Analysis of a one-dimensional Hamiltonian with a singular double well
consisting of two nonlocal $\delta'$ interactions
- URL: http://arxiv.org/abs/2307.03674v4
- Date: Sat, 20 Jan 2024 22:20:13 GMT
- Title: Analysis of a one-dimensional Hamiltonian with a singular double well
consisting of two nonlocal $\delta'$ interactions
- Authors: Silvestro Fassari, Manuel Gadella, Luis-Miguel Nieto and Fabio Rinaldi
- Abstract summary: We study a one-dimensional Hamiltonian with the interaction term given by the sum of two $delta'$-interactions of equal strength and symmetrically located with respect to the origin.
This model depends on two parameters, the interaction strength and the distance between the centre of each interaction and the origin.
- Score: 2.437390072112029
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The objective of the present paper is the study of a one-dimensional
Hamiltonian with the interaction term given by the sum of two nonlocal
attractive $\delta'$-interactions of equal strength and symmetrically located
with respect to the origin. We use the procedure known as {\it renormalisation
of the coupling constant} in order to rigorously achieve a self-adjoint
determination for this Hamiltonian. This model depends on two parameters, the
interaction strength and the distance between the centre of each interaction
and the origin. Once we have the self-adjoint determination, we obtain its
discrete spectrum showing that it consists of two negative eigenvalues
representing the energy levels. We analyse the dependence of these energy
levels on the above-mentioned parameters. We investigate the possible
resonances of the model. Furthermore, we analyse in detail the limit of our
model as the distance between the supports of the two $\delta'$ interactions
vanishes.
Related papers
- Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions.
We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
arXiv Detail & Related papers (2024-07-09T14:04:11Z) - Spin Orbit and Hyperfine Simulations with Two-Species Ultracold Atoms in a Ring [0.0]
A collective spin model is used to describe two species of mutually interacting ultracold bosonic atoms confined to a toroidal trap.
We show the linear component is an analog of a Zeeman Hamiltonian, and the quadratic component presents a macroscopic simulator for spin-orbit and hyperfine interactions.
arXiv Detail & Related papers (2024-06-04T09:17:43Z) - Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
We study the Hamiltonian for a Bose gas in three dimensions of $N geq 3$ spinless particles interacting via zero-range or contact interactions.
arXiv Detail & Related papers (2024-03-19T10:00:12Z) - Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors [46.76612530830571]
We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (detectors'')
We explore the dynamics of density and of entanglement entropy in the chain, for various values of $rho_a$ and $M$.
arXiv Detail & Related papers (2023-11-21T21:41:11Z) - Emergence of non-Abelian SU(2) invariance in Abelian frustrated
fermionic ladders [37.69303106863453]
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette.
Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry.
At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
arXiv Detail & Related papers (2023-05-11T15:57:27Z) - Spectral form factor in a minimal bosonic model of many-body quantum
chaos [1.3793594968500609]
We study spectral form factor in periodically-kicked bosonic chains.
We numerically find a nontrivial systematic system-size dependence of the Thouless time.
arXiv Detail & Related papers (2022-03-10T15:56:24Z) - Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity [77.34726150561087]
We study the Hamiltonian for a system of N identical bosons interacting with an impurity.
We introduce a three-body force acting at short distances.
The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles.
arXiv Detail & Related papers (2022-02-25T15:34:06Z) - Degeneracy and hidden symmetry -- an asymmetric quantum Rabi model with
an integer bias [0.0]
We investigate the hidden symmetry of the asymmetric quantum Rabi model (AQRM) with a half-integral bias (ibQRM$_ell$)
The existence of such symmetry has been widely believed to cause the degeneration of the spectrum, that is, the crossings on the energy curves.
In this paper we propose a conjectural relation between the symmetry and degeneracy for the ibQRM$_ell$ given explicitly.
arXiv Detail & Related papers (2021-06-16T16:17:11Z) - Multiple ground-state instabilities in the anisotropic quantum Rabi
model [0.0]
We study the anisotropic variant of the quantum Rabi model with different coupling strengths of the rotating and counter-rotating wave terms.
The anisotropy preserves the parity symmetry of the original model.
We find analytically that the ground-state and the first excited state can cross several times.
arXiv Detail & Related papers (2021-01-29T04:21:08Z) - 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) - Static and dynamic properties of a few spin $1/2$ interacting fermions
trapped in an harmonic potential [0.0]
We study the properties of a few interacting spin $1/2$ fermions trapped in a harmonic oscillator potential.
Results obtained by means of exact diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime.
arXiv Detail & Related papers (2020-05-21T20:22:09Z)
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.