Barrier scattering in field theory removal of Klein paradox

Nikishov, A. I.

doi:10.1016/0550-3213(70)90527-4

Cited by 141 publications

(115 citation statements)

References 8 publications

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“…From Eqs. (10) and (29), one finds similar decompositions between the left and right scalar functions,…”

Section: Solutions With Special Left and Right Asymptoticsmentioning

confidence: 59%

“…This configuration represents an almost symmetrical electric field that is growing "smoothly" from x = −∞ to x = 0 and then is decreasing "smoothly" to x = +∞. The configuration may be considered as a two-parameter regularization of a uniform electric field 10 . The resulting potential energy of the electron in this field is illustrated by the yellow solid line in Fig.…”

Section: Small-gradient Configurationmentioning

confidence: 99%

“…Important calculations of the particle creation by x-steps in the framework of the relativistic quantum mechanics were presented by Nikishov in Refs. [4,10] and later developed by Hansen and Ravndal in Refs. [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Vacuum instability in a constant inhomogeneous electric field: a new example of exact nonperturbative calculations

2020

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Basic quantum processes (such as particle creation, reflection, and transmission on the corresponding Klein steps) caused by inverse-square electric fields are calculated. These results represent a new example of exact nonperturbative calculations in the framework of QED.The inverse-square electric field is time-independent, inhomogeneous in the x-direction, and is inversely proportional to x squared. We find exact solutions of the Dirac and Klein-Gordon equations with such a field and construct corresponding in-and out-states. With the help of these states and using the techniques developed in the framework of QED with x-electric potential steps, we calculate characteristics of the vacuum instability, such as differential and total mean numbers of particles created from the vacuum and vacuum-to-vacuum transition probabilities. We study the vacuum instability for two particular backgrounds: for fields * widely stretches over the x-axis (small-gradient configuration) and for the fields sharply concentrates near the origin x = 0 (sharp-gradient configuration). We compare exact results with ones calculated numerically. Finally, we consider the electric field configuration, composed by inverse-square fields and by an x-independent electric field between them to study the role of growing and decaying processes in the vacuum instability.

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“…From Eqs. (10) and (29), one finds similar decompositions between the left and right scalar functions,…”

Section: Solutions With Special Left and Right Asymptoticsmentioning

confidence: 59%

Section: Small-gradient Configurationmentioning

confidence: 99%

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Vacuum instability in a constant inhomogeneous electric field: a new example of exact nonperturbative calculations

2020

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“…on φ we project the positive-energy part out, and then we can plug the number operator of (3) into (1), which yields an estimate of produced particles as This is a standard formula for the particle production obtained via the Bogoliubov transformation [31]. Now it is intriguing to check how our formula (5) gives rise to the same answer.…”

Section: Spectral Functions In the Asymptotic Statesmentioning

confidence: 99%

Spectral representation of the particle production out of equilibrium—Schwinger mechanism in pulsed electric fields

Fukushima

2014

New J. Phys.

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We develop a formalism to describe the particle production out of equilibrium in terms of dynamical spectral functions, i.e. Wigner transformed Pauli-Jordanʼs and Hadamardʼs functions. We take an explicit example of a spatially homogeneous scalar theory under pulsed electric fields and investigate the time evolution of the spectral functions. In the out-state we find an oscillatory peak in Hadamardʼs function as a result of the mixing between positive-and negativeenergy waves. The strength of this peak is of the linear order of the Bogoliubov mixing coefficient, whereas the peak corresponding to the Schwinger mechanism is of the quadratic order. Between the in-and the out-states we observe a continuous flow of the spectral peaks together with two transient oscillatory peaks. We also discuss the medium effect at finite temperature and density. We emphasize that the entire structure of the spectral functions conveys rich information on real-time dynamics including the particle production.

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“…Formally it is related to the energy degeneracy between states that (without any interaction) are associated with the positive and negative energy continuum. While many theoretical works focus on predictions for suitable laboratory conditions [8][9][10][11][12][13][14], others, including our own, are devoted to the fundamental study of the general principles underlying particle pair creation [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Instantaneous rest-frame transformation method for temporally induced pair creation

Vikartofsky

Norris

et al. 2014

Phys. Rev. A

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We introduce a computational method to determine the rate of the electron-positron pair creation triggered by a time-dependent subcritical external field. It is based on constructing a Lorentz transformation to an instantaneous rest frame, for which the pair-creation rate can be determined by standard techniques. We will discuss the accuracy and efficiency of this method by comparing its predictions with exact time-dependent quantum field theoretical solutions to the Dirac and Klein-Gordon equations for various space-time dependent external fields.

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Barrier scattering in field theory removal of Klein paradox

Cited by 141 publications

References 8 publications

Vacuum instability in a constant inhomogeneous electric field: a new example of exact nonperturbative calculations

Vacuum instability in a constant inhomogeneous electric field: a new example of exact nonperturbative calculations

Spectral representation of the particle production out of equilibrium—Schwinger mechanism in pulsed electric fields

Instantaneous rest-frame transformation method for temporally induced pair creation

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