Related papers: Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields

Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields

URL: http://arxiv.org/abs/2502.20318v1
Date: Thu, 27 Feb 2025 17:42:52 GMT
Title: Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields
Authors: Matteo Gallone, Alessandro Michelangeli, Diego Noja,
Abstract summary: We characterise the families of self-adjoint Dirac and Schr"odinger operators with Aharonov-Bohm magnetic field.<n>We exploit the non-relativistic limit of infinite light speed to connect the former to the latter.
Score: 44.99833362998488
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: We characterise the families of self-adjoint Dirac and Schr\"{o}dinger operators with Aharonov-Bohm magnetic field, and we exploit the non-relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short-scale boundary condition of self-adjointness. This ensures that the scattering length of the Aharonov-Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac-AB operators is mapped, in the non-relativistic limit, into the physically relevant sub-family of $s$-wave, angular-momentum-commuting, Schr\"{o}\-dinger-AB Hamiltonians with relativistic Dirac approximants.

Related papers

The Non-Relativistic Limit of Keldysh Spinors [0.0]
We show that despite the sign changes, Keldysh spinors have a well-defined non-relativistic limit resulting in quantum mechanics with the positive-definite Pauli Hamiltonian.<n>When non-relativistic Dirac and Keldysh fields are brought to interact, we observe curious decoupling of the two fields in mass-like and vector couplings.
arXiv Detail & Related papers (2025-01-08T14:04:39Z)
Quantum optical scattering by macroscopic lossy objects: A general approach [55.2480439325792]
We develop a general approach to describe the scattering of quantum light by a lossy macroscopic object placed in vacuum. We exploit the input-output relation to connect the output state of the field to the input one. We analyze the impact of the classical transmission and absorption dyadics on the transitions from ingoing to outgoing s-polariton.
arXiv Detail & Related papers (2024-11-27T17:44:29Z)
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)
Hearing the boundary conditions of the one-dimensional Dirac operator [0.0]
We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction.
arXiv Detail & Related papers (2023-11-29T11:48:46Z)
The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State [44.99833362998488]
We consider the fermionic entanglement entropy for the free Dirac field in a bounded spatial region of Minkowski spacetime. An area law is proven in the limiting cases where the volume tends to infinity and/or the regularization length tends to zero.
arXiv Detail & Related papers (2023-10-05T12:08:03Z)
Ehrenfest's Theorem for the Dirac Equation in Noncommutative Phase-Space [0.0]
We investigate Ehrenfest's theorem from the Dirac equation in a noncommutative phase-space. Knowing that with both the linear Bopp-Shift and Moyal-Weyl product, the noncommutativity is inserted.
arXiv Detail & Related papers (2023-09-28T11:50:43Z)
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)
Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential [0.0]
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions.
arXiv Detail & Related papers (2021-04-16T08:10:43Z)
Interior-Boundary Conditions for the Dirac Equation at Point Sources in 3 Dimensions [0.0]
A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs) Here, we study how the approach can be applied to Dirac operators.
arXiv Detail & Related papers (2020-06-30T13:13:39Z)
Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
arXiv Detail & Related papers (2020-03-16T11:37:23Z)

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