Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem

• URL: http://arxiv.org/abs/2104.10885v2
• Date: Wed, 27 Oct 2021 06:48:15 GMT
• Title: Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem
• Abstract summary: The eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron. The eigen-energies of the system depend only on the first quantum number $n$, and the second quantum number $m$ does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a {\it gauge-variant} quantity, and observation of a gauge-variant quantity would contradict a fundamental principle of physics called the {\it gauge principle}. In recent researches, however, Bliohk et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly non-trivial $m$-dependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number $m$ in the Landau eigen-states corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number $m$ in the Landau eigen-states was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the {\it particle-like} aspect but also to the {\it wave-like} aspect of the Landau electron.

Related papers

• How quantum is quantum geometry? [0.0]
  We study a purely classical system in which a magnetic moment precesses in a momentum-dependent magnetic field.<n>Within Hamiltonian classical mechanics, the component of $boldsymbolell$ along the field reproduces the Berry-curvature phenomena.<n>The particle acquires a position spread whose second moment is the metric, an orbital magnetic moment, and - most strikingly - an inertial mass generated by a position-dependent force.
  arXiv  Detail & Related papers  (2026-08-26T18:00:23Z)
• Efficient quantum algorithm for Heisenberg spin systems [1.137457877869062]
  We consider a family of Heisenberg-type quantum spin systems studied by Suzuki and Fisher in 1971.<n>We obtain an efficient quantum adiabatic algorithm for the ground energy of any model in this family.
  arXiv  Detail & Related papers  (2026-07-15T22:36:21Z)
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation [14.803730343784439]
  The $W$ state is a canonical representative of multipartite quantum entanglement.<n>This paper introduces a novel approach to identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations.
  arXiv  Detail & Related papers  (2025-11-20T14:59:48Z)
• Superstate Quantum Mechanics [35.18016233072556]
  We introduce Superstate Quantum Mechanics (SQM) as a theory that considers states in Hilbert space subject to multiple quadratic constraints.<n>In this case, the stationary SQM problem is a quantum inverse problem with multiple applications in physics, machine learning, and artificial intelligence.
  arXiv  Detail & Related papers  (2025-01-25T19:41:04Z)
• 2D magnetic stability [0.0]
  This article is a contribution to the proceedings of the 33rd/35th International Colloquium on Group Theoretical Methods in Physics (ICGTMP, Group33/35) We consider here the stability of the self-interacting almost-bosonic anyon gas, generalizing the Gross-Pitaevskii / nonlinear Schr"odinger energy functionals to include magnetic self interactions. We show that there is a type of supersymmetry in the model which holds only for higher values of the magnetic coupling but is broken for lower values, and that in the former case supersymmetric ground states exist precisely at even-integer densities
  arXiv  Detail & Related papers  (2024-10-31T17:12:27Z)
• Attractive-repulsive interaction in coupled quantum oscillators [14.37149160708975]
  We find an interesting symmetry-breaking transition from quantum limit cycle oscillation to quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from quantum homogeneous to inhomogeneous steady state. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analogue in the classical domain.
  arXiv  Detail & Related papers  (2024-08-23T10:45:19Z)
• Symmetry: a fundamental resource for quantum coherence and metrology [0.0]
  We show that when the quantum state is an eigenstate of an operator $A$, observables $G$ which are completely off-diagonal have purely quantum fluctuations. This property holds regardless of the purity of the quantum state, and it implies that off-diagonal fluctuations represent a metrological resource for phase estimation.
  arXiv  Detail & Related papers  (2024-07-01T07:19:37Z)
• Unveiling the Quantum Toroidal Dipole [41.99844472131922]
  We present a complete quantum-mechanical formalism for the TD in a nanostructure.<n>We propose the first spectroscopic method for its direct measurement.<n>This provides a clear experimental blueprint to unveil, measure, and characterize this elusive third multipole moment.
  arXiv  Detail & Related papers  (2024-01-26T13:31:32Z)
• More on the gauge principle and nonobservability of some quantum numbers characterizing the Landau eigen-states [0.0]
  The eigen-states of the Landau Hamiltonian in the symmetric gauge are characterized by two integers $n$ and $m$. Since the canonical momentum and the canonical OAM are both gauge-variant quantities, their eigenvalues $k_x$ and $m$ are standardly believed not to correspond to observables. The purpose of this paper is to show that this claim is not justified, regardless of the differences in the two theoretical formulations of the Landau problem.
  arXiv  Detail & Related papers  (2023-11-28T05:48:43Z)
• Quantumness and quantum to classical transition in the generalized Rabi model [17.03191662568079]
  We define the quantumness of a Hamiltonian by the free energy difference between its quantum and classical descriptions. We show that the Jaynes-Cummings and anti Jaynes-Cummings models exhibit greater quantumness than the Rabi model.
  arXiv  Detail & Related papers  (2023-11-12T18:24:36Z)
• Quantizing the Quantum Uncertainty [0.0]
  We discuss the quantization of the quantum uncertainty as an operator acting on wave-functions over field space. We show how this spectrum appears in the value of the coupling of the effective conformal potential driving the evolution of extended Gaussian wave-packets. We conclude with an open question: is it possible to see experimental signatures of the quantization of the quantum uncertainty in non-relativistic physics?
  arXiv  Detail & Related papers  (2023-07-03T14:40:14Z)
• Sufficient statistic and recoverability via Quantum Fisher Information metrics [12.968826862123922]
  We prove that for a large class of quantum Fisher information, a quantum channel is sufficient for a family of quantum states. We obtain an approximate recovery result in the sense that, if the quantum $chi2$ divergence is approximately preserved by a quantum channel, two states can be recovered.
  arXiv  Detail & Related papers  (2023-02-05T09:02:36Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices [13.452510519858995]
  We show a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice $mathbbZd$. We also prove that local quantum commuting interactions above a critical temperature satisfy a transportation-cost inequality.
  arXiv  Detail & Related papers  (2022-10-20T17:46:18Z)
• Physical symmetries and gauge choices in the Landau problem [0.0]
  This paper aims to clarify the meaning of gauge choice in the Landau problem based on this gauge-potential-independent formulation. At the end, our analysis is shown to disclose a physically vacuous side face of the gauge symmetry.
  arXiv  Detail & Related papers  (2022-02-08T01:34:30Z)
• Experimental measurement of the divergent quantum metric of an exceptional point [10.73176455098217]
  We report the first experimental measurement of the quantum metric in a non-Hermitian system. The specific platform under study is an organic microcavity with exciton-polariton eigenstates, which demonstrate exceptional points.
  arXiv  Detail & Related papers  (2020-11-24T11:31:03Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)
• The Quantum Wasserstein Distance of Order 1 [16.029406401970167]
  We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposed distance is invariant with respect to permutations of the qudits and unitary operations acting on one qudit. We also propose a generalization of the Lipschitz constant to quantum observables.
  arXiv  Detail & Related papers  (2020-09-09T18:00:01Z)
• A quantum system with a non-Hermitian Hamiltonian [0.0]
  relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized. In this note, a quantum system described by a non-Hermitian Hamiltonian is investigated.
  arXiv  Detail & Related papers  (2020-04-15T17:03:45Z)

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.