Transiçc oes de fase na mat eria de quarks densa
Transcrição
Transiçc oes de fase na mat eria de quarks densa
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eV) 1300 1200 materia de quarks−ud 1100 1000 56 Fe 930 900 800 Materia Nuclear (neutrons e protons) mat. de quarks−uds (materia estranha) 1 ~2 ε / ε0 . D<B "%( % ' 1 " 2 " % ' % $: ' 1" &2 " )( ' " K K H. 9' %&IDC<FFJ $ % " ""HCDJ " " " " $ %( ) % = Z % K = * 1D<F2 Z " $: & % % 1$ %2 " $: " " " % )" +" 7" +" ' D . DB ' # # 6) H - !&@ ' D <EGE 1<EEF2J %( " $: " & % K % Z K ) ** ) D 1 2 ) 1) 2 ) DG6 ) 1D<2 % % 6$1D<F2 ) ) ) " $: % )( 1) 2 1) 2 ( % 1) 2 K ) ) Q <1) ;2 Q ; ) Q 1) 2 K ) ) Q < ) Q ) Q < ) Q < 1D<C2 1D<G2 ) K H1 %£ 2 <J " $: ' " K ) ** ) K ) K Q ) ) DG6 1 2 ) ) ) ) ** ;; 1) 2 Q D 1) 2 D< 1D<E2 ) 1D2 )( ; 1) 2 6$1D2 % ; 1) 2 K ) ) Q <1< Q ) 2 ) Q ) Q< 1D<2 = '( ) % Z K ;6 1D2 " ( 16$1DG21DE22 "" '" ( " % %( 6$1D<2 % " $: & 6$1D2 $ ( * % ( ) %" % ( , 6$1D<2 % , / ' .1D2 6" %" $( ) % ' $ $ ( %( $ % ) ( ( $ HCFJ % " 7 % "%( K K + ) % $+" % " 5 ) '( % "" "%&" % Z K ;L 6 % "% " L " D 1D;2 $ + ) $%( ' " % ' $: K K K 6 ( " ( % $+" $: % K K K 1 2 1DD2 1DF2 % "%" " "" K K K 6< 1 2+ Q L 1D2 " ( "" ) 6 " %3"( * % +" $: + 1) 2 K ! % ) " % Z K Q Z 1DC2 K % Z K ) ** ) DG6 ) H 1) 2 D1) 2J 1DG2 )( 1) 2 1) 2 "" "" )" 6$1D<C D<G D<E2 % .1D;2 "% % ' ) % ) %" 5 % " ) .1D;2 " $ $ " ) " $ ) - " ( % $+" 16$DD DF2 % 6$1D2 "" '" ( 6$1DC DG2 % ) L %" "" / ' .1D2 D; 1040 SQM, C = 73 MeV/fm3 CFL, ∆ = 100 MeV CFL, ∆ = 40 MeV 1000 ε/nB [MeV] 960 920 880 840 800 1 2 3 4 5 6 7 nB/ρ0 . D;B % " ' % ) % ) 1L K L 2 ' $ $ ( ¾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eV/fm3 ] P [ MeVfm3 ] 140 ms0 = 170 MeV ∆2SC = 110 MeV 2SC CFL 180 160 140 120 100 80 60 120 100 80 coexistência de fases 60 40 40 20 20 300 a) 320 340 360 380 400 1.5 420 b) µB [ MeV ] 2 2.5 3 3.5 4 4.5 nB/ρ0 . DDB 8( ) 2 !( % $+" ' %( 7" % ' + ;FC M '2 !( ' %" % K C< " ) 6" % ( % "%" " ( %" " " " % " %" +% 3 ) 7 %( ' " " .1DD'2 3 % " % / " %" " 63 " ( % + ( " " 73 % % % " $: & % ( " + , ( %" " 6 ( ( % % .1DF2 ." " % $: & 1 K <C K < K <F 2 ( ) ) % ( % 1L K FCL 2 % 6$1<<;2 %+ < ! " $: & < ( ) ' ( ) % &" %" " ." " "3" % % ) L K << " " L K EF %1'2 " "+" L K G %12 6 " % "+" % % $ DG ∆2SC = 95 MeV 360 360 355 355 350 350 µc [ MeV ] µc [ MeV ] ∆2SC = 110 MeV 345 340 335 ms0 = 170 MeV ms0 = 160 MeV ms0 = 150 MeV 330 345 340 335 330 325 325 320 320 70 a) ms0 = 170 MeV ms0 = 160 MeV ms0 = 150 MeV 71 72 73 74 75 76 70 77 71 72 73 74 75 76 77 C [ MeV/fm3 ] b) C [ MeV/fm ] 3 ∆2SC = 80 MeV 360 355 ms0 = 170 MeV ms0 = 160 MeV ms0 = 150 MeV µc [MeV] 350 345 340 335 330 325 320 70 c) 71 72 73 74 75 76 77 C [ MeV/fm ] 3 . DFB ! ' + %" # # 6) " % ) / " $: & % 73 " B12 L K << 12L K EF 12L K G DE " ( ) ) " $: & K <F 5 ( "'" " " '" " " * $ ) " 12 ms0 = 170 MeV ∆CFL = 20 MeV PSQM - PCFL [ MeV/fm3 ] 10 8 6 4 2 0 280 320 360 400 440 480 520 µB [ MeV ] . DB ) %( % $+" ' % " " $: & K <C ) %( "' ) % + DG " " %12 .1DC2 % $ ( 5 .1D2 " "( % ' + ( % % $ ) %( " )" ,$ % .1DD2 " ( % % + , ( %" " % + ( 3"" % 73 % % % " $: & 1" " 2 N $ % " % $+" ' ( " " ' F ∆CFL = 15 MeV ∆ CFL = 20 MeV 580 580 ms0 = 170 MeV ms0 = 165 MeV ms0 = 160 MeV ms0 = 145 MeV 540 540 520 500 520 500 480 480 460 460 70 a) ms0 = 155 MeV ms0 = 150 MeV 560 µc [ MeV ] µc [ MeV ] 560 71 72 73 74 75 70 C [ MeV/fm3 ] 71 72 73 74 75 76 77 78 C [ MeV/fm3 ] b) ∆ CFL = 10 MeV 580 560 µc [MeV] 540 520 500 ms0 = 130 MeV 480 ms0 = 125 MeV ms0 = 120 MeV 460 70 c) 72 74 76 78 80 82 84 C [ MeV/fm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ransição de fase 2SC-SQM ms0 = 150 MeV ∆2SC = 110 MeV 220 200 180 P [ MeV/fm3 ] 160 140 120 100 80 coexistência de fases 60 40 20 1.5 2 2.5 3 3.5 4 4.5 5 5.5 nB/ρ0 . DGB !( ' % ( ) F; ms0 = 150 MeV ∆2SC = 110 MeV ms0 = 150 MeV ∆2SC = 80 MeV 380 380 370 SQM µ fc 370 360 360 350 350 µc [ MeV ] µc [ MeV ] SQM µic 340 330 2SC 340 320 320 310 310 300 300 70 a) 71 72 73 74 75 76 77 µ fc 330 70 b) C [ MeV/fm3 ] 2SC µic 71 72 73 74 75 76 77 C [ MeV/fm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² 5 %" )* %3"(B K ( Q ) ) ) ) % '( , $: $: )" $ K D69 5 ² ) ) )" " %" '+ " " "" " ( " $ % % $'0 K ) ) D69C$2 K D6(Æ 1F<<2 Æ %)+ % "" % ( " " 3 ; "" " ' ( K 1& & "" " ' $ K( Æ ( ( &$D K C <C ) ) D6( $2 )" "" '( 6$1FD2 "7 )" $ L < K ( Q < 9 < < $ $9 1F<2 ) ) " 2 1F<;2 5 ) " $ %$ $ K ²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² < % ) " $: % " / 12 )" % " $: $( 1'E 2 " & (& " " "'" ' ) % %$ " "%7 " " H;EJ %+ ; " " " " "% % %% " $: " %"% " ) %; " ' " " $: " %+ + 7 " "% / $+' " % $ % %( 6 %( 7 % % = K < =9 -- 1<2 - %" "% $: %( % %)+ "% %( ." " %( 1 2 " ( ) $ "" $: / 6" " / ( " %" %% %$ " $( %% "" " +" $ 3 " ( "HGJ HG;J %% "" 6" % )HGDJ " % " "% " " " )" " %"* ' " "%" % %( %% % , ( "% " 6 "% $ " '/ )+ " " 120 292 $ * $ %" " "% " " %" ") % ) $ $ " " $$ ' ! 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par - Pper P[(eV/cm^3)*10^35)] 6 5 4 3 Sem MMA ++Ppar --Pper 2 1 0 1e+18 5e+18 1e+19 5e+19 1e+20 B[Gauss] . B % %( % "B " $: " 1 "2 "" " " $ 7( " % % " $: 5 % ( K ' % " '3 "% " " $ "% " $: 5 "" 7 % $ " " $: " "" " " ' " ( " ' "% " " $: $ ( %" ! " % $: " ! 7( " GD .1e2 ___________ Sem MMA .. quark 7. B[(Gauss)*10^19] ________ Com MMA -quark - neutrons 4. 2. 1. 2e+37 5e+37 1e+38 2e+38 5e+38 1e+39 2e+39 5e+39 N[(cm^–3)] . ;B ( K % " $:B " " ! % " )HECJ GF / 6 '& " %" % % " $: ) ) % ( ( $: )"( " % % %+ % "7 + $( ) ) $ " "%&" $: ( $: ) * 3 " " "% # # 6) " $ )" %3" $ ) ( %' ( ( + " " ) $: " )"( " % % " " )" $ $ ) ( ( $: " " " $ ( 3" = " 7" " ' " % ' + %+ ( ) % " )3 ' %3" $+' " * * ) " " % " " 3" = " " " " %" " " % "% % ( " ) $: " ' ) "( "+ " % %" " $ 73 ( ' " G ) % ) " % 5 % ; % " " % %" ' % D %% %" % " % "'" % D ( " + "" ( '" + % % $+" ' 6 " '( % % %* " " ( ( % $ " " ' $ % ( 5 '& ( ( + " ) ( %" " * '" " , " " % ( '" " 1 3"% % " $: &2 % ) "3" << " ' 6$1<<2 %+ < " & '& " " " ( ( B 2 ' $ '& % " % $( ( ) > ) $ %( , &+' " 7 6 '" ' $ ( )"( " ( ( " &+' )" % %% % " $ ( / %" + ( &$: ( )" % % "H<CJ H<GJ " ( ) % "'" ( 5 3 " )"( "% ( " ( %" < SN %" & " " " ' %3"( " " " )" " " ( %( 3 )+ % ) GC " 6 ( $ " % '/ *( " " 1) & 0 2 $ % % " "%&" "'" " %% "% ( " '" " #N 2 $( % ) " $: % $: ("%& " ( ( $( " " " 3( % '& " $ % % ( "7( ( " %( " " ) % 3 ) * % " * " " " % $ " &+' 7 " " ( " " " ) ) " $: % " " 3 " & " % )" % " " ' % 7( "% " '/ 2 ! 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