Radiation Problems Accompanying Carrier Production by an Electric Field in the Graphene
Abstract
:1. Introduction
2. Kinetic Equations Describing Quantum Excitations in Graphene Placed in an Electric Field
2.1. Kinetic Equations Describing Zero Order Processes
2.2. Inclusion an Interaction with Quantized Electromagnetic Field
3. Setting of the Problem
4. Studying Processes in Specific External Fields
4.1. Models of External Fields
4.2. LowDensity Approximation
4.3. Calculating Kernels
5. Spectral Composition of Quantum Radiation
5.1. Annihilation Channel
5.2. Channel of the Momentum Redistribution
5.3. Comments on the Results Obtained
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
KE  kinetic equation 
CI  collision integral 
eh  electronhole 
BBGKY  Bogoliubov–Born–Green–Kirkwood–Yvon 
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1.  Here, and what follows, $\sigma =({\sigma}_{k},\phantom{\rule{4pt}{0ex}}k=1,2,3)$ are Pauli matrices,
$${\sigma}_{1}=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right),\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\sigma}_{2}=\left(\begin{array}{cc}0& i\\ i& 0\end{array}\right),\phantom{\rule{4pt}{0ex}}{\sigma}_{3}=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$$

2.  We note that the back reaction classical radiation accompanying the particle production by a slowly varying strong external electric field was evaluated in Ref. [43]. In this case, the backreaction field is also strong and slowly varying. 
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Gavrilov, S.P.; Gitman, D.M.; Dmitriev, V.V.; Panferov, A.D.; Smolyansky, S.A. Radiation Problems Accompanying Carrier Production by an Electric Field in the Graphene. Universe 2020, 6, 205. https://doi.org/10.3390/universe6110205
Gavrilov SP, Gitman DM, Dmitriev VV, Panferov AD, Smolyansky SA. Radiation Problems Accompanying Carrier Production by an Electric Field in the Graphene. Universe. 2020; 6(11):205. https://doi.org/10.3390/universe6110205
Chicago/Turabian StyleGavrilov, Sergei P., Dmitry M. Gitman, Vadim V. Dmitriev, Anatolii D. Panferov, and Stanislav A. Smolyansky. 2020. "Radiation Problems Accompanying Carrier Production by an Electric Field in the Graphene" Universe 6, no. 11: 205. https://doi.org/10.3390/universe6110205