Current conservation and amplitude regularisation of the Landau problem: Bohm--Madelung description

• URL: http://arxiv.org/abs/2604.12224v2
• Date: Sun, 19 Apr 2026 23:47:50 GMT
• Title: Current conservation and amplitude regularisation of the Landau problem: Bohm--Madelung description
• Abstract summary: This work investigates the dynamics of a charged particle in a uniform magnetic field within the Bohm--Madelung formulation of quantum mechanics.<n>Regularisation acts as a structural reorganisation mechanism in amplitude space, preserving the Landau spectral scale.
• Score: 0.2291770711277359
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: This work investigates the dynamics of a charged particle in a uniform magnetic field within the Bohm--Madelung formulation of quantum mechanics. In this representation, the stationary Schrodinger equation separates into coupled amplitude and phase equations, where the amplitude sector admits a Sturm--Liouville structure supporting Ermakov--Lewis invariants. The analysis considers two complementary regularisation schemes: a global Fisher--information--based regularisation and a local canonical (shell) Bohm regularisation derived from stationary flux closure. These are applied within distinct classes of stationary flow, characterised by vanishing and nonvanishing current components. It is shown that the radial and axial sectors remain globally regularisable, preserving analytic structure across the domain. In contrast, the azimuthal sector develops a nonseparable, generally complex-valued amplitude structure due to gauge-induced coupling. Nevertheless, a consistent local regularity is recovered at the level of canonical branches, where amplitude--momentum relations organise the solution in a well-defined manner. Regularisation thus acts as a structural reorganisation mechanism in amplitude space, preserving the Landau spectral scale while reorganising the flux-sector structure through branch-wise amplitude--momentum relations, thereby establishing a natural framework for the description of stationary Bohmian dynamics in the Landau problem.

Related papers

• Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions [0.0]
  We construct a class of integrable chiral fermionic quantum field theories with interactions depending on both space and time.<n>We derive the characteristic form of the spacetime-dependent interaction and illustrate the construction with a chiral $SU(2)$ Gross-Nevarity-eu realization.
  arXiv  Detail & Related papers  (2026-09-11T18:00:02Z)
• Klein--Gordon Dynamics from Intrinsic Phase Periodicity [0.0]
  We show that the Klein--Gordon equation arises as the minimal local, linear, Lorentz-invariant field equation compatible with the internal phase structure.<n>Within this framework, mass acts as an intrinsic frequency scale governing wave propagation, and relativistic kinematics is fully recovered.
  arXiv  Detail & Related papers  (2026-06-24T15:07:21Z)
• Amplitude-dependent quantum hydrodynamics from a \(\coth\)-Madelung ansatz [0.0]
  We investigate a hyperbolic phase--amplitude coupling of the form [ = R eimathcoth R, ] where (R) is a real amplitude field and () is an auxiliary phase coordinate governed by Schrdinger's equation.<n>We show that the associated velocity field acquires a density-gradient contribution, producing generalized continuity equations and modified quantum force terms.
  arXiv  Detail & Related papers  (2026-06-04T14:51:14Z)
• Geometric curvature driven by many-body collective fluctuations [45.88028371034407]
  Recently, it has been emphasized that quantum geometry can be interpreted in terms of quantum dipole fluctuations in the ground state driven by interband mixing.<n>Here, we extend this picture to include contributions from many-body collective fluctuations.<n>We show that contributions from collective fluctuations can be experimentally distinguished from bare band-geometric contributions.
  arXiv  Detail & Related papers  (2026-05-19T13:13:37Z)
• Superposition of quasi coherent Bohm Madelung waves [0.2291770711277359]
  We study the problem of superposition of stationary quantum states in the Bohm Madelung formulation.<n>In quasi coherent regime of near degenerate stationary branches, the dynamics separates into a hierarchical structure.<n>We show how amplitude modulation and phase induced sidebands organise interference patterns within a nonlinear amplitude phase framework.
  arXiv  Detail & Related papers  (2026-05-05T03:28:25Z)
• Dissipative Hamilton Jacobi Dynamics and the Emergence of Quantum Wave Mechanics [0.0]
  We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle.<n>We show that quantum mechanics corresponds to a stable symmetric phase of a broader dissipative classical theory.
  arXiv  Detail & Related papers  (2026-04-07T20:53:38Z)
• Beyond Perturbation Theory: A Resolvent-Based Framework for Strongly Correlated Many-Body Systems [1.4824891788575416]
  Traditional perturbation theory fails in many-body systems with exponentially small energy gaps and strong interactions.<n>This work presents an alternative methodological framework built on two core principles.<n>It is applicable to the quantitative analysis of global properties in nonintegrable many-body systems.
  arXiv  Detail & Related papers  (2026-04-01T08:11:58Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Quantum fields from real-time ensemble dynamics [6.0523316051636025]
  We formulate quantum fields in a real-time Schrdinger-picture framework.<n>Within this formulation, the wave $[,t]$ encodes a first-order, causal ensemble dynamics on configuration space.<n> Entanglement, scattering, and conformal field amplitudes emerge as distinct projections of the same underlying ensemble theory.
  arXiv  Detail & Related papers  (2026-02-04T05:40:38Z)
• Ermakov-Lewis Invariants in Stationary Bohm-Madelung Quantum Mechanics [0.2291770711277359]
  We show that the Ermakov Pinney equation and its associated invariant arise naturally in stationary quantum mechanics.<n>We show that the quantum potential is encoded as a curvature contribution of the self adjoint operator rather than appearing as an additional dynamical term.
  arXiv  Detail & Related papers  (2026-01-31T04:34:43Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations.<n>Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM)<n>By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.