Electrical conductivity of hot relativistic plasma in a strong magnetic field

IF 5 2区物理与天体物理 Q1 Physics and Astronomy

Physical Review D Pub Date : 2024-11-08 DOI:10.1103/physrevd.110.096009

Ritesh Ghosh, Igor A. Shovkovy

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In the relativistic regime, both conductivities exhibit an approximate scaling behavior described by <mjx-container ctxtmenu_counter=\"8\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(18 (5 0 (4 1 2 3)) 6 (17 7 16 (15 (10 8 9) (14 11 12 13))))\"><mjx-mrow data-semantic-children=\"5,17\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 17\" data-semantic-role=\"equality\" data-semantic-speech=\"sigma Subscript parallel to comma up tack Baseline equals upper T sigma overtilde Subscript parallel to comma up tack\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"18\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜎</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"1,2,3\" data-semantic-content=\"1,2\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"5\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"4\" data-semantic-role=\"metric\" data-semantic-type=\"punctuation\"><mjx-c>∥</mjx-c></mjx-mo><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"4\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mo data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"logic\" data-semantic-type=\"identifier\"><mjx-c>⊥</mjx-c></mjx-mo></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"18\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"7,15\" data-semantic-content=\"16\" data-semantic- data-semantic-owns=\"7 16 15\" data-semantic-parent=\"18\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"17\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"10,14\" data-semantic- data-semantic-owns=\"10 14\" data-semantic-parent=\"17\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mover data-semantic-children=\"8,9\" data-semantic- data-semantic-owns=\"8 9\" data-semantic-parent=\"15\" data-semantic-role=\"greekletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.102em; padding-left: 0.139em; margin-bottom: -0.533em;\"><mjx-mrow><mjx-mo data-semantic-annotation=\"accent:tilde\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\"><mjx-c>˜</mjx-c></mjx-mo></mjx-mrow></mjx-over><mjx-base><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜎</mjx-c></mjx-mi></mjx-mrow></mjx-base></mjx-mover></mjx-mrow><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"11,12,13\" data-semantic-content=\"11,12\" data-semantic- data-semantic-owns=\"11 12 13\" data-semantic-parent=\"15\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"14\" data-semantic-role=\"metric\" data-semantic-type=\"punctuation\"><mjx-c>∥</mjx-c></mjx-mo><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"14\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mo data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"logic\" data-semantic-type=\"identifier\"><mjx-c>⊥</mjx-c></mjx-mo></mjx-mrow></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container>, where <mjx-container ctxtmenu_counter=\"9\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) (6 3 4 5))\"><mjx-msub data-semantic-children=\"2,6\" data-semantic- data-semantic-owns=\"2 6\" data-semantic-role=\"greekletter\" data-semantic-speech=\"sigma overtilde Subscript parallel to comma up tack\" data-semantic-type=\"subscript\"><mjx-mover data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"greekletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.102em; padding-left: 0.33em; margin-bottom: -0.533em;\"><mjx-mo data-semantic-annotation=\"accent:tilde\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"operator\" style=\"width: 0px; margin-left: -0.191em;\"><mjx-c>˜</mjx-c></mjx-mo></mjx-over><mjx-base><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜎</mjx-c></mjx-mi></mjx-base></mjx-mover><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"3,4,5\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"3 4 5\" data-semantic-parent=\"7\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"6\" data-semantic-role=\"metric\" data-semantic-type=\"punctuation\"><mjx-c>∥</mjx-c></mjx-mo><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"6\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mo data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"logic\" data-semantic-type=\"identifier\"><mjx-c>⊥</mjx-c></mjx-mo></mjx-mrow></mjx-script></mjx-msub></mjx-math></mjx-container> are functions of the dimensionless ratio <mjx-container ctxtmenu_counter=\"10\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"10,7\" data-semantic-content=\"4\" data-semantic- data-semantic-owns=\"10 4 7\" data-semantic-role=\"division\" data-semantic-speech=\"StartAbsoluteValue e upper B EndAbsoluteValue divided by upper T squared\" data-semantic-structure=\"(11 (10 0 (9 1 8 2) 3) 4 (7 5 6))\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"9\" data-semantic-content=\"0,3\" data-semantic- data-semantic-owns=\"0 9 3\" data-semantic-parent=\"11\" data-semantic-role=\"neutral\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"10\" data-semantic-role=\"neutral\" data-semantic-type=\"fence\" style=\"vertical-align: 0.007em;\"><mjx-c>|</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"1,2\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"1 8 2\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑒</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐵</mjx-c></mjx-mi></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"10\" data-semantic-role=\"neutral\" data-semantic-type=\"fence\" style=\"vertical-align: 0.007em;\"><mjx-c>|</mjx-c></mjx-mo></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"11\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><mjx-msup data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"11\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em; margin-left: 0.052em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-math></mjx-container> (with <mjx-container ctxtmenu_counter=\"11\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-math></mjx-container> denoting temperature and <mjx-container ctxtmenu_counter=\"12\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper B\" data-semantic-type=\"identifier\"><mjx-c>𝐵</mjx-c></mjx-mi></mjx-math></mjx-container> magnetic field strength). We argue that the mechanisms for the transverse and longitudinal conductivities differ significantly, leading to a strong suppression of the former in comparison to the latter.","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"1 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.110.096009","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}

引用次数: 0

Abstract

We employ first-principles quantum field theoretical methods to investigate the longitudinal and transverse electrical conductivities of a strongly magnetized hot quantum electrodynamics (QED) plasma at the leading order in coupling. The analysis employs the fermion damping rate in the Landau-level representation, calculated with full kinematics and exact amplitudes of one-to-two and two-to-one QED processes. In the relativistic regime, both conductivities exhibit an approximate scaling behavior described by

𝜎 ∥, ⊥ = 𝑇 ˜ 𝜎 ∥, ⊥

, where

˜ 𝜎 ∥, ⊥

are functions of the dimensionless ratio

| 𝑒 𝐵 | / 𝑇 2

(with

𝑇

denoting temperature and

𝐵

magnetic field strength). We argue that the mechanisms for the transverse and longitudinal conductivities differ significantly, leading to a strong suppression of the former in comparison to the latter.

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强磁场中热相对论等离子体的电导率

我们采用第一原理量子场论方法研究了强磁化热量子电动力学（QED）等离子体在耦合前沿阶的纵向和横向电导率。分析采用了朗道级表示中的费米子阻尼率，并计算了一对二和一对一 QED 过程的完整运动学和精确振幅。在相对论系统中，两种电导率都表现出近似的缩放行为，即𝜎∥,⊥=𝑇˜𝜎∥,⊥、其中，˜𝜎∥,⊥ 是无量纲比率 |𝑒𝐵|/𝑇2 的函数（𝑇 表示温度，𝐵 表示磁场强度）。我们认为，横向导电率和纵向导电率的机制有很大不同，导致前者比后者受到强烈抑制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physical Review D 物理-天文与天体物理

CiteScore

9.20

自引率

36.00%

发文量

审稿时长

2 months

期刊介绍： Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics. PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including: Particle physics experiments, Electroweak interactions, Strong interactions, Lattice field theories, lattice QCD, Beyond the standard model physics, Phenomenological aspects of field theory, general methods, Gravity, cosmology, cosmic rays, Astrophysics and astroparticle physics, General relativity, Formal aspects of field theory, field theory in curved space, String theory, quantum gravity, gauge/gravity duality.