Time-multiscale methods for the simulation of slow transport problems in atomistic systems

En esta tesis presentamos una teoría adaptada a la simulación de fenómenos lentos de transporte en sistemas atomísticos. En primer lugar, desarrollamos el marco teórico para modelizar colectividades estadísticas de equilibrio. A continuación, lo adaptamos para construir modelos de colectividades estadísticas fuera de equilibrio. Esta teoría reposa sobre los principios de la mecánica estadística, en particular el principio de máxima entropía de Jaynes, utilizado tanto para sistemas en equilibrio como fuera de equilibrio, y la teoría de las aproximaciones del campo medio. Expresamos matemáticamente el problema como un principio variacional en el que maximizamos una entropía libre, en lugar de una energía libre. La formulación propuesta permite definir equivalentes atomísticos de variables macroscópicas como la temperatura y la fracción molar. De esta forma podemos considerar campos macroscópicos no uniformes. Completamos el marco teórico con reglas de cuadratura de Monte Carlo, gracias a las cuales obtenemos modelos computables. A continuación, desarrollamos el conjunto completo de ecuaciones que gobiernan procesos de transporte. Deducimos la desigualdad de disipación entrópica a partir de fuerzas y flujos termodinámicos discretos. Esta desigualdad nos permite identificar la estructura que deben cumplir los potenciales cinéticos discretos. Dichos potenciales acoplan las tasas de variación en el tiempo de las variables microscópicas con las fuerzas correspondientes. Estos potenciales cinéticos deben ser completados con una relación fenomenológica, del tipo definido por la teoría de Onsanger. Por último, aportamos validaciones numéricas. Con ellas ilustramos la capacidad de la teoría presentada para simular propiedades de equilibrio y segregación superficial en aleaciones metálicas. Primero, simulamos propiedades termodinámicas de equilibrio en el sistema atomístico. A continuación evaluamos la habilidad del modelo para reproducir procesos de transporte en sistemas complejos que duran tiempos largos con respecto a los tiempos característicos a escala atómica. ABSTRACT In this work, we formulate a theory to address simulations of slow time transport effects in atomic systems. We first develop this theoretical framework in the context of equilibrium of atomic ensembles, based on statistical mechanics. We then adapt it to model ensembles away from equilibrium. The theory stands on Jaynes' maximum entropy principle, valid for the treatment of both, systems in equilibrium and away from equilibrium and on meanfield approximation theory. It is expressed in the entropy formulation as a variational principle. We interpret atomistic equivalents of macroscopic variables such as the temperature and the molar fractions, wich are not required to be uniform, but can vary from particle to particle. We complement this theory with Monte Carlo summation rules for further approximation. In addition, we provide a framework for studying transport processes with the full set of equations driving the evolution of the system. We first derive a dissipation inequality for the entropic production involving discrete thermodynamic forces and fluxes. This discrete dissipation inequality identifies the adequate structure for discrete kinetic potentials which couple the microscopic field rates to the corresponding driving forces. Those kinetic potentials must finally be expressed as a phenomenological rule of the Onsanger Type. We present several validation cases, illustrating equilibrium properties and surface segregation of metallic alloys. We first assess the ability of a simple meanfield model to reproduce thermodynamic equilibrium properties in systems with atomic resolution. Then, we evaluate the ability of the model to reproduce a long-term transport process in complex systems.

Engineering Computational Emotion - A Reference Model for Emotion in Artificial Systems

Emotion is generally argued to be an influence on the behavior of life systems, largely concerning flexibility and adaptivity. The way in which life systems acts in response to a particular situations of the environment, has revealed the decisive and crucial importance of this feature in the success of behaviors. And this source of inspiration has influenced the way of thinking artificial systems. During the last decades, artificial systems have undergone such an evolution that each day more are integrated in our daily life. They have become greater in complexity, and the subsequent effects are related to an increased demand of systems that ensure resilience, robustness, availability, security or safety among others. All of them questions that raise quite a fundamental challenges in control design. This thesis has been developed under the framework of the Autonomous System project, a.k.a the ASys-Project. Short-term objectives of immediate application are focused on to design improved systems, and the approaching of intelligence in control strategies. Besides this, long-term objectives underlying ASys-Project concentrate on high order capabilities such as cognition, awareness and autonomy. This thesis is placed within the general fields of Engineery and Emotion science, and provides a theoretical foundation for engineering and designing computational emotion for artificial systems. The starting question that has grounded this thesis aims the problem of emotion--based autonomy. And how to feedback systems with valuable meaning has conformed the general objective. Both the starting question and the general objective, have underlaid the study of emotion, the influence on systems behavior, the key foundations that justify this feature in life systems, how emotion is integrated within the normal operation, and how this entire problem of emotion can be explained in artificial systems. By assuming essential differences concerning structure, purpose and operation between life and artificial systems, the essential motivation has been the exploration of what emotion solves in nature to afterwards analyze analogies for man--made systems. This work provides a reference model in which a collection of entities, relationships, models, functions and informational artifacts, are all interacting to provide the system with non-explicit knowledge under the form of emotion-like relevances. This solution aims to provide a reference model under which to design solutions for emotional operation, but related to the real needs of artificial systems. The proposal consists of a multi-purpose architecture that implement two broad modules in order to attend: (a) the range of processes related to the environment affectation, and (b) the range or processes related to the emotion perception-like and the higher levels of reasoning. This has required an intense and critical analysis beyond the state of the art around the most relevant theories of emotion and technical systems, in order to obtain the required support for those foundations that sustain each model. The problem has been interpreted and is described on the basis of AGSys, an agent assumed with the minimum rationality as to provide the capability to perform emotional assessment. AGSys is a conceptualization of a Model-based Cognitive agent that embodies an inner agent ESys, the responsible of performing the emotional operation inside of AGSys. The solution consists of multiple computational modules working federated, and aimed at conforming a mutual feedback loop between AGSys and ESys. Throughout this solution, the environment and the effects that might influence over the system are described as different problems. While AGSys operates as a common system within the external environment, ESys is designed to operate within a conceptualized inner environment. And this inner environment is built on the basis of those relevances that might occur inside of AGSys in the interaction with the external environment. This allows for a high-quality separate reasoning concerning mission goals defined in AGSys, and emotional goals defined in ESys. This way, it is provided a possible path for high-level reasoning under the influence of goals congruence. High-level reasoning model uses knowledge about emotional goals stability, letting this way new directions in which mission goals might be assessed under the situational state of this stability. This high-level reasoning is grounded by the work of MEP, a model of emotion perception that is thought as an analogy of a well-known theory in emotion science. The work of this model is described under the operation of a recursive-like process labeled as R-Loop, together with a system of emotional goals that are assumed as individual agents. This way, AGSys integrates knowledge that concerns the relation between a perceived object, and the effect which this perception induces on the situational state of the emotional goals. This knowledge enables a high-order system of information that provides the sustain for a high-level reasoning. The extent to which this reasoning might be approached is just delineated and assumed as future work. This thesis has been studied beyond a long range of fields of knowledge. This knowledge can be structured into two main objectives: (a) the fields of psychology, cognitive science, neurology and biological sciences in order to obtain understanding concerning the problem of the emotional phenomena, and (b) a large amount of computer science branches such as Autonomic Computing (AC), Self-adaptive software, Self-X systems, Model Integrated Computing (MIC) or the paradigm of models@runtime among others, in order to obtain knowledge about tools for designing each part of the solution. The final approach has been mainly performed on the basis of the entire acquired knowledge, and described under the fields of Artificial Intelligence, Model-Based Systems (MBS), and additional mathematical formalizations to provide punctual understanding in those cases that it has been required. This approach describes a reference model to feedback systems with valuable meaning, allowing for reasoning with regard to (a) the relationship between the environment and the relevance of the effects on the system, and (b) dynamical evaluations concerning the inner situational state of the system as a result of those effects. And this reasoning provides a framework of distinguishable states of AGSys derived from its own circumstances, that can be assumed as artificial emotion.

Quantum interference in atomic-sized point contacts

The conductance of atomic-sized metallic point contacts is shown to be strongly voltage dependent due to quantum interference with impurities even in samples with low impurity concentrations. Transmission through these small contacts depends not only on the local atomic structure at the contact but also on the distribution of impurities or defects within a coherence length of the contact. In contrast with other mesoscopic systems we show that transport through atomic contacts is coherent even at room temperature. The use of a scanning tunneling microscope (STM) makes it possible to fabricate one atom contacts of gold whose transmission can be controlled by manipulation of the contact allowing inelastic spectroscopy in such small contacts.

Microscopic theory for quantum mirages in quantum corrals

Scanning tunneling microscopy permits us to image the Kondo resonance of a single magnetic atom adsorbed on a metallic surface. When the magnetic impurity is placed at the focus of an elliptical quantum corral, a Kondo resonance has been recently observed both on top of the impurity and on top of the focus where no magnetic impurity is present. This projection of the Kondo resonance to a remote point on the surface is referred to as quantum mirage. We present a quantum mechanical theory for the quantum mirage inside an ideal quantum corral and predict that the mirage will occur in corrals with shapes other than elliptical.

Can model Hamiltonians describe the electron–electron interaction in π-conjugated systems?: PAH and graphene

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser–Parr–Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree–Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree–Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an 'effective' Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

The emergence of classical behaviour in magnetic adatoms

A wide class of nanomagnets shows striking quantum behaviour, known as quantum spin tunnelling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground-state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behaviour emerges in the case of magnetic adatoms, where, contrary to larger nanomagnets, the QST splitting is in some instances bigger than temperature and broadening. We analyze two different mechanisms for the renormalization of the QST splitting: Heisenberg exchange between different atoms, and Kondo exchange interaction with the substrate electrons. Sufficiently strong spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization. Importantly, we extract the strength of the Kondo exchange for various experiments on individual adatoms and construct a phase diagram for the classical to quantum transition.

Analytical and experimental investigation of rotating stall phenomena in turbine engine compressors

Technical report AFAPL-TR-67-19.

Gates for the kane quantum computer in the presence of dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is 8.3x10(-5). We also compute the fidelities of Z, X, swap, and controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.

Application of density functional theory to capillary phenomena in cylindrical mesopores with radial and longitudinal density distributions

In this paper, we applied a version of the nonlocal density functional theory (NLDFT) accounting radial and longitudinal density distributions to study the adsorption and desorption of argon in finite as well as infinite cylindrical nanopores at 87.3 K. Features that have not been observed before with one-dimensional NLDFT are observed in the analysis of an inhomogeneous fluid along the axis of a finite cylindrical pore using the two-dimensional version of the NLDFT. The phase transition in pore is not strictly vapor-liquid transition as assumed and observed in the conventional version, but rather it exhibits a much elaborated feature with phase transition being complicated by the formation of solid phase. Depending on the pore size, there are more than one phase transition in the adsorption-desorption isotherm. The solid formation in finite pore has been found to be initiated by the presence of the meniscus. Details of the analysis of the extended version of NLDFT will be discussed in the paper. (C) 2004 American Institute of Physics.

Method for a detailed measurement of image intensity nonuniformity in magnetic resonance imaging

In magnetic resonance imaging (MRI), the MR signal intensity can vary spatially and this spatial variation is usually referred to as MR intensity nonuniformity. Although the main source of intensity nonuniformity arises from B, inhomogeneity of the coil acting as a receiver and/or transmitter, geometric distortion also alters the MR signal intensity. It is useful on some occasions to have these two different sources be separately measured and analyzed. In this paper, we present a practical method for a detailed measurement of the MR intensity nonuniformity. This method is based on the same three-dimensional geometric phantom that was recently developed for a complete measurement of the geometric distortion in MR systems. In this paper, the contribution to the intensity nonuniformity from the geometric distortion can be estimated and thus, it provides a mechanism for estimation of the intensity nonuniformity that reflects solely the spatial characteristics arising from B-1. Additionally, a comprehensive scheme for characterization of the intensity nonuniformity based on the new measurement method is proposed. To demonstrate the method, the intensity nonuniformity in a 1.5 T Sonata MR system was measured and is used to illustrate the main features of the method. (c) 2005 American Association of Physicists in Medicine.

Macroscopic quantum Schrdinger and Einstein-Podolsky-Rosen paradoxes

We propose macroscopic generalizations of the Einstein-Podolsky-Rosen paradox in which the completeness of quantum mechanics is contrasted with forms of macroscopic reality and macroscopic local reality defined in relation to Schrodinger's original 'cat' paradox.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

Quantum entanglement in the two-impurity Kondo model

In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, I. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two-impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created [and quantum information processing (QIP) will only be possible] if the RKKY interaction exchange energy, I, is at least several times larger than the Kondo temperature, T-K. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.

Transfer of nonclassical properties from a microscopic superposition to macroscopic thermal states in the high temperature limit

We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.