In- and out-states of scalar particles confined between two capacitor plates

Authors

DOI:

https://doi.org/10.33910/2687-153X-2020-1-1-30-39

Keywords:

exact solutions, Klein-Gordon-Fock equation, potential step, strong electric field, non-commutative integration method

Abstract

In this article, a non-commutative integration method of linear differential equations is used to consider the Klein-Gordon-Fock equation with the L-constant electric field with large L, and light cone variables are used to find new complete sets of its exact solutions. These solutions can be related by integral transformations to previously known solutions described by Gavrilov and Gitman (2016b). Then, using the general theory developed by Gavrilov and Gitman (2016a), this article constructs (in terms of new solutions) the so-called in- and out-states of scalar particles confined between two capacitor plates.

References

Akal, I., Egger, R., Müller, C., Villalba-Chávez, S. (2019) Simulating dynamically assisted production of Dirac pairs in gapped graphene monolayers. Physical Review D, 99 (1), 016025. DOI: 10.1103/PhysRevD.99.016025 (In English)

Akhmedov, E. T., Popov, F. K. (2015) A few more comments on secularly growing loop corrections in strong electric fields. Journal of High Energy Physics, 9, 85. DOI: 10.1007/JHEP09(2015)085 (In English)

Allor, D., Cohen, T. D., McGady, D. A. (2008) Schwinger mechanism and graphene. Physical Review D, 78 (9), 096009. DOI: 10.1103/PhysRevD.78.096009 (In English)

Anderson, P. R., Mottola, E. (2014) Instability of global de Sitter space to particle creation. Physical Review D, 89 (10), 104038. DOI: 10.1103/PhysRevD.89.104038 (In English)

Bagrov, V. G., Baldiotti, M. C., Gitman, D. M., Shirokov, I. V. (2002) New solutions of relativistic wave equations in magnetic fields and longitudinal fields. Journal of Mathematical Physics, 43, 2284. DOI: 10.1063/1.1461428 (In English)

Breev, A. I., Shapovalov, A. V. (2016) The Dirac equation in an external electromagnetic field: Symmetry algebra and exact integration. Journal of Physics: Conference Series, 670, 012015. DOI: 10.1088/1742-6596/670/1/012015 (In English)

Das Sarma, S., Adam, S., Hwang, E. H., Rossi, E. (2011) Electronic transport in two-dimensional graphene. Reviews of Modern Physics, 83 (2), 407. DOI: 10.1103/RevModPhys.83.407 (In English)

Di Piazza, A., Müller, C., Hatsagortsyan, K. Z., Keitel, C. H. (2012) Extremely high-intensity laser interactions with fundamental quantum systems. Reviews of Modern Physics, 84 (3), 1177. DOI: 10.1103/RevModPhys.84.1177 (In English)

Dunne, G. V. (2009) New strong-field QED effects at extreme light infrastructure. The European Physical Journal D, 55 (2), 327. DOI: 10.1140/epjd/e2009-00022-0 (In English)

Dunne, G. V. (2014) Extreme quantum field theory and particle physics with IZEST. The European Physical Journal Special Topics, 223 (6), 1055–1061. DOI: 10.1140/epjst/e2014-02156-4 (In English)

Fradkin, E. S., Gitman, D. M. (1981) Furry picture for quantum electrodynamics with pair-creating external field. Fortschritte der Physik — Progress of Physics, 29 (9), 381–411. DOI: 10.1002/prop.19810290902 (In English)

Fradkin, E. S., Gitman, D. M., Shvartsman, S. M. (1991) Quantum electrodynamics with unstable vacuum. Berlin: Springer, 288 p. (In English)

Gavrilov, S. P., Gitman, D. M. (2016a) Quantization of charged fields in the presence of critical potential steps. Physical Review D, 93 (4), 045002. DOI: 10.1103/PhysRevD.93.045002 (In English)

Gavrilov, S. P., Gitman, D. M. (2016b) Scattering and pair creation by a constant electric field between two capacitor plates. Physical Review D, 93 (4), 045033. DOI: 10.1103/PhysRevD.93.045033 (In English)

Gavrilov, S. P., Gitman, D. M., Gonçalves, A. E. (1998) QED in external field with space-time uniform invariants: Exact solutions. Journal of Mathematical Physics, 39 (7), 3547. DOI: 10.1063/1.532451 (In English)

Gavrilov, S. P., Gitman, D. M., Shishmarev, A. A. (2017) Particle scattering and vacuum instability by exponential steps. Physical Review D, 96 (9), 096020. DOI: 10.1103/PhysRevD.96.096020 (In English)

Gavrilov, S. P., Gitman, D. M., Shishmarev, A. A. (2019) Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential. Physical Review D, 99 (11), 116014. DOI: 10.1103/PhysRevD.99.116014 (In English)

Gavrilov, S. P., Gitman, D. M., Shvartsman, Sh. M. (1979) Green’s functions in an external electric field. Soviet Journal of Nuclear Physics, 29, 567–572. (In English)

Gavrilov, S. P., Gitman, D. M., Yokomizo, N. (2012) Dirac fermions in strong electric field and quantum transport in graphene. Physical Review D, 86 (12), 125022. DOI: 10.1103/PhysRevD.86.125022 (In English)

Gelis, F., Tanji, N. (2016) Schwinger mechanism revisited. Progress in Particle and Nuclear Physics, 87, 1–49. DOI: 10.1016/j.ppnp.2015.11.001 (In English)

Gitman, D. M. (1977) Processes of arbitrary order in quantum electrodynamics with a pair-creating external field. Journal of Physics A: Mathematical and General, 10 (11), 2007–2020. DOI: 10.1088/0305-4470/10/11/026 (In English)

Hegelich, B. M., Mourou, G., Rafelski, J. (2014) Probing the quantum vacuum with ultra-intense laser pulses. The European Physical Journal Special Topics, 223 (6), 1093–1104. DOI: 10.1140/epjst/e2014-02160-8 (In English)

Kané, G., Lazzeri, M., Mauri, F. (2015) High-field transport in graphene: The impact of Zener tunneling. Journal of Physics: Condensed Matter, 27 (16), 164205. DOI: 10.1088/0953-8984/27/16/164205 (In English)

Mourou, G., Tajima, T. (2014) Summary of the IZEST science and aspiration. The European Physical Journal Special Topics, 223 (6), 979–984. DOI: 10.1140/epjst/e2014-02148-4 (In English)

Narozhnyi, N. B., Nikishov, A. I. (1976) Solutions of the Klein-Gordon and Dirac equations for a particle in a constant electric field and a plane electromagnetic wave propagating along the field. Theoretical and Mathematical Physics, 26 (1), 9–20. DOI: 10.1007/BF01038251 (In English)

Oladyshkin, I. V., Bodrov, S. B., Sergeev, Yu. A. et al. (2017) Optical emission of graphene and electron-hole pair production induced by a strong terahertz field. Physical Review B, 96 (15), 155401. DOI: 10.1103/PhysRevB.96.155401 (In English)

Ruffini, R., Vereshchagin, G., Xue, S.-S. (2010) Electron–positron pairs in physics and astrophysics: From heavy nuclei to black holes. Physics Reports, 487 (1–4), 1–140. DOI: 10.1016/j.physrep.2009.10.004 (In English)

Schwinger, J. (1951) On gauge invariance and vacuum polarization. Physical Review, 82 (5), 664. DOI: 10.1103/PhysRev.82.664 (In English)

Shapovalov, A. V., Shirokov, I. V. (1995) Noncommutative integration of linear differential equations. Theoretical and Mathematical Physics, 104 (2), 921–934. DOI: 10.1007/BF02065973 (In English)

Vafek, O., Vishwanath, A. (2014) Dirac fermions in solids: From high- cuprates and graphene to topological insulators and Weyl semimetals. Annual Review of Condensed Matter Physics, 5 (1), 83–112. DOI: 10.1146/annurev-conmatphys-031113-133841 (In English)

Published

2020-03-27

Issue

Section

Theoretical Physics