Energy spectra of the spiked harmonic oscillator using the shifted 1/N expansion

Dalabeeh, M. A.; Sandouqa, A. S.

doi:10.1140/epjp/s13360-022-02528-7

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2024

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“…The results from those works rely on the equivalence principle at the quantum level [19,20], which finds thus a very interesting application among many others reported in the literature within and outside of condensed matter physics (see, e.g., Refs. [21][22][23][24][25][26][27][28][29] and references therein).…”

Section: Introductionmentioning

confidence: 99%

The Quantum Hall Effect under the Influence of Gravity and Inertia: A Unified Approach

Landry,

Hammad,

Saadati

2024

Universe

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The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within such a combination.

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