Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 11 min ago
Peer-reviewedCC BYAIP Advances

A family of (1 + 1)-dimensional harmonic oscillators, subjected to nonlinear potentials, which can generate a quantized energy spectrum

  • Yair Zarmi1
  1. 1Jacob Blaustien Institutes for Desert Research, Ben Gurion University of the Negev, Midreshet Ben Gurion 8499000, Israel
Read full textDOICite

Abstract

We consider a large (perhaps infinite) ensemble of particles. Particle motion is governed by the equation of a harmonic oscillator affected by the addition of a nonlinear potential. The potential has an infinite number of singularities in the position variable, where it is infinite. Consequently, each particle follows oscillatory motion within the potential well confined between two adjacent singularity points. Particle energy depends on the randomly distributed initial conditions of the oscillatory motion. An observer measuring particle energies will obtain an average over the initial conditions. Depending on the nonlinear potential, the measurements may be interpreted as yielding a quantized energy spectrum.

Related

  1. Coherent Entanglement between Massive Oscillators from the Quantized Gravitational Field
    Anom Trenggana, Freddy P. Zen
    arXivPreprintCC BY 4.0Full textGravitation & general relativityHigh-energy & particle physicsarXiv
  2. First-quantized quantum simulation with non-local potentials by matrix-product-state encoding
    Kazuki Tsuoka, Taichi Kosugi, Masari Watanabe +2
    arXivPreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
  3. Modal interactions in strongly nonlinear coupled oscillators with closely spaced modes and nonclassical damping distribution
    C. A. Hubay, T. Kalmar-Nagy, L. Bergman +1
    arXivPreprintarXiv licenceFull textStatistical & nonlinear physicsarXiv
  4. Automated discovery of dimensional reductions in coupled oscillators
    Dishant Sisodia, Sarika Jalan
    arXivPreprintCC BY 4.0Full textStatistical & nonlinear physicsarXiv
  5. Planck-Scale Toroidal Closure Substrate: Dimensional Recurrence, Structural Admissibility, and Theory Appraisal in the Quantized Dimensional Ledger
    James D. Bourassa
    Zenodo (CERN European Organization for Nuclear Research)PreprintCC BY7 citedStatistical & nonlinear physicsOpenAlex

Cite

BibTeXRIS
BibTeX
@article{zarmi2026family,
  title = {{A family of (1 + 1)-dimensional harmonic oscillators, subjected to nonlinear potentials, which can generate a quantized energy spectrum}},
  author = {Yair Zarmi},
  journal = {AIP Advances},
  year = {2026},
  month = oct,
  doi = {10.1063/5.0344903},
  url = {https://doi.org/10.1063/5.0344903},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - A family of (1 + 1)-dimensional harmonic oscillators, subjected to nonlinear potentials, which can generate a quantized energy spectrum
AU  - Yair Zarmi
PY  - 2026
DA  - 2026/10/23
JO  - AIP Advances
DO  - 10.1063/5.0344903
UR  - https://doi.org/10.1063/5.0344903
AB  - We consider a large (perhaps infinite) ensemble of particles. Particle motion is governed by the equation of a harmonic oscillator affected by the addition of a nonlinear potential. The potential has an infinite number of singularities in the position variable, where it is infinite. Consequently, each particle follows oscillatory motion within the potential well confined between two adjacent singularity points. Particle energy depends on the randomly distributed initial conditions of the oscillatory motion. An observer measuring particle energies will obtain an average over the initial conditions. Depending on the nonlinear potential, the measurements may be interpreted as yielding a quantized energy spectrum.
SN  - 2158-3226
ER  -