The continuous spectrum of bound states in expulsive potentials

• URL: http://arxiv.org/abs/2602.07281v1
• Date: Sat, 07 Feb 2026 00:10:49 GMT
• Title: The continuous spectrum of bound states in expulsive potentials
• Authors: H. Sakaguchi, B. A. Malomed, A. C. Aristotelous, E. G. Charalampidis,
• Abstract summary: We show that a steep expulsive potential makes quantum states widely delocalized.<n>Asymptotic approximations for wave functions of the 1D and 2D eigenstates are derived.<n>Findings suggest an extension of the concept of bound states in the continuum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: On the contrary to the common intuition that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schrödinger equations, which include expulsive potentials that are \emph{steeper than the quadratic} (anti-harmonic-oscillator) ones, give rise to \emph{normalizable} (effectively localized) eigenstates. These states constitute full continuous spectra in the 1D and 2D cases alike. In 1D, these are spatially even and odd eigenstates. The 2D states may carry any value of the vorticity (alias magnetic quantum number). Asymptotic approximations for wave functions of the 1D and 2D eigenstates, valid far from the center, are derived analytically, demonstrating excellent agreement with numerically found counterparts. Special exact solutions for vortex states are obtained in the 2D case. These findings suggest an extension of the concept of bound states in the continuum, in quantum mechanics and paraxial photonics. Gross-Pitaevskii equations are considered as the nonlinear extension of the 1D and 2D settings. In 1D, the cubic nonlinearity slightly deforms the eigenstates, maintaining their stability. On the other hand, the quintic self-focusing term, which occurs in the photonic version of the 1D model, initiates the dynamical collapse of states whose norm exceeds a critical value.

Related papers

• Observation of string breaking on a (2 + 1)D Rydberg quantum simulator [59.63568901264298]
  We report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator. Our work paves a way to explore phenomena in high-energy physics using programmable quantum simulators.
  arXiv  Detail & Related papers  (2024-10-21T22:33:16Z)
• 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.<n>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)
• The Potential Inversion Theorem [0.0]
  We prove the potential inversion theorem, which says that wavefunction probability in these models is preserved under the sign inversion of the potential energy. We show how the potential inversion theorem illustrates several seemingly unrelated physical phenomena, including Bloch oscillations, localization, particle-hole symmetry, negative potential scattering, and magnetism.
  arXiv  Detail & Related papers  (2023-05-12T05:32:53Z)
• 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)
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
  A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2022-06-30T18:00:01Z)
• The bound-state solutions of the one-dimensional pseudoharmonic oscillator [0.0]
  We study the bound states of a quantum mechanical system governed by a constant $alpha$. For attractive potentials within the range $-1/4leqalpha0$, there is an even-parity ground state with increasingly negative energy. We show how the regularized excited states approach their unregularized counterparts.
  arXiv  Detail & Related papers  (2021-11-24T23:03:10Z)
• Wave functions for high-symmetry, thin microstrip antennas and two-dimensional quantum boxes [48.7576911714538]
  For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. In two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature that has often been overlooked in the literature.
  arXiv  Detail & Related papers  (2021-08-18T00:57:42Z)
• Dimerization of many-body subradiant states in waveguide quantum electrodynamics [137.6408511310322]
  We study theoretically subradiant states in the array of atoms coupled to photons propagating in a one-dimensional waveguide. We introduce a generalized many-body entropy of entanglement based on exact numerical diagonalization. We reveal the breakdown of fermionized subradiant states with increase of $f$ with emergence of short-ranged dimerized antiferromagnetic correlations.
  arXiv  Detail & Related papers  (2021-06-17T12:17:04Z)
• Bose-Einstein condensate soliton qubit states for metrological applications [58.720142291102135]
  We propose novel quantum metrology applications with two soliton qubit states. Phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes.
  arXiv  Detail & Related papers  (2020-11-26T09:05:06Z)
• Multidimensional hydrogenic states: Position and momentum expectation values [0.0]
  The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $langle ralpha rangle$ and $leftlangle palpha rightrangle$, respectively. These quantities have not been calculated in an analytical and effective manner up until now except for a number of three-dimensional hydrogenic states.
  arXiv  Detail & Related papers  (2020-11-24T17:34:14Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.