Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System

We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint.

A Conditional Approach for Modelling Patient Re-admissions in Hospital using a mixture of Coxian phase-type distributions incorporating Bayes Theorem

The number of elderly patients requiring hospitalisation in Europe is rising. With a greater proportion of elderly people in the population comes a greater demand for health services and, in particular, hospital care. Thus, with a growing number of elderly patients requiring hospitalisation competing with non-elderly patients for a fixed (and in some cases, decreasing) number of hospital beds, this results in much longer waiting times for patients, often with a less satisfactory hospital experience. However, if a better understanding of the recurring nature of elderly patient movements between the community and hospital can be developed, then it may be possible for alternative provisions of care in the community to be put in place and thus prevent readmission to hospital. The research in this paper aims to model the multiple patient transitions between hospital and community by utilising a mixture of conditional Coxian phase-type distributions that incorporates Bayes' theorem. For the purpose of demonstration, the results of a simulation study are presented and the model is applied to hospital readmission data from the Lombardy region of Italy.

On lattices from combinatorial game theory modularity and a representation theorem: Finite case

We show that a self-generated set of combinatorial games, S, may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question “Is there a set which will give an on-distributive but modular lattice?” appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

An Interactive Theorem Prover for First-Order Dynamic Logic

Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs. The method of proving correctness of properties of a computer program using the well-known Hoare Logic can be implemented by utilizing the robustness of dynamic logic. For a very broad range of languages and applications in program veri cation, a theorem prover named KIV (Karlsruhe Interactive Veri er) Theorem Prover has already been developed. But a high degree of automation and its complexity make it di cult to use it for educational purposes. My research work is motivated towards the design and implementation of a similar interactive theorem prover with educational use as its main design criteria. As the key purpose of this system is to serve as an educational tool, it is a self-explanatory system that explains every step of creating a derivation, i.e., proving a theorem. This deductive system is implemented in the platform-independent programming language Java. In addition, a very popular combination of a lexical analyzer generator, JFlex, and the parser generator BYacc/J for parsing formulas and programs has been used.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Harsanyi’s Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions

This paper provides new versions of Harsanyi’s social aggregation theorem that are formulated in terms of prospects rather than lotteries. Strengthening an earlier result, fixed-population ex-ante utilitarianism is characterized in a multi-profile setting with fixed probabilities. In addition, we extend the social aggregation theorem to social-evaluation problems under uncertainty with a variable population and generalize our approach to uncertain alternatives, which consist of compound vectors of probability distributions and prospects.

A Generalization of a Theorem of Boyd and Lawton

Ce mémoire s’applique à étudier d’abord, dans la première partie, la mesure de Mahler des polynômes à une seule variable. Il commence en donnant des définitions et quelques résultats pertinents pour le calcul de telle hauteur. Il aborde aussi le sujet de la question de Lehmer, la conjecture la plus célèbre dans le domaine, donne quelques exemples et résultats ayant pour but de résoudre la question. Ensuite, il y a l’extension de la mesure de Mahler sur les polynômes à plusieurs variables, une démarche semblable au premier cas de la mesure de Mahler, et le sujet des points limites avec quelques exemples. Dans la seconde partie, on commence par donner des définitions concernant un ordre supérieur de la mesure de Mahler, et des généralisations en passant des polynômes simples aux polynômes à plusieurs variables. La question de Lehmer existe aussi dans le domaine de la mesure de Mahler supérieure, mais avec des réponses totalement différentes. À la fin, on arrive à notre objectif, qui sera la démonstration de la généralisation d’un théorème de Boyd-Lawton, ce dernier met en évidence une relation entre la mesure de Mahler des polynômes à plusieurs variables avec la limite de la mesure de Mahler des polynômes à une seule variable. Ce résultat a des conséquences en termes de la conjecture de Lehmer et sert à clarifier la relation entre les valeurs de la mesure de Mahler des polynômes à une variable et celles des polynômes à plusieurs variables, qui, en effet, sont très différentes en nature.

Études de l’effet tunnel des spins quantiques macroscopiques

Dans cette thèse, nous présentons quelques analyses théoriques récentes ainsi que des observations expérimentales de l’effet tunnel quantique macroscopique et des tran- sitions de phase classique-quantique dans le taux d’échappement des systèmes de spins élevés. Nous considérons les systèmes de spin biaxial et ferromagnétiques. Grâce à l’approche de l’intégral de chemin utilisant les états cohérents de spin exprimés dans le système de coordonnées, nous calculons l’interférence des phases quantiques et leur distribution énergétique. Nous présentons une exposition claire de l’effet tunnel dans les systèmes antiferromagnétiques en présence d’un couplage d’échange dimère et d’une anisotropie le long de l’axe de magnétisation aisé. Nous obtenons l’énergie et la fonc- tion d’onde de l’état fondamentale ainsi que le premier état excité pour les systèmes de spins entiers et demi-entiers impairs. Nos résultats sont confirmés par un calcul utilisant la théorie des perturbations à grand ordre et avec la méthode de l’intégral de chemin qui est indépendant du système de coordonnées. Nous présentons aussi une explica- tion claire de la méthode du potentiel effectif, qui nous laisse faire une application d’un système de spin quantique vers un problème de mécanique quantique d’une particule. Nous utilisons cette méthode pour analyser nos modèles, mais avec la contrainte d’un champ magnétique externe ajouté. La méthode nous permet de considérer les transitions classiques-quantique dans le taux d’échappement dans ces systèmes. Nous obtenons le diagramme de phases ainsi que les températures critiques du passage entre les deux régimes. Nous étendons notre analyse à une chaine de spins d’Heisenberg antiferro- magnétique avec une anisotropie le long d’un axe pour N sites, prenant des conditions frontière périodiques. Pour N paire, nous montrons que l’état fondamental est non- dégénéré et donné par la superposition des deux états de Néel. Pour N impair, l’état de Néel contient un soliton, et, car la position du soliton est indéterminée, l’état fondamen- tal est N fois dégénéré. Dans la limite perturbative pour l’interaction d’Heisenberg, les fluctuations quantiques lèvent la dégénérescence et les N états se réorganisent dans une bande. Nous montrons qu’à l’ordre 2s, où s est la valeur de chaque spin dans la théorie des perturbations dégénérées, la bande est formée. L’état fondamental est dégénéré pour s entier, mais deux fois dégénéré pour s un demi-entier impair, comme prévu par le théorème de Kramer

Studies on Thermodynamics and No-hair Theorem in Black hole Spacetime

Department of Physics, Cochin University of Science and Technology