.
  arXiv  Detail & Related papers  (2023-03-17T09:27:02Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Twisted quantum walks, generalised Dirac equation and Fermion doubling [0.0]
  We introduce a new family of quantum walks, said twisted, which admits as continuous limit, a generalized Dirac operator equipped with a dispersion term. This quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.
  arXiv  Detail & Related papers  (2022-12-28T15:22:16Z)
• Manipulating Generalized Dirac Cones In Quantum Metasurfaces [68.8204255655161]
  We consider a collection of single quantum emitters arranged in a honeycomb lattice with subwavelength periodicity. We show that introducing uniaxial anisotropy in the lattice results in modified dispersion relations.
  arXiv  Detail & Related papers  (2022-03-21T17:59:58Z)
• Solutions of the Dirac equation in one-dimensional variable width potential well [0.0]
  This paper investigates the solutions of the Dirac equation for spin-$frac12$ particles like electrons.<n>It demonstrates that Dirac particles can exhibit complex-valued momentum states via the Fermi acceleration mechanism.
  arXiv  Detail & Related papers  (2021-06-26T06:26:16Z)
• Instantons with Quantum Core [79.45476975925384]
  We consider new instantons that appear as a result of accounting for quantum fluctuations. These fluctuations naturally regularize the O(4) singular solutions abandoned in Coleman's theory. Unlike the Coleman instantons, the instantons with quantum cores always exist in the cases where the vacuum must be unstable.
  arXiv  Detail & Related papers  (2021-05-05T11:51:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.