AdS null deformations with inhomogeneities

Abstract

We study $AdS\times X$ null deformations arising as near horizon limits of D3-brane analogs of inhomogenous plane waves. Restricting to normalizable deformations for the $AdS_5$ case, these generically correspond in the dual field theory to SYM states with lightcone momentum density $T_{++}$ varying spatially, the homogenous case studied in arXiv:1202.5935 [hep-th] corresponding to uniform $T_{++}$. All of these preserve some supersymmetry. Generically these inhomogenous solutions exhibit analogs of horizons in the interior where a timelike Killing vector becomes null. From the point of view of $x^+$-dimensional reduction, the circle pinches off on these horizon loci in the interior. We discuss similar inhomogenous solutions with asymptotically Lifshitz boundary conditions, as well as aspects of Lifshitz singularities in string constructions involving $AdS$ null deformations. We also briefly discuss holographic entanglement entropy for some of these.Comment: Latex, 25pgs, v2: references, clarifications added, PRD versio

Notes on hyperscaling violating Lifshitz and shear diffusion

“…[5,6,7,8,9,10,11,12,13,14,15,16]. Null x +reductions of AdS plane waves [17,18], which are large boost, low temperature limits [19] of boosted black branes [20] provide certain gauge/string realizations of these. See e.g.…”

Thermoelectric and electrical transport in mesoscopic two-dimensional electron gases

“…3). In terms of absolute magnitude, however, S was found to exceed the Mott value by over two orders of magnitude [12]. It is important to note that in the hopping regime S is expected to diverge as T → 0 K. The precise form of the divergence depends on the precise hopping mechanism, i.e., whether it is nearest-neighbour, variable-ranged or hopping in the presence of the Coulomb gap, but clearly this is totally inconsistent with the experimental observations in Fig.…”

“…In sharp contrast to macroscopic samples, and as was consistently reported in a number of works on m2DEGs (Refs. [23,24,12,18,11,10,25]) , the activated growth of ρ(T ) shows a striking slowing down below ≈ 1 K. More precisely, dρ/dT is found to be ≥ 0 for T 1 K, with ρ appearing to saturate to a large albiet finite value as T → 0 K. This behaviour was found to be robust over a wide range of system parameters [23,24], as well as over a wide range of sample dimensions [10,25], only appearing to vanish in the macroscopic system limit [23]. We stress that this is behaviour is totally at odds with anything observed in macroscopic 2DEGs which, when at comparable ρ, are deep within the Anderson localised regime with ρ being strongly T -dependent.…”

“…The measurement of the resultant temperature difference ∆T across the m2DEG is described in detail in Refs. [12] and [14]. Briefly, this was done closely following the scheme initially demonstrated in Ref.…”

“…Typically, 2DEGs have been studied in the macroscopic limit where the system size L >> φ , giving rise to the so-called '2D metal-to-insulator' (MIT) transition [5,6,7] and integer and fractional quantum Hall effects [8,9]. In this Review we focus on some of our recent works on 2DEGs of spatial extent 10 µm where both the electrical and thermoelectrical transport contain striking signatures of phase coherent behaviour even at temperature T = 10 K. These include (1) a systematic dependence of σ on L [10], (2) an apparent breakdown of the canonical Mott relation between the electrical conductivity σ and Seebeck coefficient (or thermopower) S [11], and (3) a giant enhancement in the magnitude of S [12]. In Section 4 we explain how these striking observations can be understood as arising due to phase coherent transport.…”