Quantum effects with an X-ray free electron laser

A quantum kinetic equation coupled with Maxwell's equation is used to estimate the laser power required at an XFEL facility to expose intrinsically quantum effects in the process of QED vacuum decay via spontaneous pair production. A 9 TW-peak XFEL laser with photon energy 8.3 keV could be sufficient to initiate particle accumulation and the consequent formation of a plasma of spontaneously produced pairs. The evolution of the particle number in the plasma will exhibit non-Markovian aspects of the strong-field pair production process and the plasma's internal currents will generate an electric field whose interference with that of the laser leads to plasma oscillations.Comment: 4 pages, LaTeX2

Comment on ``Superconducting PrBa_2Cu_3O_x''

Recently, Zou et al. (Phys. Rev. Lett. 80, 1074, 1998) reported the observation of bulk superconductivity (SC) for a PrBa_2Cu_3O_x (Pr123) single crystal grown by the traveling-solvent floating zone (TSFZ) method. The aim of this Comment is to show the inconsistency of the value of effective magnetic moment \mu_{eff} reported by Zou et al. (2.92\mu_B) with their magnetic susceptibility data. The estimation made directly from their data points gives a considerably smaller value of \mu_{eff}=2.09\mu_B. At the same time the values of mu_{eff}=2.9\mu_B and 3.1\mu_B were obtained for our Pr123 single crystals grown by flux method for H||ab-plane and H||c-axis, respectively. This suggests that Pr occupies only about a half of the RE sites in TSFZ crystal. The other half of the RE sites is occupied most probably by the nonmagnetic Ba. Noteworthy, SC with T_c=43 K was observed earlier for Pr_{0.5}Ca_{0.5}Ba_2Cu_3O_{7-y} thin films. Ba^{2+} has a larger ionic radius than Pr^{3+} and so the substitution of Ba for Pr could give a natural explanation not only for the SC in TSFZ Pr123 but also for the elongation of the distance between the CuO_2 planes observed by Zou et al.Comment: Slightly extended version of Comment accepted to Phys. Rev. Lett. (v.81, N24, 1998), tentatevely to be publ. 14Dec98. 1 page, REVTex; 1 EPS fi

Effective Action of QED in Electric Field Backgrounds II: Spatially Localized Fields

We find the Bogoliubov coefficient from the tunneling boundary condition on a charged particle coupled to a static electric field $E_0 sech^2 (z/L)$ and, using the regularization scheme in Phys. Rev. D 78, 105013 (2008), obtain the exact one-loop effective action in scalar and spinor QED. It is shown that the effective action satisfies the general relation between the vacuum persistence and the mean number of produced pairs. We advance an approximation method for general electric fields and show the duality between the space-dependent and time-dependent electric fields of the same form at the leading order of the effective actions.Comment: RevTex 7 pages, no figure; extension of arXiv:0807.2696 to space-dependent electric fields; new section added on approximate effective actions in general electric fields and conclusion shortened; references added; replaced by the version to be published in Phys. Rev.

The probability distribution of the number of electron-positron pairs produced in a uniform electric field

The probability-generating function of the number of electron-positron pairs produced in a uniform electric field is constructed. The mean and variance of the numbers of pairs are calculated, and analytical expressions for the probability of low numbers of electron-positron pairs are given. A recursive formula is derived for evaluating the probability of any number of pairs. In electric fields of supercritical strength |eE| > \pi m^2/ \ln 2, where e is the electron charge, E is the electric field, and m is the electron mass, a branch-point singularity of the probability-generating function penetrates the unit circle |z| = 1, which leads to the asymptotic divergence of the cumulative probability. This divergence indicates a failure of the continuum limit approximation. In the continuum limit and for any field strength, the positive definiteness of the probability is violated in the tail of the distribution. Analyticity, convergence, and positive definiteness are restored upon the summation over discrete levels of electrons in the normalization volume. Numerical examples illustrating the field strength dependence of the asymptotic behavior of the probability distribution are presented.Comment: 7 pages, REVTeX, 4 figures; new references added; a short version of this e-print has appeared in PR

Schwinger Pair Production in dS_2 and AdS_2

We study Schwinger pair production in scalar QED from a uniform electric field in dS_2 with scalar curvature R_{dS} = 2 H^2 and in AdS_2 with R_{AdS} = - 2 K^2. With suitable boundary conditions, we find that the pair-production rate is the same analytic function of the scalar curvature in both cases.Comment: RevTex 6 pages, no figure; replaced by the version published in PR

Multidimensional Worldline Instantons

We extend the worldline instanton technique to compute the vacuum pair production rate for spatially inhomogeneous electric background fields, with the spatial inhomogeneity being genuinely two or three dimensional, both for the magnitude and direction of the electric field. Other techniques, such as WKB, have not been applied to such higher dimensional problems. Our method exploits the instanton dominance of the worldline path integral expression for the effective action.Comment: 22 pages, 13 figure

Renormalized Effective Actions in Radially Symmetric Backgrounds I: Partial Wave Cutoff Method

The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate one-dimensional radial determinant. While these individual radial determinants can be evaluated simply and efficiently using the Gel'fand-Yaglom method, the sum over all partial-wave contributions diverges. A renormalization procedure is needed to unambiguously define the finite renormalized effective action. Here we use a combination of the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This provides a more elegant technique for extracting the large partial-wave contribution, compared to the higher order radial WKB approach which had been used in previous work. We illustrate the general method with a complete analysis of the scalar one-loop effective action in a class of radially separable SU(2) Yang-Mills background fields. We also show that this method can be applied to the case where the background gauge fields have asymptotic limits appropriate to uniform field strengths, such as for example in the Minkowski solution, which describes an instanton immersed in a constant background. Detailed numerical results will be presented in a sequel.Comment: 35 page

Fermion Pair Production From an Electric Field Varying in Two Dimensions

The Hamiltonian describing fermion pair production from an arbitrarily time-varying electric field in two dimensions is studied using a group-theoretic approach. We show that this Hamiltonian can be encompassed by two, commuting SU(2) algebras, and that the two-dimensional problem can therefore be reduced to two one-dimensional problems. We compare the group structure for the two-dimensional problem with that previously derived for the one-dimensional problem, and verify that the Schwinger result is obtained under the appropriate conditions.Comment: Latex, 14 pages of text. Full postscript version available via the worldwide web at http://nucth.physics.wisc.edu/ or by anonymous ftp from ftp://nucth.physics.wisc.edu:/pub/preprints

Momentum dependence in the dynamically assisted Sauter-Schwinger effect

Recently it has been found that the superposition of a strong and slow electric field with a weaker and faster pulse can significantly enhance the probability for non-perturbative electron-positron pair creation out of the vacuum -- the dynamically assisted Sauter-Schwinger effect. Via the WKB method, we estimate the momentum dependence of the pair creation probability and compare it to existing numerical results. Besides the theoretical interest, a better understanding of this pair creation mechanism should be helpful for the planned experiments aiming at its detection.Comment: 4 pages RevTeX, 1 figur

Infra-red divergences in plane wave backgrounds

We show that the emission of soft photons via nonlinear Compton scattering in a pulsed plane wave (laser field) is in general infra-red divergent. We give examples of both soft and soft-collinear divergences, and we pay particular attention to the case of crossed fields in both classical and quantum theories.Comment: 15 pages, 7 figure