×

Non-thermal fixed point in a holographic superfluid. (English) Zbl 1388.83234

Summary: We study the far-from-equilibrium dynamics of a (2 + 1)-dimensional super-fluid at finite temperature and chemical potential using its holographic description in terms of a gravitational system in 3 + 1 dimensions. Starting from various initial conditions corresponding to ensembles of vortex defects we numerically evolve the system to long times. At intermediate times the system exhibits Kolmogorov scaling the emergence of which depends on the choice of initial conditions. We further observe a universal late- time regime in which the occupation spectrum and different length scales of the superfluid exhibit scaling behaviour. We study these scaling laws in view of superfluid turbulence and interpret the universal late-time regime as a non-thermal fixed point of the dynamical evolution. In the holographic superfluid the non-thermal fixed point can be understood as a stationary point of the classical equations of motion of the dual gravitational description.

MSC:

83C47 Methods of quantum field theory in general relativity and gravitational theory
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Anderson, BP; etal., Watching dark solitons decay into vortex rings in a Bose-Einstein condensate, Phys. Rev. Lett., 86, 2926, (2001)
[2] Eiermann, B.; etal., Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett., 92, 230401, (2004)
[3] Sadler, LE; etal., Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate, Nature, 443, 312, (2006)
[4] Weller, A.; etal., Experimental observation of oscillating and interacting matter wave dark solitons, Phys. Rev. Lett., 101, 130401, (2008)
[5] Weiler, CN; etal., Spontaneous vortices in the formation of Bose-Einstein condensates, Nature, 455, 948, (2008)
[6] Neely, TW; etal., Observation of vortex dipoles in an oblate Bose-Einstein condensate, Phys. Rev. Lett., 104, 160401, (2010)
[7] Kasprzak, J.; etal., Bose-Einstein condensation of exciton polaritons, Nature, 443, 409, (2006)
[8] Lagoudakis, KG; etal., Quantized vortices in an exciton-polariton condensate, Nature Phys., 4, 706, (2008)
[9] Lagoudakis, KG; etal., Observation of half-quantum vortices in an exciton-polariton condensate, Science, 326, 974, (2009)
[10] Amo, A.; etal., Polariton superfluids reveal quantum hydrodynamic solitons, Science, 332, 1167, (2011)
[11] Berges, J.; Blaizot, J-P; Gelis, F., EMMI rapid reaction task force on ‘thermalization in non-abelian plasmas’, J. Phys., G 39, 085115, (2012)
[12] J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [Adv. Theor. Math. Phys.2 (1998) 231] [hep-th/9711200] [INSPIRE]. · Zbl 0914.53047
[13] Gubser, SS; Klebanov, IR; Polyakov, AM, Gauge theory correlators from noncritical string theory, Phys. Lett., B 428, 105, (1998) · Zbl 1355.81126
[14] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253, (1998) · Zbl 0914.53048
[15] Adams, A.; etal., Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality, New J. Phys., 14, 115009, (2012)
[16] Hartnoll, SA, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav., 26, 224002, (2009) · Zbl 1181.83003
[17] McGreevy, J., Holographic duality with a view toward many-body physics, Adv. High Energy Phys., 2010, 723105, (2010) · Zbl 1216.81118
[18] Gubser, SS, Breaking an abelian gauge symmetry near a black hole horizon, Phys. Rev., D 78, 065034, (2008)
[19] Hartnoll, SA; Herzog, CP; Horowitz, GT, Building a holographic superconductor, Phys. Rev. Lett., 101, 031601, (2008)
[20] Herzog, CP; Kovtun, PK; Son, DT, Holographic model of superfluidity, Phys. Rev., D 79, 066002, (2009)
[21] Dias, OJC; Horowitz, GT; Iqbal, N.; Santos, JE, Vortices in holographic superfluids and superconductors as conformal defects, JHEP, 04, 096, (2014)
[22] Keranen, V.; Keski-Vakkuri, E.; Nowling, S.; Yogendran, KP, Inhomogeneous structures in holographic superfluids: II. vortices, Phys. Rev., D 81, 126012, (2010)
[23] Bhaseen, MJ; etal., Holographic superfluids and the dynamics of symmetry breaking, Phys. Rev. Lett., 110, 015301, (2013)
[24] Adams, A.; Chesler, PM; Liu, H., Holographic vortex liquids and superfluid turbulence, Science, 341, 368, (2013) · Zbl 1355.76013
[25] Berges, J.; Rothkopf, A.; Schmidt, J., Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium, Phys. Rev. Lett., 101, 041603, (2008)
[26] Berges, J.; Hoffmeister, G., Nonthermal fixed points and the functional renormalization group, Nucl. Phys., B 813, 383, (2009) · Zbl 1194.81176
[27] Scheppach, C.; Berges, J.; Gasenzer, T., Matter wave turbulence: beyond kinetic scaling, Phys. Rev., A 81, 033611, (2010)
[28] Berges, J.; Sexty, D., Strong versus weak wave-turbulence in relativistic field theory, Phys. Rev., D 83, 085004, (2011)
[29] B. Nowak, D. Sexty and T. Gasenzer, Superfluid turbulence: nonthermal fixed point in an ultracold Bose gas, Phys. Rev.B 84 (2011) 020506(R) [arXiv:1012.4437] [INSPIRE].
[30] Nowak, B.; Schole, J.; Sexty, D.; Gasenzer, T., Nonthermal fixed points, vortex statistics and superfluid turbulence in an ultracold Bose gas, Phys. Rev., A 85, 043627, (2012)
[31] Karl, M.; Nowak, B.; Gasenzer, T., Tuning universality far from equilibrium, Sci. Rep., 3, 2394, (2013)
[32] Gasenzer, T.; Nowak, B.; Sexty, D., Charge separation in reheating after cosmological inflation, Phys. Lett., B 710, 500, (2012)
[33] Gasenzer, T.; McLerran, L.; Pawlowski, JM; Sexty, D., Gauge turbulence, topological defect dynamics and condensation in Higgs models, Nucl. Phys., A 930, 163, (2014)
[34] T. Gasenzer and J.M. Pawlowski, Functional renormalisation group approach to far-from-equilibrium quantum field dynamics, arXiv:0710.4627 [INSPIRE].
[35] S. Mathey, T. Gasenzer and J.M. Pawlowski, Anomalous scaling at non-thermal fixed points of Burgersand Gross-Pitaevskii turbulence, arXiv:1405.7652 [INSPIRE].
[36] Albash, T.; Johnson, CV, Vortex and droplet engineering in holographic superconductors, Phys. Rev., D 80, 126009, (2009)
[37] Chesler, PM; Yaffe, LG, Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes, JHEP, 07, 086, (2014)
[38] Tisza, L., Transport phenomena in helium II, Nature, 141, 913, (1938)
[39] D.R. Tilley and J. Tilley, Superfluidity and superconductivity, Institute of Physics Publishing (2003).
[40] Sonner, J.; Withers, B., A gravity derivation of the tisza-Landau model in AdS/CFT, Phys. Rev., D 82, 026001, (2010)
[41] J. Sonner, A. del Campo and W.H. Zurek, Universal far-from-equilibrium dynamics of a holographic superconductor, arXiv:1406.2329 [INSPIRE].
[42] P.M. Chesler, A.M. Garcia-Garcia and H. Liu, Far-from-equilibrium coarsening, defect formation, and holography, arXiv:1407.1862 [INSPIRE].
[43] Schole, J.; Nowak, B.; Gasenzer, T., Critical dynamics of a two-dimensional superfluid near a non-thermal fixed point, Phys. Rev., A 86, 013624, (2012)
[44] Karl, M.; Nowak, B.; Gasenzer, T., Universal scaling at nonthermal fixed points of a two-component Bose gas, Phys. Rev., A 88, 063615, (2013)
[45] Raman, C.; etal., Vortex nucleation in a stirred Bose-Einstein condensate, Phys. Rev. Lett., 87, 210402, (2001)
[46] Abo-Shaeer, JR; Raman, C.; Vogels, JM; Ketterle, W., Observation of vortex lattices in Bose-Einstein condensates, Science, 292, 476, (2001)
[47] Neely, TW; etal., Characteristics of two-dimensional quantum turbulence in a compressible superfluid, Phys. Rev. Lett., 111, 235301, (2013)
[48] Kwon, WJ; etal., Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates, Phys. Rev., A 90, 063627, (2014)
[49] R.J. Donnelly, Quantized vortices in liquid He II, Cambridge University Press, Cambridge U.K. (1991).
[50] M. Inguscio, S. Stringari and C.E. Wieman eds., Bose-Einstein condensation in atomic gases: Proceedings of the International School of PhysicsEnrico Fermi, Varenna 1998, IOS Press (1999).
[51] M. Tsubota, K. Kasamatsu, and M. Kobayashi, Quantized vortices in superfluid helium and atomic Bose-Einstein condensates, arXiv:1004.5458.
[52] Gross, EP, Structure of a quantized vortex in boson systems, Nuovo Cim., 20, 454, (1961) · Zbl 0100.42403
[53] L.P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. Phys. JETP13 (1961) 451 [Zh. Eksp. Teor. Fiz.40 (1961) 646].
[54] Lagally, M., Über ein verfahren zur transformation ebener wirbelprobleme, Math. Z., 10, 231, (1921) · JFM 48.0949.04
[55] Lin, C., On the motion of vortices in 2D — I. existence of the Kirchhoff-Routh function, Proc. Nat. Acad. Sci., 27, 570, (1941) · Zbl 0063.03560
[56] Onsager, L., Statistical hydrodynamics, Nuovo Cim. Suppl., 6, 279, (1949)
[57] Bray, AJ, Theory of phase ordering kinetics, Adv. Phys., 43, 357, (1994)
[58] Damle, K.; Majumdar, SN; Sachdev, S., Phase ordering kinetics of the Bose gas, Phys. Rev., A 54, 5037, (1996)
[59] S. Nazarenko and M. Onorato, Wave turbulence and vortices in Bose-Einstein condensation, PhysicaD 219 (2006) 1 [nlin/0507051]. · Zbl 1107.35103
[60] I.S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Rev. Mod. Phys.74 (2002) 99 [cond-mat/0106115]. · Zbl 1205.35299
[61] A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR30 (1941) 299 [Proc. Roy. Soc. Lond.A 434 (1991) 9].
[62] Kolmogorov, AN, On the degeneration of isotropic turbulence in an incompressible viscous fluid, Dokl. Akad. Nauk. SSSR, 31, 538, (1941)
[63] Kolmogorov, AN, Dissipation of energy in locally isotropic turbulence, Dokl. Akad. Nauk. SSSR, 32, 16, (1941) · Zbl 0063.03292
[64] U. Frisch, Turbulence: the legacy of A.N. Kolmogorov, Cambridge University Press, Cambridge U.K. (2004).
[65] Kraichnan, R., Inertial ranges in two-dimensional turbulence, Phys. Fl., 10, 1417, (1967)
[66] Berges, J.; Sexty, D., Bose condensation far from equilibrium, Phys. Rev. Lett., 108, 161601, (2012)
[67] Nore, C.; Abid, M.; Brachet, ME, Decaying Kolmogorov turbulence in a model of superflow, Phys. Fl., 9, 2644, (1997) · Zbl 1185.76669
[68] Hohenberg, PC; Halperin, BI, Theory of dynamic critical phenomena, Rev. Mod. Phys., 49, 435, (1977)
[69] Nowak, B.; Gasenzer, T., Universal dynamics on the way to thermalization, New J. Phys., 16, 093052, (2014)
[70] Berges, J.; Borsányi, S.; Wetterich, C., Prethermalization, Phys. Rev. Lett., 93, 142002, (2004)
[71] Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R., Universal attractor in a highly occupied non-abelian plasma, Phys. Rev., D 89, 114007, (2014)
[72] Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R., Universality far from equilibrium: from superfluid Bose gases to heavy-ion collisions, Phys. Rev. Lett., 114, 061601, (2015)
[73] Berges, J.; Schenke, B.; Schlichting, S.; Venugopalan, R., Turbulent thermalization process in high-energy heavy-ion collisions, Nucl. Phys., A 931, 348, (2014)
[74] Hunter, JD, Matplotlib: a 2D graphics environment, Comp. Sci. Engineer., 9, 90, (2007)
[75] Ramachandran, P.; Varoquaux, G., Mayavi: 3D visualization of scientific data, Comp. Sci. Engineer., 13, 40, (2011)
[76] Son, DT; Starinets, AO, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP, 09, 042, (2002)
[77] J.P. Boyd, Chebyshev and Fourier spectral methods, 2\^{}{nd} edition, Dover Publications, U.S.A. (2000).
[78] J.F. Epperson, An introduction to numerical methods and analysis, John Wiley & Sons, U.S.A. (2013). · Zbl 1280.65001
[79] Frigo, M.; Johnson, SG, The design and implementation of FFTW3, Proc. IEEE, 93, 216, (2005)
[80] G. Guennebaud et al., Eigen v3, http://eigen.tuxfamily.org (2010).
[81] Dagum, L.; Menon, R., Openmp: an industry standard API for shared-memory programming, IEEE Comput. Sci. Engineer., 5, 46, (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.