Solutions of the Dirac equation in one-dimensional variable width potential well

• URL: http://arxiv.org/abs/2107.05361v6
• Date: Thu, 20 Feb 2025 14:23:19 GMT
• Title: Solutions of the Dirac equation in one-dimensional variable width potential well
• Authors: Qiuyu Shan,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Fermi acceleration mechanism is a significant source of cosmic rays. When the width of a potential well changes over time, the velocity of particles within the well also changes. For quantum systems, such dynamics should be described by the Schr\"odinger, Klein-Gordon, and Dirac equations. Previous studies have solved the Schr\"odinger and Klein-Gordon equations under these conditions, but no research has addressed the Dirac equation for spin-$\frac{1}{2}$ particles like electrons. This paper investigates the solutions of the Dirac equation in a dynamically varying potential well and demonstrates that Dirac particles can exhibit complex-valued momentum states via the Fermi acceleration mechanism, enabling Tachyon-like states preparation.

Related papers

• Preserving Mass Shell Condition in the Stochastic Optimal Control Derivation of the Dirac Equation [0.0]
  Dirac equation governs spin-$frac12$ particles and their antiparticles. We introduce a novel SOC derivation that retains the nonlinear kinetic term and integrates spin-electromagnetic coupling into the potential.
  arXiv  Detail & Related papers  (2025-03-11T07:21:51Z)
• Analogue black string in a quantum harmonic oscillator [49.1574468325115]
  We write the exact solution of the Klein-Gordon equation in the background of a chargeless, static black string. The eigenvalue problem provides complex energy values for the particle, which may indicate the presence of quasinormal modes. We show a simple quantum system that can imitate the particle in the black string background, whose solutions are also applications of the biconfluent Heun function.
  arXiv  Detail & Related papers  (2024-12-31T15:03:57Z)
• Classical characters of spinor fields in torsion gravity [0.0]
  We consider the problem of having relativistic quantum mechanics re-formulated with hydrodynamic variables. We will demonstrate that when plane waves are considered the MPD equations acquire the form given in [1], but we will also see that in such a form the MPD equations become trivial.
  arXiv  Detail & Related papers  (2024-11-14T18:20:09Z)
• Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation [33.76659022113328]
  This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension.
  arXiv  Detail & Related papers  (2024-07-22T03:52:14Z)
• Closed-form solutions for the Salpeter equation [41.94295877935867]
  We study the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent problem, namely the B"aumer equation. This B"aumera corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy for small times and Gaussian diffusion for large times.
  arXiv  Detail & Related papers  (2024-06-26T15:52:39Z)
• Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism [55.2480439325792]
  We analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media. We prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.
  arXiv  Detail & Related papers  (2024-04-07T14:37:04Z)
• Unveiling the Quantum Toroidal Dipole in Nanosystems: Quantization, Interaction Energy, and Measurement [44.99833362998488]
  We investigate a quantum particle confined to a toroidal surface in the presence of a filiform current along the system's rotational axis. Our analysis reveals that the interaction between the particle and the current induces a non-zero toroidal dipole in the particle's stationary states.
  arXiv  Detail & Related papers  (2024-01-26T13:31:32Z)
• Comment on "Deformations of the spin currents by topological screw dislocation and cosmic dispiration'' [0.0]
  The Dirac equation in the screw dislocation space-time carries a term that represents the torsion of such topological defect, given by $K_mu$. It is only possible to work with the Dirac equation in the form presented by Wang et al. if the space-time is torsion-free.
  arXiv  Detail & Related papers  (2024-01-15T03:02:36Z)
• Quantum mechanics without quantum potentials [0.0]
  Non-locality in quantum mechanics can be resolved by considering relativistically covariant diffusion in spacetime. We introduce the concept of momentum equilinear to replace the second-order Bohm-Newton equations of motion.
  arXiv  Detail & Related papers  (2024-01-08T18:51:38Z)
• Ultracold Neutrons in the Low Curvature Limit: Remarks on the post-Newtonian effects [49.1574468325115]
  We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime. We calculate the next-to-leading order corrections to the neutron's energy spectrum. While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
  arXiv  Detail & Related papers  (2023-12-30T16:45:56Z)
• Heun-type solutions for the Dirac particle on the curved background of Minkowski space-times [0.0]
  We study the Dirac equation in the background of Minkowski space-time on a light cone. Results are valid for a spinless charged particle in the context of the magnetic field.
  arXiv  Detail & Related papers  (2023-08-21T07:11:25Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Helical beams of electrons in a magnetic field: New analytic solutions of the Schr\"odinger and Dirac equations [0.0]
  We derive new solutions of the Schr"odinger, Klein-Gordon and Dirac equations. Our solutions exhibit the behavior of quantum particles which very closely resembles classical helical trajectories.
  arXiv  Detail & Related papers  (2023-03-26T19:09:12Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Quantum simulation of partial differential equations via Schrodingerisation: technical details [31.986350313948435]
  We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential equations into a Schrodingerised' or Hamiltonian system, using a new and simple transformation called the warped phase transformation. We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations.
  arXiv  Detail & Related papers  (2022-12-30T13:47:35Z)
• Quantum simulation of partial differential equations via Schrodingerisation [31.986350313948435]
  We present a simple new way to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations. This can be seen directly on the level of the dynamical equations without more sophisticated methods.
  arXiv  Detail & Related papers  (2022-12-28T17:32:38Z)
• Scattering solution of Schr\"odinger equation with $\delta$-potential in deformed space with minimal length [0.0]
  We consider the Dirac $delta$-function potential problem in general case of deformed Heisenberg algebra leading to the minimal length. For some resonance energy the incident wave is completely reflected.
  arXiv  Detail & Related papers  (2021-10-24T17:27:56Z)
• 2D Relativistic Oscillators with a Uniform Magnetic Field in Anti-deSitter Space [0.0]
  We study the two dimensional deformed bosonic oscillator equations for charged particles (both spin 0 and spin 1 particles) We consider the presence of a minimal uncertainty in momentum caused by the Anti-deSitter model. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein-Gordon and scalar Duffin-Kemmer-Petiau cases.
  arXiv  Detail & Related papers  (2021-02-23T14:33:03Z)
• What can we learn from the conformal noninvariance of the Klein-Gordon equation? [0.0]
  The Klein-Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels.
  arXiv  Detail & Related papers  (2020-12-22T21:09:20Z)
• New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
  We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We modify the time-dependent Schr"odinger equation through a change of representation. The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
  arXiv  Detail & Related papers  (2020-11-23T17:29:31Z)
• Enhanced decoherence for a neutral particle sliding on a metallic surface in vacuum [68.8204255655161]
  We show that non-contact friction enhances the decoherence of the moving atom. We suggest that measuring decoherence times through velocity dependence of coherences could indirectly demonstrate the existence of quantum friction.
  arXiv  Detail & Related papers  (2020-11-06T17:34:35Z)

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.