Hyperscaling violation, quasinormal modes and shear diffusion

We study quasinormal modes of shear gravitational perturbations for hyperscaling violating Lifshitz theories, with Lifshitz and hyperscaling violating exponents $z$ and $\theta$. The lowest quasinormal mode frequency yields a shear diffusion constant which is in agreement with that obtained in previous work by other methods. In particular for theories with $z< d_i+2-\theta$ where $d_i$ is the boundary spatial dimension, the shear diffusion constant exhibits power-law scaling with temperature, while for $z=d_i+2-\theta$, it exhibits logarithmic scaling. We then calculate certain 2-point functions of the dual energy-momentum tensor holographically for $z\leq d_i+2-\theta$, identifying the diffusive poles with the quasinormal modes above. This reveals universal behaviour $\eta/s=1/4\pi$ for the viscosity-to-entropy-density ratio for all $z\leq d_i+2-\theta$.Comment: v2: Latex, 21pgs, more details of analysis, review of shear diffusion from membrane paradigm, references added, matches version to be publishe

Structured semiconductor fibers for mid=infrared transmission

Thesis (M.S.)--Boston UniversityThe mid-Infrared (mid-IR: 3-12 µm wavelength range) spectral range represents a part of the electromagnetic spectrum that impacts practically every aspect of human society, and is used for biomedical surgery, chemical sensing to technologies that enhance defense capabilities. Semiconductors like silicon and germanium can effectively transmit light in the mid infrared region of the electromagnetic spectrum. In addition to remote transmission ofmid-Infrared light, by tailoring the index of refraction of a semiconductor fiber waveguide, one can manipulate the nonlinear properties of light pulses, which leads to temporally and spectrally shaping them, thus using the passive optical fiber itself as a medium to create new color sources, or detection systems. To create low loss waveguides and to be able to manipulate light, there is the necessity to fabricate refractive index structures. Current semiconductor waveguides that have refractive index structures are short in length (~30cm), while long semiconductor waveguides do not possess refractive index structures. Optical fiber is fabricated by drawing preforms in a fiber draw tower. The most versatile technique for preform fabrication with refractive index structures is the Modified Chemical V apor Deposition (NICVD) process. In this research, the MCVD and the draw tower in the BU Photonics Center were used to deposit silicon and germanium inside glass tubes which has not been done before. Precursor gases like silane and germane were flown through Duran, Vycor and Fused silica tubes in a tube fm·nce to deposit silicon and germanium in the inner surface of the tubes. The as-deposited glass tubes were collapsed in the flame on the MCVD lathe to form solid preforms. The preforms were characterized using X-Ray Diffraction, optical and electron microscopy to understand the MCVD reaction kinetics. The characterization data was used to model the deposition behaviour with temperature and gas flow rates. Fluid dynamics software was used to model the tube collapse parameters. Several of these preforms were subsequently drawn to fiber in the fiber draw tower. This was the first time a refractive index structure was created in a semiconductor preform

Hyperscaling violation and the shear diffusion constant

We consider holographic theories in bulk $(d+1)$-dimensions with Lifshitz and hyperscaling violating exponents $z,\theta$ at finite temperature. By studying shear gravitational modes in the near-horizon region given certain self-consistent approximations, we obtain the corresponding shear diffusion constant on an appropriately defined stretched horizon, adapting the analysis of Kovtun, Son and Starinets. For generic exponents with $d-z-\theta>-1$, we find that the diffusion constant has power law scaling with the temperature, motivating us to guess a universal relation for the viscosity bound. When the exponents satisfy $d-z-\theta=-1$, we find logarithmic behaviour. This relation is equivalent to $z=2+d_{eff}$ where $d_{eff}=d_i-\theta$ is the effective boundary spatial dimension (and $d_i=d-1$ the actual spatial dimension). It is satisfied by the exponents in hyperscaling violating theories arising from null reductions of highly boosted black branes, and we comment on the corresponding analysis in that context.Comment: Latex, 17pgs, v3: clarifications added on z<2+d_{eff} and standard quantization, to be publishe

Higher Spin Gravity in AdS3AdS_3 and Folds on Fermi Surface

In this paper, we introduce new sets of boundary conditions for higher spin gravity in $AdS_3$ where the boundary dynamics of spin two and other higher spin fields are governed by the interacting collective field theory Hamiltonian of Avan and Jevicki. We show that the time evolution of spin two and higher spin fields can be captured by the classical dynamics of folded fermi surfaces in the similar spirit of Lin, Lunin and Maldacena. We also construct infinite sequences of conserved charges showing the integrable structure of higher spin gravity under the boundary conditions we considered. Further, we observe that there are two possible sequences of conserved charges depending on whether the underlying boundary fermions are non-relativistic or relativistic.Comment: 26 pages, 2 figure

Flow of shear response functions in hyperscaling violating Lifshitz theories

We study the flow equations of the shear response functions for hyperscaling violating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating exponents $z$ and $\theta$. Adapting the membrane paradigm approach of analysing response functions as developed by Iqbal and Liu, we focus specifically on the shear gravitational modes which now are coupled to the perturbations of the background gauge field. Restricting to the zero momenta sector, we make further simplistic assumptions regarding the hydrodynamic expansion of the perturbations. Analysing the flow equations shows that the shear viscosity at leading order saturates the Kovtun-Son-Starinets (KSS) bound of $\frac{1}{4\pi}$. When $z=d_i-\theta$, ($d_i$ being the number of spatial dimension in the dual field theory) the first-order correction to shear viscosity exhibits logarithmic scaling, signalling the emergence of a scale in the UV regime for this class of hvLif theories. We further show that the response function associated to the gauge field perturbations diverge near the boundary when $z>d_i+2-\theta$. This provides a holographic understanding of the origin of such a constraint and further vindicates results obtained in previous works that were obtained through near horizon and quasinormal mode analysis.Comment: Includes new subsection on Markovianity index and breakdown of hydrodynamic expansion; Matches with published version; 19 + 3 page

N = 3 Poincare Supergravity in Four Dimensions

In this paper, we use the superconformal approach to derive the action for N = 3 Poincare supergravity in four space-time dimensions. We first study the coupling of N = 3 vector multiplets to conformal supergravity. Thereafter we combine it with the pure N = 3 conformal supergravity action and use a minimum of three vector multiplets as compensators to arrive at Poincare supergravity with higher derivative corrections. We give a general prescription on how to eliminate the auxiliary fields in an iterative manner and obtain the supergravity action order by order in derivatives. We also show that the truncation of the action at fourth order in derivatives is a consistent truncation.Comment: 31 pages,minor change

Scale-invariant inflation

We examine a scalar-tensor model of gravity that is globally scale-invariant. When adapted to a spatially flat Robertson-Walker metric, the equations of motion describe a dynamical system that flows from an unstable de Sitter space to a stable one. We show that during this transition inflation can occur. Moreover, at the final fixed point, a mass scale naturally emerges that can be identified with the Planck mass. We compute the inflationary spectral indices and the tensor perturbation and we compare them with observations. We also study the possibility that primordial magnetic fields are generated during inflation.Comment: Proceedings of the Workshop "Avenues of Quantum Field Theory in Curved Spacetime" (AQFTCS 2022), University of Genova, Ital

Atomic Scale Measurement of Polar Entropy

Entropy is a fundamental thermodynamic quantity that is a measure of the accessible microstates available to a system, with the stability of a system determined by the magnitude of the total entropy of the system. This is valid across truly mind boggling length scales - from nanoparticles to galaxies. However, quantitative measurements of entropy change using calorimetry are predominantly macroscopic, with direct atomic scale measurements being exceedingly rare. Here for the first time, we experimentally quantify the polar configurational entropy (in meV/K) using sub-\r{a}ngstr\"{o}m resolution aberration corrected scanning transmission electron microscopy. This is performed in a single crystal of the prototypical ferroelectric $\mathsf{LiNbO_3}$ through the quantification of the niobium and oxygen atom column deviations from their paraelectric positions. Significant excursions of the niobium - oxygen polar displacement away from its symmetry constrained direction is seen in single domain regions which increases in the proximity of domain walls. Combined with first principles theory plus mean field effective Hamiltonian methods, we demonstrate the variability in the polar order parameter, which is stabilized by an increase in the magnitude of the configurational entropy. This study presents a powerful tool to quantify entropy from atomic displacements and demonstrates its dominant role in local symmetry breaking at finite temperatures in classic, nominally Ising ferroelectrics.Comment: 23 pages, 21 figures (5 main, 16 supplemental