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SUMMARY:Transport properties in magnetized compact stars
DTSTART;VALUE=DATE-TIME:20190917T183000Z
DTEND;VALUE=DATE-TIME:20190917T190000Z
DTSTAMP;VALUE=DATE-TIME:20200407T212535Z
UID:indico-contribution-3566507@indico.cern.ch
DESCRIPTION:Speakers: Toshitaka Tatsumi (Kyoto U.)\nNowadays strong magnet
ic field has been observed or expected in compact stars or during\nrelativ
istic heavy-ion collisions. In particular\, magnetars may have a huge magn
etic field of\nO(10 15 G) at the surface. We here consider the transport p
roperties of Dirac particles in the\npresence of a strong magnetic field.
As a phenomenological implication\, the heat conductivity is\ninteresting
and important in the context of the thermal evolution of magnetars: The he
at\nconductivity is\, in general\, a tensor in the coordinate space\,$\\ka
ppa_{ij}$ (I\,j=x\,y\,z)\; the off-diagonal\ncomponents represent the ther
mal Hall conductivity.\nFirst\, we discuss the electron contribution in th
e crust of magnetars\, since the main\nmechanism of thermal transport is r
esponsible for conducting electrons. The diagonal\ncomponents give the the
rmal currents proportional to the gradient of temperature. It comes\nfrom
some dissipative effects for electron propagation and has a classical anal
ogy to the\nDrude-Zener formula. On the other hand\, the off-diagonal comp
onents consist of two parts\n$\\kappa_{ij}$ =$\\kappa_{ij}$ I + $\\kappa_
{ij}$ II ($i\\neq j$)\, where the first term represents the dissipative c
ontribution similar to the\ndiagonal components and has been studied by ma
ny authors [1]. However\, there is a little\nstudy about the second term\,
which is a genuine quantum effect and gives a non-dissipative\ncontributi
on. It comes from the field-dependent level density and has no classical a
nalogy [2]:\nthe Landau levels become essential in the strong magnetic fie
ld and the density of states\n(DOS) is a field-dependent quantity\, while
DOS is not field dependent in the classical limit.\nSometimes $\\kappa_{ij
}$ II has been missed in the literature. We elucidate its contribution by
way of the\nKubo formula and estimate its importance.\nNext\, we discuss
the anomalous thermal Hall effect in quark matter\, which may develop in t
he\ncore of compact stars. Recently we have shown a possibility of the ano
malous Hall effect in\ndense QCD matter by the use of the Kubo formula [3]
\, where inhomogeneous chiral phase\n(DCDW phase) is realized [4]. The imp
ortant consequence is that the Hall conductivity $\\kappa_{ij}$ \nbecomes
nonvanishing even in the absence of the magnetic field. It has a geometric
al origin\nand modifies the Maxwell equation as in the Weyl semimetal [5]:
the energy spectrum\nexhibits asymmetry with respect to the zero energy t
o produce a kind of “magnetization” in\nthe DCDW phase\, and the Hall
current flows in the direction perpendicular to the\nmagnetization. Since
thermal conductivity is closely related to conductivity $\\kappa_{ij} $\,
we can expect\nthe anomalous thermal Hall effect there as well [6]. It the
n should give another contribution to\nthe thermal conductivity independen
t of the magnetic field. We discuss the interplay of these\nterms in the n
on-dissipative contribution $\\kappa_{ij}$ II .\nFinally\, we briefly dis
cuss some implications of the non-dissipative thermal Hall conductivity\n$
\\kappa_{ij}$ II \, in the context of thermal evolution of magnetars.\n\n[
1] A.Y. Potekhin\, J.A. Pons\, D. Page\, Space Sci.Rev. 191 (2015) 239.\n[
2] P. Streda\, Solid State Phys. 15 (1982) L717.\n[3] T.Tatsumi\, R. Yoshi
ike\, K. Kashiwa\, PLB 785(2018) 46.\n[4] E. Nakano and T. Tatsumi\, PRD 7
1 (2005) 114006.\n[5] N.P. Armitage\, E.J. Mele\, A. Vishwanath\, Rev.Mod.
Phys. 90\, 015001\n[6] L. Smrcka and P. Streda\, J.Phys. C10 (1977) 2153.\
n\nhttps://indico.cern.ch/event/769736/contributions/3566507/
LOCATION:Yerevan\, Armenia
URL:https://indico.cern.ch/event/769736/contributions/3566507/
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