Characteristics ofn-InSb Hot Electron Submillimeter Detector

Abstract

We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in [1]. R 3,1 ii h / ϕ horizon t,x z z = z Figure 1: A cartoon of the relation between shear viscosity and h 12 graviton absorption, and between bulk viscosity and absorption of a mixture of the h ii graviton and the scalar φ.as explored for example in [11,12]. Earlier works [4 -8, 1] have focused on calculating the leading dissipative term in the dispersion relation for sound waves. We instead appeal directly to a Kubo formula. Our computation comes down to understanding the bulk propagation of some linear superposition of gravitons and scalar perturbations. The strategy, as illustrated in figure 1, is to start with an infinite, static, thermal background, linearize the equations of motion around it, and solve these linearized equations in some appropriate approximation. A large-wavelength, low-frequency approximation is the appropriate one because ζ describes an effect in hydrodynamics, which is to say the infrared approximation to the dynamics. The absorption probability of low-energy quanta is proportional to ζ. This is entirely analogous to the well-known computation of shear viscosity [13], but more technically involved because of the mixing between the scalar and metric perturbations. We can decouple these perturbations through a judicious choice of gauge, namely the gauge where the value of the scalar is used as a radial variable. In this gauge, we need only solve a single ordinary differential equation, given in equation (2.9a). The bulk viscosity to shear viscosity ratio can then be extracted from the solution of (2.9a) by using equation (2.41), which is our main result. In examples, a conjectured bound [1] on the ratio ζ/η of bulk to shear viscosity is observed to be satisfied in most but not all circumstances.The structure of the rest of this paper is as follows. In section 2 we explain our method for computing the bulk viscosity from AdS/CFT. Section 2.1 summarizes the relevant gravitational backgrounds. Section 2.2 shows how to perturb the backgrounds in a rotationally invariant fashion. Section 2.3 reviews the treatment of metric perturbations that control the shear viscosity, explaining in particular how to extract the imaginary part of the retarded Green's function of an off-diagonal component T 12 of the gauge theory stress tensor. Section 2.4 adapts this treatment to the case of bulk viscosity, using equations derived in section 2.2. Section 2.5 detours once again to a review of the shear viscosity computation, showing ho...

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