Related papers: Hearing the boundary conditions of the one-dimensional Dirac operator

Hearing the boundary conditions of the one-dimensional Dirac operator

URL: http://arxiv.org/abs/2311.17561v1
Date: Wed, 29 Nov 2023 11:48:46 GMT
Title: Hearing the boundary conditions of the one-dimensional Dirac operator
Authors: Giuliano Angelone
Abstract summary: 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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. We analyze all the self-adjoint extensions of the Hamiltonian in terms of the boundary conditions at the junction, characterizing the energy spectrum by means of a spectral function. By determining the symmetries of the latter, we are able to divide the self-adjoint extensions in two classes, identifying all the families of isospectral Hamiltonians, and thus completely characterizing the isospectrality problem.

Related papers

The Aharonov-Bohm Hamiltonian: self-adjointness, spectral and scattering properties [0.0]
This work provides an introduction and overview on some basic mathematical aspects of the single-flux Aharonov-Bohm Schr"odinger operator. The whole family of self-adjoint realizations is characterized by means of four different methods. Special attention is devoted to those self-adjoint realizations which preserve the same rotational symmetry and homogeneity under dilations of the basic differential operator.
arXiv Detail & Related papers (2024-07-21T10:51:52Z)
Entanglement Hamiltonian of a nonrelativistic Fermi gas [0.0]
We study the entanglement Hamiltonian for a spherical domain in the ground state of a nonrelativistic free-fermion gas in arbitrary dimensions. We show that the entanglement spectrum in each sector is identical to that of a hopping chain in a linear potential, with the angular momentum playing the role of the subsystem boundary.
arXiv Detail & Related papers (2023-11-27T22:27:56Z)
Dynamical abelian anyons with bound states and scattering states [0.0]
We introduce a family of quantum spin Hamiltonians on $mathbbZ2$. In particular, the anyons exhibit a non-trivial holonomy with a quantized phase, consistent with the gauge and duality symmetries of the Hamiltonian.
arXiv Detail & Related papers (2023-03-13T18:01:02Z)
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)
Hearing the shape of a quantum boundary condition [0.0]
We study the isospectrality problem for a free quantum particle confined in a ring with a junction. We classify the self-adjoint realizations in two classes, identifying all the families of isospectral Hamiltonians.
arXiv Detail & Related papers (2022-04-21T16:33:13Z)
Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z)
Fano interference in quantum resonances from angle-resolved elastic scattering [62.997667081978825]
We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
arXiv Detail & Related papers (2021-05-12T20:41:25Z)
Spectral properties of relativistic quantum waveguides [0.0]
We find an effective Hamiltonian on the base curve which approximates the original operator in the thin-strip limit. We also investigate the existence of bound states in the non-relativistic limit and give a geometric condition for the bound states to exist.
arXiv Detail & Related papers (2021-01-11T16:33:52Z)
Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z)
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.