An economic approach to consumer product ratings

In three essays we examine user-generated product ratings with aggregation. While recommendation systems have been studied extensively, this simple type of recommendation system has been neglected, despite its prevalence in the field. We develop a novel theoretical model of user-generated ratings. This model improves upon previous work in three ways: it considers rational agents and allows them to abstain from rating when rating is costly; it incorporates rating aggregation (such as averaging ratings); and it considers the effect on rating strategies of multiple simultaneous raters. In the first essay we provide a partial characterization of equilibrium behavior. In the second essay we test this theoretical model in laboratory, and in the third we apply established behavioral models to the data generated in the lab. This study provides clues to the prevalence of extreme-valued ratings in field implementations. We show theoretically that in equilibrium, ratings distributions do not represent the value distributions of sincere ratings. Indeed, we show that if rating strategies follow a set of regularity conditions, then in equilibrium the rate at which players participate is increasing in the extremity of agents' valuations of the product. This theoretical prediction is realized in the lab. We also find that human subjects show a disproportionate predilection for sincere rating, and that when they do send insincere ratings, they are almost always in the direction of exaggeration. Both sincere and exaggerated ratings occur with great frequency despite the fact that such rating strategies are not in subjects' best interest. We therefore apply the behavioral concepts of quantal response equilibrium (QRE) and cursed equilibrium (CE) to the experimental data. Together, these theories explain the data significantly better than does a theory of rational, Bayesian behavior -- accurately predicting key comparative statics. However, the theories fail to predict the high rates of sincerity, and it is clear that a better theory is needed.

Cavity Optomechanics at Millikelvin Temperatures

The field of cavity optomechanics, which concerns the coupling of a mechanical object's motion to the electromagnetic field of a high finesse cavity, allows for exquisitely sensitive measurements of mechanical motion, from large-scale gravitational wave detection to microscale accelerometers. Moreover, it provides a potential means to control and engineer the state of a macroscopic mechanical object at the quantum level, provided one can realize sufficiently strong interaction strengths relative to the ambient thermal noise. Recent experiments utilizing the optomechanical interaction to cool mechanical resonators to their motional quantum ground state allow for a variety of quantum engineering applications, including preparation of non-classical mechanical states and coherent optical to microwave conversion. Optomechanical crystals (OMCs), in which bandgaps for both optical and mechanical waves can be introduced through patterning of a material, provide one particularly attractive means for realizing strong interactions between high-frequency mechanical resonators and near-infrared light. Beyond the usual paradigm of cavity optomechanics involving isolated single mechanical elements, OMCs can also be fashioned into planar circuits for photons and phonons, and arrays of optomechanical elements can be interconnected via optical and acoustic waveguides. Such coupled OMC arrays have been proposed as a way to realize quantum optomechanical memories, nanomechanical circuits for continuous variable quantum information processing and phononic quantum networks, and as a platform for engineering and studying quantum many-body physics of optomechanical meta-materials.

However, while ground state occupancies (that is, average phonon occupancies less than one) have been achieved in OMC cavities utilizing laser cooling techniques, parasitic absorption and the concomitant degradation of the mechanical quality factor fundamentally limit this approach. On the other hand, the high mechanical frequency of these systems allows for the possibility of using a dilution refrigerator to simultaneously achieve low thermal occupancy and long mechanical coherence time by passively cooling the device to the millikelvin regime. This thesis describes efforts to realize the measurement of OMC cavities inside a dilution refrigerator, including the development of fridge-compatible optical coupling schemes and the characterization of the heating dynamics of the mechanical resonator at sub-kelvin temperatures.

We will begin by summarizing the theoretical framework used to describe cavity optomechanical systems, as well as a handful of the quantum applications envisioned for such devices. Then, we will present background on the design of the nanobeam OMC cavities used for this work, along with details of the design and characterization of tapered fiber couplers for optical coupling inside the fridge. Finally, we will present measurements of the devices at fridge base temperatures of T_f = 10 mK, using both heterodyne spectroscopy and time-resolved sideband photon counting, as well as detailed analysis of the prospects for future quantum applications based on the observed optically-induced heating.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Light-matter Interactions in Semiconductors and Metals: From Nitride Optoelectronics to Quantum Plasmonics

This thesis puts forth a theory-directed approach coupled with spectroscopy aimed at the discovery and understanding of light-matter interactions in semiconductors and metals.

The first part of the thesis presents the discovery and development of Zn-IV nitride materials.The commercial prominence in the optoelectronics industry of tunable semiconductor alloy materials based on nitride semiconductor devices, specifically InGaN, motivates the search for earth-abundant alternatives for use in efficient, high-quality optoelectronic devices. II-IV-N2 compounds, which are closely related to the wurtzite-structured III-N semiconductors, have similar electronic and optical properties to InGaN namely direct band gaps, high quantum efficiencies and large optical absorption coefficients. The choice of different group II and group IV elements provides chemical diversity that can be exploited to tune the structural and electronic properties through the series of alloys. The first theoretical and experimental investigation of the ZnSnxGe1−xN2 series as a replacement for III-nitrides is discussed here.

The second half of the thesis shows ab−initio calculations for surface plasmons and plasmonic hot carrier dynamics. Surface plasmons, electromagnetic modes confined to the surface of a conductor-dielectric interface, have sparked renewed interest because of their quantum nature and their broad range of applications. The decay of surface plasmons is usually a detriment in the field of plasmonics, but the possibility to capture the energy normally lost to heat would open new opportunities in photon sensors, energy conversion devices and switching. A theoretical understanding of plasmon-driven hot carrier generation and relaxation dynamics in the ultrafast regime is presented here. Additionally calculations for plasmon-mediated upconversion as well as an energy-dependent transport model for these non-equilibrium carriers are shown.

Finally, this thesis gives an outlook on the potential of non-equilibrium phenomena in metals and semiconductors for future light-based technologies.