MAGNETIC FIELDS EVERYWHERE

Transcription

1 MAY 1, 016

2 MAGNETIC FIELDS EVERYWHERE [Miransky & Shovkovy, Physics Reports 576 (015) pp. 1-09] May 1, 016

3 Universe Current galactic magnetic fields ~ 10-6 G Current magnetic fields in voids ~ G Problem of magnetogenesis in Early Universe Perhaps during the electro-weak phase transition 100 to 104 G (~ 1 GeV to 100 GeV) May 1, 016 3

4 Dense baryonic matter Magnetized dense baryonic matter 1010 to 1018 G (10 kev to 100 MeV) Magnetic field may affect Competition of ground state phases EoS of dense baryonic matter the M-R relation of compact stars Transport and emission properties Evolution of supernovas & protoneutron stars May 1, 016 4

5 Little Bangs Magnetized QGP at RHIC/LHC B ~ 1018 to 1019 G (~ 100 MeV) B v v [Rafelski & Müller, PRL, 36, 517 (1976)], [Kharzeev et al., arxiv: ], [Skokov et al., arxiv: ], [Voronyuk et al., arxiv: ], [Bzdak &. Skokov, arxiv: ], [Deng & Huang, arxiv: ] Using Lienard-Wiechert potentials, May 1, 016 5

6 CME, CSE, CMW, etc. Chiral magnetic/separation effects, chiral magnetic waves (correlations of charged particle in HIC) Signs of local P-violation? [Kharzeev, McLerran, Warringa, Nucl. Phys. A 803, 7 (008)] [Fukushima, Kharzeev, Warringa, Phys. Rev. D 78, (008)] [Kharzeev, Liao, Voloshin, Wang, Prog. Part. Nucl. Phys. 88, 1 (016)] Signs of a chiral magnetic wave? [Yee, Kharzeev, Phys. Rev. D 83, (011)] [Gorbar, Miransky, Shovkovy, Phys. Rev. D 83, (011)] [Burnier, Kharzeev, Liao, Yee, Phys. Rev. Lett. 107 (011) 05303] May 1, 016 6

7 Dirac/Weyl materials High magnetic field lab 105 G (~ 100 vf=c/300) Graphene 3D materials with Dirac/Weyl quasiparticles Bi1-xSbx alloy (at x 4%) Na3Bi [Z. K. Liu et al., arxiv: ] [M. Neupane et al., arxiv: ] Cd3As [S. Borisenko et al., arxiv: ] [X. Li et al., arxiv: ] ZrTe5 TaAs, NbAs, TaP, [arxiv: , arxiv: , arxiv: , arxiv: ] May 1, 016 7

8 CHIRAL SEPARATION EFFECT May 1, 016 8

9 Chirality & Anomaly Chirality/helicity of a massless (or ultrarelativistic) particle is (approximately) conserved Right-handed Left-handed Σ p 5 Ψ = sign( p0 )γ Ψ p Conservation of chiral charge is a property of massless Dirac theory (classically) The symmetry is anomalous at quantum level (nr nl ) e µνκλ + j5 = ε Fµν Fκλ t 16 π May 1, 016 9

10 Chiral separation effect Slowly changing electric/chemical potential µ(z) = eφ(z) ee z = z (eφ) = z µ From the anomaly relation, e e z j 53 = Bz E z = Bz z µ π π Suggesting that, for massless fermions, [Vilenkin, Phys. Rev. D (1980) 3067] [Metlitski & Zhitnitsky, Phys. Rev. D 7, (005)] [Newman & Son, Phys. Rev. D 73 (006) ] May 1,

11 Landau spectrum at B 0 Dirac equation with massless fermions $i γ i γ + i e A & Ψ = 0 0 % ' ( 0 ) Energy spectrum E (3+1) n ( p3 ) = ± n eb + p where 3 s = ± 1 (spin) Occupied 1 n = s+ k + k = 0, 1,, (orbital) May 1,

12 Landau spectrum & µ 0 Right-handed: Left-handed: µ May 1, 016 What if LLL is partially filled? 1

13 Partially filled LLL Spin polarized LLL is chirally asymmetric states with p3<0 (and s= ) are R-handed states with p3>0 (and s= ) are L-handed i.e., a nonzero axial current is induced er er er er p3 p3 p3 p3 s s s s Nonzero axial current j5 May 1, 016 s s s s j5 p3 p3 p3 p3 el el el el 13

14 MOTIVATION Real systems are finite in size inhomogeneous time-dependent May 1,

15 Any effects of finite size? Magnetic field + electric chemical potential = chiral current Positive chiral charge? j5 B µ 0 eb µ j5 = π Is the chiral charge truly separated? Negative chiral charge? May 1,

16 CSE in finite system Model of Dirac semimetal with a slab geometry y B z where and a m(z) = M θ (z a ) + m θ (a z ), -a x with vacuum band gap: M (broken chiral symmetry) Boundary conditions: [Gorbar, Miransky, Shovkovy, Sukhachov, Phys. Rev. B 9, (015)] May 1,

17 Wave functions Wave functions are standing waves, e.g., where the wave vector pz is determined by the spectral equation [Gorbar, Miransky, Shovkovy, Sukhachov, Phys. Rev. B 9, (015)] May 1,

18 Discretized CSE Only LLL contributes For m 0: m=0 m=0.05 ev vf=.5 ev Å vf=.5 ev Å a=100 Å a=100 z=0 [Gorbar, Miransky, Shovkovy, Sukhachov, Phys. Rev. B 9, (015)] May 1,

19 Quantization of axial current Axial current density is non-uniform when m 0 m=0 m=0.05 ev vf=.5 ev Å vf=.5 ev Å a=100 Å a=100 Å Note that axial charge density vanishes: j50 = 0 [Gorbar, Miransky, Shovkovy, Sukhachov, Phys. Rev. B 9, (015)] May 1,

20 Axial current as a standing wave? L-handed B R-handed Recall that LLL is spin polarized B A perfect chirality flip at the boundary [Gorbar, Miransky, Shovkovy, Sukhachov, Phys. Rev. B 9, (015)] May 1, 016 0

21 Key observations Chiral current in the CSE is discretized m 0: chiral current density is non-uniform m=0: chiral current density is uniform Chiral current is not necessarily connected with a flow of chiral charge Chiral current need not lead to chiral charge accumulation on the boundary May 1, 016 1

22 FURTHER DEVELOPMENTS Anomalous Maxwell equations for chiral plasmas [Gorbar, Shovkovy, Vilchinskii, Rudenok, Boyarsky, Ruchayskiy, arxiv: ] May 1, 016

23 Magnetic field/helicity Magnetic helicity evolution (inverse cascade) in the Early Universe 1 E 4π B = (σ E +C5µ5B ) + c 1 B E = c t E = 4π ρ, c t B = 0 [Vilenkin, Phys. Rev. D, 3080 (1980)] [Joyce & Shaposhnikov, astro-ph/ ] [Giovannini & Shaposhnikov, hep-ph/971034] For specific helicity eigenmodes: dbk c k ck C 5µ5 4π dt σ May 1, 016 Bk [Boyarsky et al., arxiv: ] [Tashiro et al., arxiv: ] [Manuel et al., arxiv: ] [Buividovich et al., arxiv: ] [Hirono et al., arxiv: ] 3

24 Feedback on µ5(t) Constraint of the total helicity conservation hfermion = h0 - hgauge Common homogeneous approximation: n5 ( x,t ) n5 ( x,t ) 3 3c, µ5 (t ) n5 ( x,t ) space T space In other words, the value of µ5 remains constant on distance scales Δx ~ (kcrit)-1 ~ (µ5)-1 May 1, 016 4

25 Magnetic field/helicity Magnetic helicity is transferred from short to longwavelengths modes, while the value of µ5 decreases From [Hirono et al., arxiv: ] From [Boyarsky et al., arxiv: ] May 1, 016 5

26 Open questions Will the cascade survive if there are variations of order δµ5 on distance scales (kcrit)-1? How large δµ5 can be tolerated? Will dynamical fluctuations of µ5 stay under control? How to account for inhomogeneities in the anomalous Maxwell equations? nλ ( x,t ) =? j λ ( x,t ) =? How to obtain equations for µ(t,x) and µ5(t,x)? May 1, 016 6

27 Framework Chiral kinetic theory as a starting point: where is an expansion in powers of e-m field & µ λ, t µ λ [Gorbar, Shovkovy, Vilchinskii, Rudenok, Boyarsky, Ruchayskiy, arxiv: ] May 1, 016 7

28 Equations for chemical potentials Resulting equation of motion for µλ: nλ(0) µ λ e τ c e τ µ λ µ λ λ e E = + Eλ B E λ + λ µ λ t 3 x 4π c 3π c ( 3 µ + π T µλ (0) λ where nλ = 3π c 3 and ) 1 µ Eλ = E λ e x The corresponding equations for the currents: CME e µ5 B 3 µ + µ eτt c π c π T eµ B e τ T 3 µ + µ5 j5 = 1+ 9c π T π c j= ( ( CSE May 1, 016 Hall type drift & diffusion diffusion ) ee µ + e τ µ ee µ B + j ) x 3π x new µ5 + e τ µ5 µ ee µ + j x x 5,new 3π c CESE 8

29 New types of currents New contribution to the electric current: ( 5 τ µ µ5 µ5 e τ µ5 µ5 e τ 3µ + 3µ + π T B j new = 3π c x 3π x 9 π c Chiral diffusion ) E t Hall diffusion New contribution to the chiral current: Chiral Hall diffusion j5,new Chiral Hall effect e τ µ µ5 e τ µ5 µ e τ µ µ5 E B + = ee B x 3 3 c t 3π x π π There is also a term May 1, 016 e τ µ E x 6π 9

30 Question about Hall current Note that we had (Hall) e τ µ E B j = 3π Why is this proportional to τ? What do you observe in the usual experimental setup (jy=0 and jx 0)? e e e e e e May 1,

31 Question about Hall current Enforcing jy=0 gives aτ E y = bτ E x B z Then, in the approximation used, j x = aτ E x + bτ E y B z aτ ) ( = a E y + bτ E y B z Ey b Bz bτ B z e e e e e e May 1,

32 Plasma drift Plasma as a whole experiences a non-dissipative (0) drift. Can this be included in f λ? Why should plasma drift? Consider E B (with E < B): B qe May 1, B E v B q v B q v B v - qe 3

33 Frames of reference Another viewpoint f (0) λ Drifting frame: Lab frame: May 1,

34 f (0) λ for magnetized plasma Consider a special case Plasma consists of only e-m charged degrees of freedom Fields so that E B (with E < B) No electric field in the drift frame Lab frame: use boosted Fermi-Dirac distribution f with v drift May 1, = c p p v µ λ drift +1 exp T E B =c B (lab) λ 34

35 1st Perturbation in drifting plasma Charge density nλ(lab) (0) n µ (0) (0) λ λ = nλ τ + vdrift µ λ + τ nλ vdrift + µ λ t ( ) Current density (lab) jλ λeµλ (0) E B + = c nλ 4π c B nλ(0) e E B τ g1 B µ λ ( May 1, 016 λeµ λ B+ E 4π c ) ( E B B B + E ln 1 E E B E ) µ λ B µ λ + g vdrift vdrift µ λ + g 3 vdrift + t ( ) 35

36 Drift in QGP plasma? In QGP, gluons play a profound role Gluons are neutral and, thus, are not drifting The zeroth approximation is the usual Fermi-Dirac distribution 1 (0) fλ = c p µ λ exp +1 T Expansion in small e-m fields and gradients is well define (0) (1) () f λ = f λ + f λ + f λ +... Expansion of the 1st type (no drift) may be better May 1,

37 Summary Chiral plasmas have widespread applications Anomaly plays a profound role in such plasmas Many interesting chiral/anomalous effects are triggered by a magnetic field There are nontrivial effects due to a finite size Accounting for inhomogeneities is possible in a systematic way Consequences of these effects in physical systems are still to be fully investigated May 1,