Notes on the optimum character of the sequential probability ratio test

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Modeling liquid-liquid phase transitions and quasicrystal formation

Thesis (Ph. D.)--Boston University, 2003.In this thesis, studies which concern two different subjects related to phase transitions in fluids and crystalline solids are presented. Condensed matter formation, structure, and phase transitions are modeled using molecular dynamics simulations of simple discontinuous potentials with attractive and repulsive interactions. Novel phase diagrams are proposed for quasicrystals, crystals, and liquids. In the first part of the thesis, the formation of a quasicrystal in a two dimensional monodisperse system is investigated using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. It is found that for certain values of the square-well parameters more than one stable crystalline phase can form. By quenching the liquid phase at a very low temperature, an amorphous phase is obtained. When this the amorphous phase is heated, a quasicrystalline structure with five-fold symmetry forms. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, it is concluded that within a specific temperature range, the observed quasicrystal phase can be the stable phase. The second part of the thesis concerns a study of the liquid-liquid phase transition for a single-component system in three dimensions, interacting via an isotropic potential with a repulsive soft-core shoulder at short distance and an attractive well at an intermediate distance. The potential is similar to potentials used to describe [TRUNCATED

Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range

We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy U R ( U A ) and the repulsive (attractive) range w R ( w A ) the relation U R ∕ U A ∝ w R ∕ w A holds for short soft-core ranges, while U R ∕ U A ∝ 3 w R ∕ w A holds for large soft-core ranges

Optical properties of nanocrystal films: blue shifted transitions as signature of strong coupling

We present a theoretical study at the atomistic level of the optical properties of semiconductor nanocrystal films. We investigate the dependence of the absorption coefficient on size, inter-dot separation, surface stoichiometry and morphology, temperature, position of the Fermi level and light polarization. Our results show that, counter-intuitively, huge blue shifts are expected in some intra-band transitions for strongly coupled arrays, in contrast with the predicted and observed red shift of the band gap absorption in such systems. Furthermore, we find that the energies of such transitions can be tuned within a range of several hundreds of meV, just by engineering the inter-dot separation in the film through the choice of appropriately sized capping ligands. Finally we discuss the application of this effect to nanocrystal-based intermediate-band solar cells

Optical Absorption in N-Dimensional Colloidal Quantum Dot Arrays: Influence of Stoichiometry and Applications in Intermediate Band Solar Cells

We present a theoretical atomistic study of the optical properties of non-toxic InX (X = P, As, Sb) colloidal quantum dot arrays for application in photovoltaics. We focus on the electronic structure and optical absorption and on their dependence on array dimensionality and surface stoichiometry motivated by the rapid development of experimental techniques to achieve high periodicity and colloidal quantum dot characteristics. The homogeneous response of colloidal quantum dot arrays to different light polarizations is also investigated. Our results shed light on the optical behaviour of these novel multi-dimensional nanomaterials and identify some of them as ideal building blocks for intermediate band solar cells.Junta de Andalucia P18-RT-3303School of Electronic and Electrical Engineering, University of LeedsUK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC)Junta de Andaluci

Band-like transport in “green” quantum dot films: The effect of composition and stoichiometry

ACKNOWLEDGMENTS This work was undertaken on ARC3, part of the High Performance Computing Facilities at the University of Leeds, UK. P.R. gratefully acknowledges financial support from EPSRC through a Doctoral Training Grant. F.M.G.C., S.R.B., and E.S.S.-G. received financial support from Project No. P18-RT-3303 from the Spanish Junta de Andalucia. M.C. is thankful to the School of Electronic and Electrical Engineering, University of Leeds, for financial support.SUPPLEMENTARY MATERIAL https://www.scitation.org/doi/suppl/10.1063/5.0078375 See the supplementary material for the mobility calculations for the rest of the materials considered here. The lowermost conduction miniband visualization in the reciprocal space is also included, along with the tables of flight times and fitting parameters.Two-dimensional quantum dot (QD) arrays are considered as promising candidates for a wide range of applications that heavily rely on their transport properties. Existing QD films, however, are mainly made of either toxic or heavy-metal-based materials, limiting their applications and the commercialization of devices. In this theoretical study, we provide a detailed analysis of the transport properties of “green” colloidal QD films (In-based and Ga-based), identifying possible alternatives to their currently used toxic counterparts. We show how changing the composition, stoichiometry, and the distance between the QDs in the array affects the resulting carrier mobility for different operating temperatures. We find that InAs QD films exhibit high carrier mobilities, even higher compared to previously modeled CdSe (zb) QD films. We also provide the first insights into the transport properties of properly passivated InP and GaSb QD films and envisage how realistic systems could benefit from those properties. Ideally passivated InP QD films can exhibit mobilities an order of magnitude larger compared to what is presently achievable experimentally, which show the smallest variation with (i) increasing temperature when the QDs in the array are very close and (ii) an increasing interdot distance at low operating temperatures (70 K), among the materials considered here, making InP a potentially ideal replacement for PbS. Finally, we show that by engineering the QD stoichiometry, it is possible to enhance the film’s transport properties, paving the way for the synthesis of higher performance devices.Spanish Junta de AndaluciaEngineering and Physical Sciences Research Council P18-RT-330

Large Deviations for Random Matricial Moment Problems

We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or K=\D). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \rightarrow \infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\times p$ matrices. Then we lift a random element of $\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP on Carth\'eodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions.Comment: 34 page

Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range

Recent experimental and theoretical results have shown the existence of a liquid-liquid phase transition in isotropic systems, such as biological solutions and colloids, whose interaction can be represented via an effective potential with a repulsive soft-core and an attractive part. We investigate how the phase diagram of a schematic general isotropic system, interacting via a soft-core squared attractive potential, changes by varying the parameters of the potential. It has been shown that this potential has a phase diagram with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition and that, for a short-range soft-core, the phase diagram resulting from molecular dynamics simulations can be interpreted through a modified van der Waals equation. Here we consider the case of soft-core ranges comparable with or larger than the hard-core diameter. Because an analysis using molecular dynamics simulations of such systems or potentials is too time-demanding, we adopt an integral equation approach in the hypernetted-chain approximation. Thus we can estimate how the temperature and density of both critical points depend on the potential's parameters for large soft-core ranges. The present results confirm and extend our previous analysis, showing that this potential has two fluid-fluid critical points that are well separated in temperature and in density only if there is a balance between the attractive and repulsive part of the potential. We find that for large soft-core ranges our results satisfy a simple relation between the potential's parameters

Efficient, non-stochastic, Monte-Carlo-like-accurate method for the calculation of the temperature-dependent mobility in nanocrystal films

We present a new non-stochastic framework for the calculation of the temperature dependence of the mobility in nanocrystal films, that enables speed-ups of several orders of magnitude compared to conventional Monte Carlo approaches, while maintaining a similar accuracy. Our model identifies a new contribution to the reduction of the mobility with increasing temperature in these systems (conventionally attributed to interactions with phonons), that alone is sufficient to explain the observed experimental trend up to room temperature. Comparison of our results with the theoretical predictions of the hopping model and the observed temperature dependence of recent field-effect mobility measurements in nanocrystal films, provides the means to discriminate between band-like and hopping transport and a definitive answer to whether the former has been achieved in quantum dot films