Transport in Anisotropic Superfluids: A Holographic Description

Journal of High Energy Physics (Impact Factor: 6.11). 09/2011; 2012(1). DOI: 10.1007/JHEP01(2012)059
Source: arXiv


We study transport phenomena in p-wave superfluids in the context of
gauge/gravity duality. Due to the spacetime anisotropy of this system, the
tensorial structure of the transport coefficients is non-trivial in contrast to
the isotropic case. In particular, there is an additional shear mode which
leads to a non-universal value of the shear viscosity even in an Einstein
gravity setup. In this paper, we present a complete study of the helicity two
and helicity one fluctuation modes. In addition to the non-universal shear
viscosity, we also investigate the thermoelectric effect, i.e. the mixing of
electric and heat current. Moreover, we also find an additional effect due to
the anisotropy, the so-called flexoelectric effect.

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    • "The breakdown of (1.1) in [34] [35] [36] [37] [38] [39] is not too surprising. Heuristically, the robustness of (1.1) can be argued for by observing that the shear viscosity tensor η is susceptible only to tensor mode fluctuations of the dual bulk metric which, in an isotropic background, decouple from the other metric fluctuations thereby leading to universal behavior. "
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    ABSTRACT: We study correlation functions in an equilibrated spatially modulated phase of Einstein-Maxwell two-derivative gravity. We find that the ratio of the appropriate low frequency limit of the stress-stress two point function to the entropy density is modulated. The conductivity, the stress-current and current-stress correlation functions are also modulated. At temperatures close to the phase transition we obtain analytic expressions for some of the correlation functions.
    Journal of High Energy Physics 07/2014; 2014(11). DOI:10.1007/JHEP11(2014)019 · 6.11 Impact Factor
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    • "In fact the more exotic phenomenon arise in the rapidly varying limit as mentioned above. Anisotropic phases along with their viscosity was discussed in [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]. It was found that the shear viscosity can acquire components in some cases which violate the KSS bound [30], [31], [32], [33], [35]. "
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    Journal of High Energy Physics 06/2014; 2015(1). DOI:10.1007/JHEP01(2015)005 · 6.11 Impact Factor
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    • "In the broken phase we see a temperature dependence and the resulting curve does not fall below 1/(4π) for any backreaction parameter α and for any temperature. Since we have completed our analysis of all fluctuation modes in the p-wave system, let us now summarize them, as well as the transport phenomena they correspond to: 1. h yz (helicity two) is related to the shear viscosity η yz which for all values of T takes the universal value η/s = 1/4π (see [19]), 2. h x⊥ (helicity one) is related to the shear viscosity η x⊥ which shows a temperature dependence in the broken phase (see [19]), 3. The coupling between a ± ⊥ = a 1 ⊥ ± ia 2 ⊥ (helicity one) and h x⊥ leads to an effect which is similar to the flexoelectric effect known from crystals (see [19]), 4. a 3 ⊥ is related to the " electrical " conductivity σ ⊥⊥ (helicity one), and its coupling to h t⊥ (helicity one) is related to the so called thermoelectric effect transverse to the condensate (see [19]), 5. Φ 4 ∼ a 3 x (helicity zero) is related to the " electrical " conductivity σ xx , and its coupling to h tx (helicity zero) gives the thermoelectric effect in the direction of the condensate (see section 4), 6. Φ 3 ∼ h xx − h yy (helicity zero) is related to the transport coefficient λ found in the viscosity tensor η ijkl and its coupling to Φ ± ∼ a ± x (helicity zero) shows a behaviour similar to the piezoelectric effect (see section 4). "
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    ABSTRACT: We complete the analysis of transport phenomena in p-wave superfluids within gauge/gravity duality, using the SU(2) Einstein-Yang-Mills model with backreaction. In particular, we analyze the fluctuation modes of helicity zero in addition to the helicity one and two modes studied earlier. We compute a further transport coefficient, associated to the first normal stress difference, not previously considered in the holographic context. In the unbroken phase this is related to a minimally coupled scalar on the gravity side. Moreover we find transport phenomena related to the thermoelectric and piezoelectric effects, in particular in the direction of the condensate, as well as the flexoelectric effect. These are similar to phenomena observed in condensed matter systems.
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