Rotating Relativistic Systems

Transkrypt

1

2 Rotating Relativistic Systems NASA/JPL-Caltech NASA/Tod Strohmayer binary star merger neutron star black hole noncentral heavy-ion collision Angular momentum of heavy-ions Vorticity (or Rotation) First evidence: global Λ-polarization (2017) 21 & 10 <latexit sha1_base64="ndyehz3ksfd0fgvno0gcvbpxlhk=">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</latexit> Hz ' 10 2 m Necessary to know Rotational effect on QFT

3 <latexit sha1_base64="zb8jtfkksllwpdnltyhsx2xyals=">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</latexit> <latexit sha1_base64="zb8jtfkksllwpdnltyhsx2xyals=">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</latexit> <latexit sha1_base64="zb8jtfkksllwpdnltyhsx2xyals=">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</latexit> <latexit sha1_base64="zb8jtfkksllwpdnltyhsx2xyals=">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</latexit> <latexit sha1_base64="ktljh817btd/u4avd8zw4y6wq3u=">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</latexit> <latexit sha1_base64="ktljh817btd/u4avd8zw4y6wq3u=">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</latexit> <latexit sha1_base64="ktljh817btd/u4avd8zw4y6wq3u=">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</latexit> <latexit sha1_base64="ktljh817btd/u4avd8zw4y6wq3u=">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</latexit> angular momentum conservation Hz ' 10 MeV STAR (2017) Ampere's law eb G ' m 2 Skokov, Illarionov, Toneev (2009) How are the magnetic properties modified by rotation? e.g. anomalous transport and chiral symmetry breaking

4 v edge = R apple 1 R apple 1/ < 1 R Ω v edge = R Ω x µ lab x µ rot

5 Ω eb Ω eb

6 Ω

7 <latexit sha1_base64="z1g2mi5hn19/byhcg0vvmnwccoq=">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</latexit> <latexit sha1_base64="z1g2mi5hn19/byhcg0vvmnwccoq=">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</latexit> <latexit sha1_base64="z1g2mi5hn19/byhcg0vvmnwccoq=">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</latexit> <latexit sha1_base64="z1g2mi5hn19/byhcg0vvmnwccoq=">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</latexit> <latexit sha1_base64="woqvt5ngyrcsutzmwpmllw7dxe4=">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</latexit> <latexit sha1_base64="woqvt5ngyrcsutzmwpmllw7dxe4=">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</latexit> <latexit sha1_base64="woqvt5ngyrcsutzmwpmllw7dxe4=">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</latexit> <latexit sha1_base64="woqvt5ngyrcsutzmwpmllw7dxe4=">aaaci3icsyriyswumtc4ycjezmlkxs7bycxnw8vhlyaoffacx1qunbqanj+txxsrlficmpozlxpaklmskxprujsamjuukxqelo0mkg8vsy0qzszpcympleinzu1mz8tmy0xolaekxquoxwqklij4xfcp2crozmpuxbqkfpvkjubev+pwitia8qlkbnogykcaytcempqzocagx2a5qwxdckm+qzjdkumuqypdhkmjkj3dkmhqditrdiymbgwfqlfyhmqgwbgqlqmwt2wozeac6i0fqkofqkgeimydyxqglxoqmgfkg8wsbutobtqsa8rfqj0kdkogvw1wgnw2oggw2uclwr+czlwdzqc5prjij0h0phbe83djbh8nqcsxsjcwzcb04xvzcumagwxyrzlatxearuc+sibol6ua/jnykki1ws1gkcfropsxgtw0oaz0qv7zl+slgalbsxm4gbfgib7cmiwwiz1daz3dqbnlbydovhawsdmomwgaw9ucwyhbgygairrobw/djobddhuyejmmmayybcbkmriheoqzuactkwal0pfg</latexit> [i µ µ + µ ) m] =0 R x z Ω y g µ = 0 1 r 2 2 y x 0 y x C A f(") = 1 e {" (l+1/2)} +1 ˆL z = i(x@ y y@ y )

8 R<latexit sha1_base64="bb2djehy55aoi3+peen9ch9jpc4=">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</latexit> <latexit sha1_base64="bb2djehy55aoi3+peen9ch9jpc4=">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</latexit> <latexit sha1_base64="bb2djehy55aoi3+peen9ch9jpc4=">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</latexit> <latexit sha1_base64="bb2djehy55aoi3+peen9ch9jpc4=">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</latexit> <latexit sha1_base64="qkl3svdccmanxxg9cxlc9cxq7/s=">aaaczhichvhlssnafd2nr1ofryogcfisfvflrgtfvdgns9taw1crje5rajqejc3u4g/ovnhhskfe/aw3/oalf0aqlxxcupa2dygw9q4zc+bmpxfozki2obse0vni6unt6x8id0aghkdgo7gx8s3xqjmayguwytlfvxgfozsi7+meiyq2i5sqaoicwllr7xfqwnf1y9z0grbyrspluy/pmuixlbh3yglkkr/xbiahiiegnqzydxawdwsaaqhcwith2iacl9s2zbbs5nbrzm5hppv7akeislbgwyizfgyrpjz5tr2wjq/bnv1frfepbnehlxek6zfuquupdecv9pfrrazfo+2lwbpa0qp7l3o8lxv/v1xl2cpbl+ppzx5kwpa96uzd9pn2lbsovn543sqtzjpnobqiv/z/su90zzcw62/aduzklxdhd5b/pnc32fpiyzssm4uj9grwfwfmyxbz/n5lsgmdg8jzuqinomvz6fkaliakyu6qfao0e/gw0swn5kyj8a==</latexit> <latexit sha1_base64="qkl3svdccmanxxg9cxlc9cxq7/s=">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</latexit> <latexit sha1_base64="qkl3svdccmanxxg9cxlc9cxq7/s=">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</latexit> <latexit sha1_base64="qkl3svdccmanxxg9cxlc9cxq7/s=">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</latexit> <latexit sha1_base64="9vdwfek3rtes1sset4ktxmmif2y=">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</latexit> <latexit sha1_base64="9vdwfek3rtes1sset4ktxmmif2y=">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</latexit> <latexit sha1_base64="9vdwfek3rtes1sset4ktxmmif2y=">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</latexit> <latexit sha1_base64="9vdwfek3rtes1sset4ktxmmif2y=">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</latexit> <latexit sha1_base64="gafg05qafuekxrbga0w2yvewbq0=">aaacm3ichvfns9xqfd3gz45wr7spibaclf2u4ayufugquiniqkdhbsmhsz/jyzljm8kmapg/0d/qrbupicl+c90idtufp0g6tnbnf97jbkwv6g1577xz77nvvpcc5ckojrrq0dq7unt6+57l+geedw7lh0fwoqaeuqlsbl4qbjh2jdzpi3isy09sqfdyncct6051vpvfb4gwkog/gu8rsvwzk77clq4dm2xlj5vlkheqfvzpzd1pjd6batmmwkkxmnrorijdu4rxn7dybspsgvpdygsggcywgvwxthxeabd11cdgi2bswube3yymebrzw0iycxnjnc/qri61da4sxgezw+wxwqvnjpv53eozpwqxd/h4d1mpy4j+0and0awd0jx9+w+vjo3r8rlps9pwcmunfxq58vtjvy3ngdv3qkc9x9jgdopvsnevmq1tug194+dzzcpmasj5ryf0k/1/oys65xp4jv/u0biofugoh8d497ofgrw3ryokxvk7wtz77cn6mipxvob7nsicpmajzd73k85wie/amdavlwil7vkti9o8wf+hlw8b8ccehg==</latexit> <latexit sha1_base64="gafg05qafuekxrbga0w2yvewbq0=">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</latexit> <latexit sha1_base64="gafg05qafuekxrbga0w2yvewbq0=">aaacm3ichvfns9xqfd3gz45wr7spibaclf2u4ayufugquiniqkdhbsmhsz/jyzljm8kmapg/0d/qrbupicl+c90idtufp0g6tnbnf97jbkwv6g1577xz77nvvpcc5ckojrrq0dq7unt6+57l+geedw7lh0fwoqaeuqlsbl4qbjh2jdzpi3isy09sqfdyncct6051vpvfb4gwkog/gu8rsvwzk77clq4dm2xlj5vlkheqfvzpzd1pjd6batmmwkkxmnrorijdu4rxn7dybspsgvpdygsggcywgvwxthxeabd11cdgi2bswube3yymebrzw0iycxnjnc/qri61da4sxgezw+wxwqvnjpv53eozpwqxd/h4d1mpy4j+0and0awd0jx9+w+vjo3r8rlps9pwcmunfxq58vtjvy3ngdv3qkc9x9jgdopvsnevmq1tug194+dzzcpmasj5ryf0k/1/oys65xp4jv/u0biofugoh8d497ofgrw3ryokxvk7wtz77cn6mipxvob7nsicpmajzd73k85wie/amdavlwil7vkti9o8wf+hlw8b8ccehg==</latexit> <latexit sha1_base64="gafg05qafuekxrbga0w2yvewbq0=">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</latexit> L p p? sin(px) x=l =0 Z r =0 J`(x) p = n L r=r p? = l,k R L l,1 R l,k :thekth root of J l (x) `2 `4 x `1 `3

9 T = 0 q " = p 2? + p2 z p? = l,4 /R p? = l,3 /R p? = l,2 /R p? = l,1 /R l,1 /R p z

10 <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">aaac+xichvhlahrbfl3dvml7ykgbwu3hejkxzlwdbeuqgm7cmyetbnjxqo7u9bspflbdmxkb/ghxggtxectx0k/ijj/gip8glimi4slbpq0mxsdtuuruufeculxlp0pmbnhpso8dp3hy1mrp58zzc+cngxculmfjuaeigyqq0as+z4sssegaazrytbxgka/eir95v8yvjitozbi/mlupwi94gmu+dlghqtd43m95i65fmkmvxg3g7jkvr3mqu0uuhueelwz38gmlbmz7gimqt9s0e2o27rwsmhylx6nuqgu4mfzr5alz/ubrbqwzl8pwiyuzg+5lut1rnlgdvbcjwk1be+qytxpvwimnsccaiuqgiazdwaghjl41caehjw4dcui0ivnlbrtgkhzivyiqolgbnia0wqvzmnalz1apa9pf0a9jywakp+e73mdd/icf8cdfvflko+xli2z/rbvpb/lz5avv/1vfnbsy/fl9s2cdfbhd9sqp97riylmey/3o6yv9ptulu/k1fivfqp9t3mmdoke8+hq8xhcll8ghb3b/v+6jyhm242lhxbjznltxp8uexigr0kl7vgvz8admouv7frey1bau27m9bb+1349lbavwxijdyx/8cqy/vw8=</latexit> <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> T = 0 f(") = 1 e {" (l+1/2)} +1! f(") = (l +1/2) " (l +1/2) l,1 /R p z

11 <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> <latexit sha1_base64="9dvm0iu/m0yzvf0se0ffus4hs5e=">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</latexit> T = 0 f(") = 1 e {" (l+1/2)} +1! f(") = (l +1/2) " (l +1/2) l,1 /R p z

12 T = 0 apple 1/R " l,1 /R > (l +1/2) l T = 0 p z j 5 = T 2 12

13 eb

14 1/ p eb R eb R p? = p 2neB l 1/ p eb 1/ p eb. R l p? ' p 2neB eb l

15 eb [i µ µ + iea µ ) m] =0 R p l l = ebr 2 /2 p l [R 1 ] p 0 [R 1 ] p 0 = 0,1 /R ' 2.4/R l<0 eb l 0 p 0 =0

16 Ω eb

17 eb p 0 [R 1 ] R = ebr 2 /2 l,1 /R p z p z

18 eb p 0 [R 1 ] R = ebr 2 /2 (l +1/2) l,1 /R (l +1/2) p z p z

19 <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="bs8qllljyyde7wbnfuyzjjm+zmk=">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</latexit> <latexit sha1_base64="gjjedj3y6xf1//spjk6tlar0m3g=">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</latexit> <latexit sha1_base64="gjjedj3y6xf1//spjk6tlar0m3g=">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</latexit> <latexit sha1_base64="36qpxyhdfc7cx9qlrm3wsrwm7ds=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="s+vtfahl6kv4wlzvju0coozxbhg=">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</latexit> <latexit sha1_base64="tqpv1s0jb2dqdqwugoxzno8idw8=">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</latexit> <latexit sha1_base64="tqpv1s0jb2dqdqwugoxzno8idw8=">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</latexit> <latexit sha1_base64="tqpv1s0jb2dqdqwugoxzno8idw8=">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</latexit> <latexit sha1_base64="tqpv1s0jb2dqdqwugoxzno8idw8=">aaacinichvfnlyxbfd2a52n4ddysm4njvfhnbove10awsms8qwjk0t1qrtht3emumyto/af+giuviyhy2bk08qcs/iqxsxibc3d6wgr5791o1z116p5bp6pmz5abinpo0vrbfrr3dhylunt+9vyl+wdwa7fqwyjvubbrr5tgigzpilysyhbrni+mimmlnxn3vrg+vhn+if3nt9rzxgbfkduyjc1dmvvmzgol37dcwpawlzeqleqpv38nysvq7ttrxwsashrf6jvqy5bghetu8hwfbmgfhsoqehcggnswepc3ar0ej7lnhmz5jgs0llbhgrvvrhjcytc7y2ozzxsx6/c80toi1bbvyvpvszkfdn3tbt3rhv3sh3r9a68w6thwssfzbgqfv+w7gmq9/fdv4ayw/ah6p2efeiyjr5k9exhtoixv1nf2j55y0yuz8bed0ip7p6ehuuutolvn62xzrbwjwq+gf73u72b1lkttvl8et8/oxu/riwgmyjtvewkzwmqs8rzvia5wjrutrxvtprszzqnwemsg8sm0htcqlzhy</latexit> [i µ µ + iea µ + µ )] =0 R Ω eb n(r) =h (x) (x)i = X h i f + (") f (") p z,p? 1 f ± (") = e (" j) +1 r-dependence n(r = 0)! p eb eb 4 2 S S µb = µg ij B i j g ij T ij =#eb i j

20 M T =0 R = 10 3 [ 1 ] eb M eb M

21 <latexit sha1_base64="tqg6fhaxvab/rc2hefobw23l4g0=">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</latexit> <latexit sha1_base64="tqg6fhaxvab/rc2hefobw23l4g0=">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</latexit> <latexit sha1_base64="tqg6fhaxvab/rc2hefobw23l4g0=">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</latexit> µ<latexit sha1_base64="tqg6fhaxvab/rc2hefobw23l4g0=">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</latexit>

22 T ij =#eb i j B