Generally covariant geometric momentum and geometric potential for a Dirac fermion on a two-dimensional hypersurface

• URL: http://arxiv.org/abs/2403.15982v1
• Date: Sun, 24 Mar 2024 02:20:03 GMT
• Title: Generally covariant geometric momentum and geometric potential for a Dirac fermion on a two-dimensional hypersurface
• Authors: Z. Li, L. Q. Lai,
• Abstract summary: In the context of multi-component quantum states, geometric momentum should be rewritten as generally covariant geometric momentum. For a Dirac fermion constrained on a two-dimensional hypersurface, we show that on the pseudosphere and the helical surface there exist no curvature-induced geometric potentials.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Geometric momentum is the proper momentum for a moving particle constrained on a curved surface, which depends on the outer curvature and has observable effects. In the context of multi-component quantum states, geometric momentum should be rewritten as generally covariant geometric momentum. For a Dirac fermion constrained on a two-dimensional hypersurface, we give the generally covariant geometric momentum, and show that on the pseudosphere and the helical surface there exist no curvature-induced geometric potentials. These results verify that the dynamical quantization conditions are effective in dealing with constrained systems on hypersurfaces, and one could obtain the generally convariant geometric momentum and the geometric potential of a spin particle constrained on surfaces with definite parametric equations.

Related papers

• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• Laser-Dressed States on Riemannian Manifolds: A Generalization of the Kramers-Henneberger Transformation [0.0]
  We analytically study the laser-driven nonlinear dynamics of a quantum particle. The geometry of space results in a potential-like term that supports bound states on the manifold. We deduce a Schr"odinger-like equation in the Kramers-Henneberger frame.
  arXiv  Detail & Related papers  (2024-02-16T10:57:34Z)
• Quantum Scattering of Spinless Particles in Riemannian Manifolds [0.0]
  Quantum mechanics is sensitive to the geometry of the underlying space. We present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space.
  arXiv  Detail & Related papers  (2024-02-16T10:50:50Z)
• Action formalism for geometric phases from self-closing quantum trajectories [55.2480439325792]
  We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
  arXiv  Detail & Related papers  (2023-12-22T15:20:02Z)
• Gravitational quantum switch on a superposition of spherical shells [0.0]
  In a gravitational quantum switch, the order of operations applied by two agents on a target system is entangled with the state of the geometry. We consider a model describing the superposition of geometries produced by distinct arrangements of spherical mass shells. We show that a protocol for the implementation of a gravitational quantum switch can be formulated in such a system.
  arXiv  Detail & Related papers  (2023-06-19T14:52:09Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Causality and dimensionality in geometric scattering [0.0]
  The scattering matrix describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials. The effect of spatial dimensionality is investigated by considering scattering in two and three dimensions.
  arXiv  Detail & Related papers  (2021-12-06T01:49:45Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Geometry-induced Monopole Magnetic Field and Quantum Spin Hall Effect [7.6280835896399966]
  A relativistic particle confined to a nontrivial M"obius surface is studied. We find a geometric gauge potential that results from the rotation transformation of the local frame moving on M"obius strip. As potential applications, effective monopole magnetic fields and spin Hall phenomena can be generated and manipulated by designing geometries and topologies of two-dimensional nanodevices.
  arXiv  Detail & Related papers  (2021-09-19T13:55:16Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)

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.