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This theoretical study derives exact solutions for an inverted Dirac-Moshinsky oscillator in 1+1 dimensions, revealing a purely continuous energy spectrum and identifying Gamow resonances linked to vacuum instability. The work establishes a PT-symmetric Hamiltonian governed by the SU(1,1) algebra, offering a mathematical framework analogous to the Schwinger effect for spontaneous pair production. While the results are significant for fundamental quantum field theory, they currently represent a specialized mathematical physics contribution rather than an immediate advancement in applied quantum computing or hardware.
The Inverted Dirac-Moshinsky Oscillator in $(1+1)$ Dimensions
arXiv:2606.02637v1 Announce Type: new Abstract: We derive and analyze the exact solutions of the inverted Dirac-Moshinsky oscillator (IDMO) in $(1+1)$ dimensions, obtained from the standard model via the substitution $p \to p + im\omega\beta x$. The upper spinor component satisfies a Weber equation with complex spectral parameter $\lambda = (E^2-m^2)/(2m\omega)+i/2$, whose solutions are parabolic cylinder functions $D_\nu(\xi)$ with complex order $\nu = \lambda - 1/2$. The physical spectrum is purely continuous ($|E|>m$), with no discrete bound states. Three normalization schemes are developed, and the discrete Gamow resonances at $E_n^\pm = \pm\sqrt{m^2+(2n+1)m\omega-im\omega}$ are identified as poles of the resolvent. The negative-energy sector describes antiparticle anti-resonances whose positive imaginary part signals vacuum instability and spontaneous pair production, analogous to the Schwinger effect. The algebraic structure is governed by the principal series of $SU(1,1)$, and the Hamiltonian is $\mathcal{PT}$-symmetric with unbroken symmetry for $|E|>m$.
Abstract:We derive and analyze the exact solutions of the inverted Dirac-Moshinsky oscillator (IDMO) in $(1+1)$ dimensions, obtained from the standard model via the substitution $p \to p + im\omega\beta x$. The upper spinor component satisfies a Weber equation with complex spectral parameter $\lambda = (E^2-m^2)/(2m\omega)+i/2$, whose solutions are parabolic cylinder functions $D_\nu(\xi)$ with complex order $\nu = \lambda - 1/2$. The physical spectrum is purely continuous ($|E|>m$), with no discrete bound states. Three normalization schemes are developed, and the discrete Gamow resonances at $E_n^\pm = \pm\sqrt{m^2+(2n+1)m\omega-im\omega}$ are identified as poles of the resolvent. The negative-energy sector describes antiparticle anti-resonances whose positive imaginary part signals vacuum instability and spontaneous pair production, analogous to the Schwinger effect. The algebraic structure is governed by the principal series of $SU(1,1)$, and the Hamiltonian is $\mathcal{PT}$-symmetric with unbroken symmetry for $|E|>m$.
arXiv:2606.02637 [quant-ph]
(or arXiv:2606.02637v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.02637 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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