Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we address the derivation of causal relativistic hydrodynamics, formulated within the framework of divergence type theories (DTTs), from kinetic theory for spinless particles obeying Fermi-Dirac statistics. The approach leads to expressions for the particle current and energy momentum tensor that are formally divergent, but may be given meaning through a process of regularization and renormalization. We demonstrate the procedure through an analysis of the stability of an homogeneous anisotropic configuration. In the DTT framework, as in kinetic theory, these configurations are stable. By contrast, hydrodynamics as derived from the Grad approximation would predict that highly anisotropic configurations are unstable. © 2017 American Physical Society.

Registro:

Documento: Artículo
Título:Causal relativistic hydrodynamics of conformal Fermi-Dirac gases
Autor:Aguilar, M.; Calzetta, E.
Filiación:Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, C1428EGA, Argentina
CONICET, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, C1428EGA, Argentina
Año:2017
Volumen:95
Número:7
DOI: http://dx.doi.org/10.1103/PhysRevD.95.076022
Título revista:Physical Review D
Título revista abreviado:Phy. Rev. D
ISSN:24700010
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_24700010_v95_n7_p_Aguilar

Referencias:

  • Eckart, C., The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid (1940) Phys. Rev., 58, p. 919
  • Landau, L.D., Lifshitz, E.M., (1959) Fluid Mechanics, , (Pergamon Press, Oxford, England)
  • Israel, W., Nonstationary irreversible thermodynamics: A causal relativistic theory (1976) Ann. Phys. (NY), 100, p. 310
  • Israel, W., Stewart, J.M., Progress in relativistic thermodynamics and electrodynamics of continuous media (1980) General Relativity and Gravitation, 2, p. 491. , edited by A. Held (Plenum, New York)
  • Israel, W., (1988) Relativistic Fluid Dynamics, , edited by A. Anile and Y. Choquet-Bruhat (Springer, New York)
  • Rezzolla, L., Zanotti, O., (2013) Relativistic Hydrodynamics, , (Oxford University Press, New York)
  • Schaefer, T., Fluid dynamics and viscosity in strongly correlated fluids (2014) Annu. Rev. Nucl. Part. Sci., 64, p. 125148
  • Romatschke, P., New developments in relativistic viscous hydrodynamics (2010) Int. J. Mod. Phys. e, 19, p. 1
  • Florkowski, W., (2010) Phenomenology of Ultra-Relativistic Heavy-Ion Collisions, , (World Scientific, Singapore)
  • Calzetta, E., Real Relativistic Fluids in Heavy Ion Collisions, Proceedings of Summer School on Geometric, Algebraic and Topological Methods for Quantum Field Theory, (Villa de Leyva Colombia, 2013), , arXiv:1310.0841
  • Monnai, A., (2014) Relativistic Dissipative Hydrodynamic Description of the Quark-Gluon Plasma, , (Springer, New York)
  • Strickland, M., Anisotropic hydrodynamics: Three lectures (2014) Acta Phys. Pol. B, 45, p. 2355
  • Jeon, S., Heinz, U., Introduction to hydrodynamics (2015) Int. J. Mod. Phys. e, 24, p. 1530010
  • Romatschke, P., Do nuclear collisions create a locally equilibrated quarkgluon plasma? (2017) Eur. Phys. J. C, 77, p. 21
  • Chapman, S., Cowling, T.G., (1970) The Mathematical Theory of Non-Uniform Gases, , (Cambridge University Press, Cambridge, England)
  • Enskog, D., (1917) Kinetische Theorie der Vorgänge in Mässig Verdünnten Gasen, , (Almqvist & Wiksell, Uppsala)
  • Grad, H., On the kinetic theory of rarified gases (1949) Commun. Pure Appl. Math., 2, p. 331
  • Grad, H., Thermodynamik der Gase (1958) Handbuch der Physik XII, p. 205. , edited by S. Flügge (Springer, Berlin)
  • Liu, I.S., Method of Lagrange multipliers for exploitation of the entropy principle (1972) Arch. Ration. Mech. Anal., 46, p. 131
  • Liu, I.-S., Müller, I., Ruggeri, T., Relativistic thermodynamics of gases (1986) Ann. Phys. (N.Y.), 169, p. 191
  • Geroch, R., Lindblom, L., Dissipative relativistic fluid theories of divergence type (1990) Phys. Rev. D, 41, p. 1855
  • Geroch, R., Lindblom, L., Causal theories of dissipative relativistic fluids (1991) Ann. Phys. (N.Y.), 207, p. 394
  • Manuel, C., Mrówczyński, S., Chromohydrodynamic approach to the unstable quark-gluon plasma (2006) Phys. Rev. D, 74, p. 105003
  • Peralta-Ramos, J., Calzetta, E., Effective dynamics of a non-Abelian plasma out of equilibrium (2012) Phys. Rev. D, 86, p. 125024
  • Calzetta, E., Non abelian hydrodynamics and heavy ion collisions (2014) AIP Conf. Proc., 1578, p. 74
  • Schenke, B., Strickland, M., Greiner, C., Thoma, M.H., Model of the effect of collisions on QCD plasma instabilities (2006) Phys. Rev. D, 73, p. 125004
  • Mannarelli, M., Manuel, C., Model of the effect of collisions on QCD plasma instabilities (2007) Phys. Rev. D, 76, p. 094007
  • Peralta-Ramos, J., Calzetta, E., Hydrodynamic approach to QGP instabilities (2013) Phys. Rev. D, 87, p. 034003
  • Mrówczyński, S., Schenke, B., Strickland, M., Color Instabilities in the Quark-gluon Plasma, , arXiv:1603.08946
  • Calzetta, E., Kandus, A., A hydrodynamic approach to the study of anisotropic instabilities in dissipative relativistic plasmas (2016) Int. J. Mod. Phys. A, 31, p. 1650194
  • Lewis, W.E., Romatschke, P., Higher-harmonic collective modes in a trapped gas from second-order hydrodynamics (2017) New J. Phys., 19, p. 023042
  • Denicol, G.S., Koide, T., Rischke, D.H., Dissipative relativistic fluid dynamics: A new way to derive the equations of motion from kinetic theory (2010) Phys. Rev. Lett., 105, p. 162501
  • Denicol, G.S., Molnár, E., Niemi, H., Rischke, D.H., Derivation of fluid dynamics from kinetic theory with the 14-moment approximation (2012) Eur. Phys. J. A, 48, p. 170
  • Denicol, G.S., Niemi, H., Molnár, E., Rischke, D.H., Derivation of transient relativistic fluid dynamics from the Boltzmann equation (2012) Phys. Rev. D, 85, p. 114047
  • Vega, C., Calzetta, E., (to be published); Stewart, J.M., Non-equilibrium relativistic kinetic theory (1971) Lect. Notes Phys., 10, p. 1
  • Israel, W., (1972) General Relativity: Papers in Honour of J. L. Synge, p. 201. , edited by L. O'Raifeartaigh (Clarendon Press, Oxford)
  • Israel, W., Stewart, J.M., Transient relativistic thermodynamics and kinetic theory (1979) Ann. Phys. (N.Y.), 118, p. 341
  • De Groot, S.R., Van Leeuwen, W.A., Van Weert, Ch.G., (1980) Relativistic Kinetic Theory. Principles and Applications, , (North-Holland, Amsterdam)
  • Calzetta, E.A., Hu, B.-L., (2008) Nonequilibrium Quantum Field Theory, , (Cambridge University Press, Cambridge, England)
  • Anderson, J.L., Witting, H.R., A relativistic relaxation-time model for the Boltzmann equation (1974) Physica (Amsterdam), 74, p. 466
  • Anderson, J.L., Witting, H.R., Relativistic quantum transport coefficients (1974) Physica (Amsterdam), 74, p. 489
  • Takamoto, M., Inutsuka, S.-I., The relativistic kinetic dispersion relation: Comparison of the relativistic Bhatnagar-Gross-Krook model and Grad's 14-moment expansion (2010) Physica (Amsterdam), 389 A, p. 4580
  • Marle, C., Sur l'établissement des équations de l'hydrodynamique des fluides relativistes dissipatifs. I.-L'équation de Boltzmann relativiste (1969) Ann. Inst. Henri Poincaré A, 10, p. 67
  • Marle, C., Sur l'établissement des équations de l'hydrodynamique des fluides relativistes dissipatifs. II.-Méthodes de résolution approchée de l'équation de Boltzmann relativiste (1969) Ann. Inst. Henri Poincaré A, 10, p. 127
  • Hiscock, W., Lindblom, L., Stability and causality in dissipative relativistic fluids (1983) Ann. Phys. (N.Y.), 151, p. 466
  • Hiscock, W.A., Lindblom, L., Generic instabilities in first-order dissipative relativistic fluid theories (1985) Phys. Rev. D, 31, p. 725
  • Hiscock, W., Lindblom, L., Mathematics and general relativity (1988) Contemp. Math., 71, p. 181
  • Joseph, D.D., Preziosi, L., Heat waves (1989) Rev. Mod. Phys., 61, p. 41
  • Joseph, D.D., Preziosi, L., Addendum (1990) Rev. Mod. Phys., 62, p. 375
  • Jaiswal, A., Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation (2013) Phys. Rev. C, 87, p. 051901
  • Plumari, S., Guardo, G.L., Greco, V., Ollitrault, J.-Y., Viscous corrections to anisotropic flow and transverse momentum spectra from transport theory (2015) Nucl. Phys., A941, p. 87
  • Reula, O., Nagy, G., A causal statistical family of dissipative divergence type fluids (1997) J. Phys. A, 30, p. 1695
  • Calzetta, E., Relativistic fluctuating hydrodynamics (1998) Classical Quantum Gravity, 15, p. 653
  • Calzetta, E., Hydrodynamic approach to boost invariant free streaming (2015) Phys. Rev. D, 92, p. 045035
  • Peralta-Ramos, J., Calzetta, E., Divergence-type nonlinear conformal hydrodynamics (2009) Phys. Rev. D, 80, p. 126002
  • Peralta-Ramos, J., Calzetta, E., Divergence-type (Equation presented) dissipative hydrodynamics applied to heavy-ion collisions (2010) Phys. Rev. C, 82, p. 054905
  • Peralta-Ramos, J., Calzetta, E., Divergence-type theory of conformal fields (2010) Int. J. Mod. Phys. D, 19, p. 1721
  • Romatschke, P., Strickland, M., Collective modes of an anisotropic quark-gluon plasma (2003) Phys. Rev. D, 68, p. 036004
  • Florkowski, W., Ryblewski, R., Spaliński, M., Gradient expansion for anisotropic hydrodynamics (2016) Phys. Rev. D, 94, p. 114025
  • Tinti, L., Anisotropic matching principle for the hydrodynamic expansion (2016) Phys. Rev. C, 94, p. 044902
  • Galapon, E.A., The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals (2016) J. Math. Phys. (N.Y.), 57, p. 033502
  • Cramér, H., (1957) Mathematical Methods of Statistics, , (Princeton University Press, Princeton)
  • Bassett, B., Tsujikawa, S., Wands, D., Inflation dynamics and reheating (2006) Rev. Mod. Phys., 78, p. 537
  • Amin, M.A., Hertzberg, M.P., Kaiser, D.I., Karouby, J., Nonperturbative dynamics of reheating after inflation: A review (2015) Int. J. Mod. Phys. D, 24, p. 1530003
  • Boyanovsky, D., De Vega, H.J., Schwarz, D.J., Phase transitions in the early and the present universe (2006) Annu. Rev. Nucl. Part. Sci., 56, p. 441
  • Calzetta, Esteban, Kandus, A., Primordial magnetic field amplification from turbulent reheating J. Cosmol. Astropart. Phys., 2010 (8), p. 007
  • Calzetta, Esteban, Kandus, A., Primordial magnetic helicity from stochastic electric currents (2014) Phys. Rev. D, 89, p. 083012
  • Molnár, E., Niemi, H., Denicol, G.S., Rischke, D.H., Relative importance of second-order terms in relativistic dissipative fluid dynamics (2014) Phys. Rev. D, 89, p. 074010
  • Samojeden, L.L., Kremer, G.M., The relativistic Burnett equations from a moment closure of the Anderson and Witting model equation (2002) Physica A (Amsterdam), 307, p. 354
  • Bhalerao, R.S., Jaiswal, A., Pal, S., Sreekanth, V., Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods (2014) Phys. Rev. C, 89, p. 054903
  • Jaiswal, A., Ryblewski, R., Strickland, M., Transport coefficients for bulk viscous evolution in the relaxation time approximation (2014) Phys. Rev. C, 90, p. 044908
  • Florkowski, W., Jaiswal, A., Maksymiuk, E., Ryblewski, R., Strickland, M., Relativistic quantum transport coefficients for second-order viscous hydrodynamics (2015) Phys. Rev. C, 91, p. 054907
  • Jaiswal, A., Friman, B., Redlich, K., Relativistic second-order dissipative hydrodynamics at finite chemical potential (2015) Phys. Lett. B, 751, p. 548
  • Bazow, D., Heinz, U., Strickland, M., Second-order (2+1)-dimensional anisotropic hydrodynamics (2014) Phys. Rev. C, 90, p. 054910
  • Molnár, E., Niemi, H., Rischke, D.H., Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation (2016) Phys. Rev. D, 93, p. 114025
  • Tinti, L., Ryblewski, R., Florkowski, W., Strickland, M., Testing different formulations of leading-order anisotropic hydrodynamics (2016) Nucl. Phys, A946, p. 29
  • Florkowski, W., Ryblewski, R., Strickland, M., Tinti, L., Non-boost-invariant dissipative hydrodynamics (2016) Phys. Rev. C, 94, p. 064903
  • Florkowski, W., Maksymiuk, E., Ryblewski, R., Tinti, L., Anisotropic hydrodynamics for mixture of quark and gluon fluids (2015) Phys. Rev. C, 92, p. 054912
  • Jaiswal, A., Bhalerao, R., Pal, S., Complete relativistic second-order dissipative hydrodynamics from the entropy principle (2013) Phys. Rev. C, 87, p. 021901
  • Martinez, M., Strickland, M., Dissipative dynamics of highly anisotropic systems (2010) Nucl. Phys., A848, p. 183
  • Denicol, G.S., Noronha, J., Divergence of the Chapman-Enskog Expansion in Relativistic Kinetic Theory, , arXiv:1608.07869
  • Aniceto, I., Spaliński, M., Resurgence in extended hydrodynamics (2016) Phys. Rev. D, 93, p. 085008

Citas:

---------- APA ----------
Aguilar, M. & Calzetta, E. (2017) . Causal relativistic hydrodynamics of conformal Fermi-Dirac gases. Physical Review D, 95(7).
http://dx.doi.org/10.1103/PhysRevD.95.076022
---------- CHICAGO ----------
Aguilar, M., Calzetta, E. "Causal relativistic hydrodynamics of conformal Fermi-Dirac gases" . Physical Review D 95, no. 7 (2017).
http://dx.doi.org/10.1103/PhysRevD.95.076022
---------- MLA ----------
Aguilar, M., Calzetta, E. "Causal relativistic hydrodynamics of conformal Fermi-Dirac gases" . Physical Review D, vol. 95, no. 7, 2017.
http://dx.doi.org/10.1103/PhysRevD.95.076022
---------- VANCOUVER ----------
Aguilar, M., Calzetta, E. Causal relativistic hydrodynamics of conformal Fermi-Dirac gases. Phy. Rev. D. 2017;95(7).
http://dx.doi.org/10.1103/PhysRevD.95.076022