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Vacuum effects for a one-dimensional “hydrogen atom” with Z > Zcr

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Abstract

For a supercritical Coulomb source with a chargeZ > Zcr in 1+1 dimensions, we study the nonperturbative properties of the vacuum density ρVP(x) and the energy ɛVP. We show that for corresponding problem parameters, nonlinear effects in the supercritical region can lead to behavior of the vacuum energy differing significantly from the perturbative quadratic growth, to the extent of an (almost) quadratic decrease of the form −|η|Z2 into the negative region. We also show that although approaches for calculating vacuum expectations values and the behavior of ρVP(x) in the supercritical region for various numbers of spatial dimensions indeed have many common features, ɛVP for 1+1 dimensions in the supercritical region nevertheless has several specific features determined by the one-dimensionality of the problem.

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Authors and Affiliations

  1. Bogoliubov Institute of Theoretical Problems of the Microworld, Lomonosov Moscow State University, Moscow, Russia

    Yu. S. Voronina, A. S. Davydov & K. A. Sveshnikov

Authors
  1. Yu. S. Voronina
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  2. A. S. Davydov
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  3. K. A. Sveshnikov
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Correspondence to Yu. S. Voronina.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 193, No. 2, pp. 276–308, November, 2017.

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Voronina, Y.S., Davydov, A.S. & Sveshnikov, K.A. Vacuum effects for a one-dimensional “hydrogen atom” with Z > Zcr. Theor Math Phys 193, 1647–1674 (2017). https://doi.org/10.1134/S004057791711006X

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  • DOI: https://doi.org/10.1134/S004057791711006X

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