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We review the lore of effective field theories as a background to hierarchy problems in general and the cosmological constant problem in particular. We outline some of the attempted four-dimensional solutions to the cosmological con stant problem and conclude that ones based upon the usual assumptions of four-dimensiona lfield theory typically do not work. We argue that one way to relax the assumptions is to seek solutions to the cosmological constant problem which rely on the presence of extra dimensions. We explicitly exhibit that standard compactification techniques fail to solve the cosmological constant problem because they reduce the problem to a four-dimensional one. / We argue that brave-world models may be helpful in solving the cosmological constant problem because standard model loops contribute to the tension and not to the vacuum energy directly, and can fulfill our stated aim of constructing a model which uses the extra dimensions to mitigate the cosmological constant problem. We identify necessary (not sufficient) properties a theory must possess to successfully use this observation. These properties are: a scaling symmetry encoded in a dilaton-like scalar, and bulk supersymmetry. / We therefore investigate supersymmetric six-dimensional brave-world models. Our models are imbedded within a 6D supergravity that has many of the features of realistic string models. We explicitly show that the compactification of the 6D theory has many of the same features as string compactifications, including flat four-dimensional space, chiral fermions, rnoduli, moduli-stabilisation using fluxes, and gluino condensation. We show that by calculating the non-perturbative correction to the superpotential and loop-corrections to the Kahler function that a meta-stable deSitter vacuum can be found. The vacuum energy can be tuned to be ∼ 10-6 M4Planck . / We find that all solutions of the supergravity equations of motion, under a symmetry ansatz, have flat braves. This implies that this property is independent of some of the details of the braves, such as their tensions. The source of the branes' flatness is the required classical scaling symmetry of the action. / We consider whether this class of models may provide a solution to the cosmological constant problem within the large extra dimensions scenario, in which the radius r ∼ 0.1mm, and in which the standard-model fields are trapped on a 3-brave. We conclude that it may be possible to produce naturally a cosmological constant that is of order r -4 ∼ (10-3eV)4 due to loops because the supersymmetry-breaking scale in the bulk is MSUSY ∼ r-1; although there remains a great deal of work to be done. We comment on recent extensions to cosmological backgrounds. / Further work within these models is outlined, including higher-dimensional models, use of effective field-theory techniques in theories with sharp boundaries, and the treatment of quantum corrections.

The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form for a pitchfork bifurcation, and add multiplicative or parametric noise and linear delayed feedback. The latter is sufficient to originate a Hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback. We find a sharp bifurcation in parameter space, and define the threshold as the point in which the stationary distribution function p(x) changes from a delta function at the trivial state x=0 to p(x) ~ x^α at small x (with α = −1 exactly at threshold). We find that the bifurcation threshold is shifted by fluctuations relative to the deterministic limit by an amount that scales linearly with the noise intensity. Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for the model considered. Our results assume that the delay time $\tau$ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average < x(t)|x (t-τ) >, where x(t) is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied. Moreover, we obtain the characteristic correlation time associated to the model. In particular, the validity of the common assumption of statistical independence between the state at time t and that at t-τ is examined. We find that the correlation time diverges at the model's bifurcation line, thus signalling the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small τ. The correlation time T diverges as T ~ a^-1, where a is the control parameter so that a_{c}=0 is the bifurcation threshold. The small-τ expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time. / Le diagramme de bifurcation d'une équation différentielle stochastique incluant une échelle de temps retardée est présenté. Nous sommes motivés par des recherches récentes portant sur des modèles de régulation des gènes. Nous débutons avec la forme normale d'une bifurcation de type fourchette auquelle est ajoutée un terme stochastique de manière paramétrique ainsi qu'un terme linéaire incluant le délai. Ce dernier terme introduit une bifurcation de type Hopf où le délai négatif est particulièrement fort dans l'espace des paramètres. Une bifurcation abrupte est trouvée et nous définissons le seuil de bifurcation comme étant le point dans l'espace des paramètres pour lequel la fonction de distribution stationnaire p(x) change d'une fonction delta autour de l'origine à p(x) ~ x^α pour x petit (avec α = -1 exactement au seuil). Nous démontrons que le seuil de bifurcation est modifié par les fluctuations comparé à la limite déterministique par une valeur qui suit une relation linéraire avec l'intensité du bruit. Des expressions analytiques pour les seuils de bifurcation de type fourchette et Hopf du modèle considéré sont présentées. Nos résultats assument que le temps retardé τ est petit comparé aux autres temps charactéristiques du système, une limitation qui n'est pas significative près de la ligne de bifurcation. L'expression pour la bifurcation de type fourchette est déterminée suite à une expansion stochastique de Taylor. La location de cette bifurcation dépend de la moyenne conditionnelle < x(t)|x (t-τ) >, où x(t) est la variable dynamique. Cette probabilité conditionnelle comprend les effets combinés des fluctuations corrélées et du retardement rétroactif. Nous déterminons aussi une expression pour la bifurcation de type Hopf obtenue à l'aide d'une expansion des échelles de temps autour de la solution près du seuil. Nous obtenons une équation de Fokker-Planck associée à la dynamique des amplitudes des oscillations et nous utilisons celle-ci pour déterminer la location du seuil. Contrairement au cas sans délai, nous démontrons que la location des lignes de bifurcation est modifiée comparé à la limite déterministique et donc que l'intéraction entre les corrélations des fluctuations et le délai affectent la stabilité des solutions du modèle étudié. De plus, nous obtenons le temps de corrélation charactéristique associé au modèle. En particulier, la validité de l'hypothèse d'indépendance statistique entre l'état au temps t ainsi qu'au temps t-τ est examinée. Nous trouvons que le temps de corrélation diverge à la bifurcation, signalant l'infirmation de l'indépendence statistique au seuil de bifurcation. Nous déterminons le temps de corrélation par une intégration directe de l'équation gouvernant le modèle ainsi qu'analytiquement dans la limite où le délai est petit. Le temps de corrélation T diverge suivant une relation du type T ~ a^-1, où a est le paramètre de contrôle et où a_{c}=0 est la location de la bifurcation. L'expansion dans la limite où le délai est petit prédit correctement la location du seuil de bifurcation. Néanmoins, des déviations systématiques dans la magnitude du temps de corrélation sont observées entre les deux résultats.

The study of string theory has recently opened the way to many ground-breaking ideas in theoretical physics. An aspect that had been neglected until recently concerns the role played by time in this theory. It is an important subject because of its possible connections with the field of cosmology. In the first part of this thesis we study S(pacelike)D-branes which are objects arising naturally in string theory when Dirichlet boundary conditions are imposed on the time direction. SD-brane physics is inherently time-dependent. We set up the problem of coupling the most relevant open-string tachyonic mode to massless closed-string modes in the bulk, with back-reaction and Ramond-Ramond fields included. We find solutions (numerically) that are asymptotically flat in the future but plagued with a singularity in the past. The second part of the thesis is concerned with the study of important aspects related to the proposed duality between quantum gravity in de Sitter space and a Euclidean eonformal field theory: the dS/CFT correspondence. First, we study solutions of Einstein gravity coupled to a positive cosmological constant and matter which are asymptotically de Sitter and homogeneous. These solutions are 'tall', meaning that the perturbed universe lives through enough eonformal time for an entire spherical Cauchy surface to enter any observer's past light cone. Our main focus is on the implications of tall universes for the correspondence. Particular attention is given to the associated renormalization group flows, leading to a more general de Sitter c-theorem. We also discuss the eonformal diagrams for various classes of homogeneous flows. Then, we consider the evolution of massive scalar fields in (asymptotically) de Sitter spacetimes of arbitrary dimension. Through the dS/CFT correspondence, our analysis points to the existence of new non-local dualities for the eonformal field theory.

We use a quantum master equation approach to study the transport properties of a triple quantum dot ring. Unlike double quantum dots and triple quantum dot chains, this geometry gives two transport paths with a relative phase sensitive to magnetic flux via the Aharonov-Bohm effect. This gives rise to a coherent population trapping effect and what is known as a "dark state". Unlike other master equation techniques valid only in the high bias voltage limit, our treatment reproduces such results as well as giving an analytic zero-bias conductance formula. As well as providing a more robust signature of this "dark state" physics, our model further predicts a negative differential resistance in connection with high bias rectification already predicted. / Nous utilisons une approche d´equation quantique maîtresse pour étudier les propriétés de transport des points quantiques triples en forme d'anneau. Contrairement aux points quantiques doubles et triples en forme de chaînes, cette géométrie offre deux chemins pour le transport avec une phase quantique relative qui est sensible au flux magnétique en raison de l'effet Aharonov-Bohm. Ceci méne à un effet de piégeage de population cohérent et cela est connu sous le nom d'un "état sombre". Contrairement à d'autres techniques d'équation maîtresse qui sont seulement valides dans la limite d'un potentiel électrique élevé, notre méthode reproduit les résultats de ces derniers en plus de donner une expression analytique pour la conductance différentielle de zéro potentiel électrique. En plus de donner une optique plus robuste de la physique "d´etats sombres", notre modèle prédit une résistance différentielle négative qui est reliée au phénomène déjà prédit de rectification à potentiel élevé.

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