Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

• URL: http://arxiv.org/abs/2205.10477v1
• Date: Sat, 21 May 2022 01:09:04 GMT
• Title: Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system
• Authors: Yi-Cai Zhang
• Abstract summary: We investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level formula.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level formula with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the Coulomb-like potential strength $\alpha$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $\alpha_c$ at which the bound state energy reaches the threshold of continuous spectrum. \textbf{After crossing the threshold, the bound states in the continuum (BIC) may exist in such a flat band system.

Related papers

• Dissipation-induced bound states as a two-level system [0.0]
  An anti-parity-time symmetric system can have a single pair of real energy levels, while all the remaining levels are unstable due to the negative imaginary part of the energy. In this work, we investigate the formation of bound states in a tight-binding chain induced by a harmonic imaginary potential.
  arXiv  Detail & Related papers  (2024-05-28T03:25:31Z)
• Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum [44.99833362998488]
  This paper calculates the potential energy curve for the state $X1Sigma+$ of the Cr$$$ dimer. It is found for the first time for the whole range of internuclear distances $R$.
  arXiv  Detail & Related papers  (2024-01-06T17:00:12Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Adiabatic amplification of the harmonic oscillator energy when the frequency passes through zero [77.34726150561087]
  After a single frequency passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again. The dependence on the initial state disappears after averaging over phases of initial states with the same energy. The original Born-Fock theorem does not work after the frequency passes through zero.
  arXiv  Detail & Related papers  (2023-03-15T01:18:55Z)
• Bound states without potentials: localization at singularities [0.0]
  We discuss a paradigm where bound states arise purely due to kinetic energy considerations. This phenomenon occurs in certain non-manifold spaces that consist of multiple smooth surfaces that intersect one another. We find a ground state that is localized around the singular point, bound by the kinetic energy of shuttling' among the $M$ surfaces.
  arXiv  Detail & Related papers  (2023-02-06T19:04:42Z)
• Quantum Speed Limit for States with a Bounded Energy Spectrum [0.0]
  We report on an additional bound that exists for states with a bounded energy spectrum. This bound is dual to the Margolus-Levitin one in the sense that it depends on the difference between the state's mean energy and the energy of the highest occupied eigenstate. Each of the three bounds can become the most restrictive one, depending on the spread and mean of the energy.
  arXiv  Detail & Related papers  (2022-06-29T17:58:25Z)
• Emergence of Fermi's Golden Rule [55.73970798291771]
  Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a continuum of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing.
  arXiv  Detail & Related papers  (2022-06-01T18:35:21Z)
• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band [0.0]
  We investigate the bound state problem in one dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that, the flat band has significant effects on the bound states.
  arXiv  Detail & Related papers  (2022-05-21T00:50:02Z)
• 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)
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems [0.0]
  A quantum emitter is coupled near threshold (band edge) to a one-dimensional continuum with a van Hove in the density of states. A characteristic triple level convergence occurs directly on the threshold as the coupling $g$ is shut off. We show that the combination of these effects results in quantum emitter decay of the unusual form $1 - C t3/2$ on the key timescale.
  arXiv  Detail & Related papers  (2021-04-14T15:27:30Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)

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.