Numerical Stochastic Perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice quantum field theory. The standard algorithm based on the Langevin equation, however, suffers from several limitations which in practice restrict the potential of this technique: first of all it is not exact, a sequence of simulations with finer and finer discretization of the relevant equations have to be performed in order to extrapolate away the systematic errors in the results; and, secondly, the numerical simulations suffer from critical slowing down as the continuum limit of the theory is approached. In this thesis I investigate some alternative methods which improve upon the standard approach. In particular, I present a formulation of Numerical Stochastic Perturbation theory based on the Generalised Hybrid Molecular Dynamics algorithm and a study of the recently proposed Instantaneous Stochastic Perturbation Theory. The viability of these methods is investigated in φ4 theory.

Made available in DSpace on 2014-06-11T19:25:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-17Bitstream added on 2014-06-13T20:14:03Z : No. of bitstreams: 1 bauke_fc_me_rcla.pdf: 1413465 bytes, checksum: 5695187aaf8a438767e3a8684e26c073 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão “portadores quentes”. Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo / We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle´s effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression “hot carriers”. This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions

<p>Heavy flavor hadrons serve as valuable probes of the transport properties of the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. In this dissertation, we introduce a comprehensive framework that describes the full-time evolution of heavy flavor in heavy-ion collisions, including its initial production, in-medium evolution inside the QGP matter, hadronization process from heavy quarks to their respective mesonic bound states and the subsequent interactions between heavy mesons and the hadron gas.</p><p>The in-medium energy loss of heavy quarks is studied within the framework of a Langevin equation coupled to hydrodynamic models that simulate the space-time evolution of the hot and dense QGP matter. We improve the classical Langevin approach such that, apart from quasi-elastic scatterings between heavy quarks and the medium background, radiative energy loss is incorporated as well by treating gluon radiation as a recoil force term. The subsequent hadronization of emitted heavy quarks is simulated via a hybrid fragmentation plus recombination model. The propagation of produced heavy mesons in the hadronic phase is described using the ultra-relativistic quantum molecular dynamics (UrQMD) model. Our calculation shows that while collisional energy loss dominates the heavy quark motion inside the QGP in the low transverse momentum (pT) regime, contributions from gluon radiation are found to be significant at high pT. The recombination mechanism is important for the heavy flavor meson production at intermediate energies. The hadronic final state interactions further enhance the suppression and the collective flow of heavy mesons we observe. Within our newly developed framework, we present numerical results for the nuclear modification and the elliptic flow of D mesons, which are consistent with measurements at both the CERN Large Hadron Collider (LHC) and the BNL Relativistic Heavy-Ion Collider (RHIC); predictions for B mesons are also provided.</p><p>In addition, various transport properties of heavy quarks are investigated within our numerical framework, such as the thermalization process of heavy quarks inside the QGP, and how the initial configuration of the QGP as well as its properties affect the final state spectra and the elliptic flow of heavy mesons and their decay electrons. The effects of initial state fluctuations in heavy-ion collisions are also studied and found to enhance the heavy quark energy loss in a (2+1)-dimensional boost invariant scenario. Furthermore, a new set of observables -- heavy-flavor-tagged angular correlation functions -- are explored and found to be potential candidates for distinguishing different energy loss mechanisms of heavy quarks inside the QGP.</p> / Dissertation

No description available.

This thesis presents the benchmarking and development of a method to study ground state properties of hydrogen clusters using molecular dynamics. Benchmark studies are performed on our Path Integral Molecular Dynamics code using the Langevin equation for finite temperature studies and our Langevin equation Path Integral Ground State code to study systems in the zero-temperature limit when all particles occupy their nuclear ground state. A simulation is run on the first 'real' system using this method, a parahydrogen molecule interacting with a fixed water molecule using a trivial unity trial wavefunction. We further develop a systematic method of optimizing the necessary parameters required for our ground state simulations and introduce more complex trial wavefunctions to study parahydrogen clusters and their isotopologues orthodeuterium and paratritium. The effect of energy convergence with parameters is observed using the trivial unity trial wavefunction, a Jastrow-type wavefunction that represents a liquid-like system, and a normal mode wavefunction that represents a solid-like system. Using a unity wavefunction gives slower energy convergence and is inefficient compared to the other two. Using the Lindemann criterion, the normal mode wavefunction acting on floppy systems introduces an ergodicity problem in our simulation, while the Jastrow does not. However, even for the most solid-like clusters, the Jastrow and the normal mode wavefunctions are equally efficient, therefore we choose the Jastrow trial wavefunction to look at properties of a range of cluster sizes. The energetic and structural properties obtained for parahydrogen and orthodeuterium clusters are consistent with previous studies, but to our knowledge, we may be the first to predict these properties for neutral paratritium clusters. The results of our ground state simulations of parahydrogen clusters, namely the distribution of pair distances, are used to calculate Raman vibrational shifts and compare to experiment. We investigate the accuracy of four interaction potentials over a range of cluster sizes and determine that, for the most part, the ab initio derived interaction potentials predict shifts more accurately than the empirically based potentials for cluster sizes smaller than the first solvation shell and the trend is reversed as the cluster size increases. This work can serve as a guide to simulate any system in the nuclear ground state using any trial wavefunction, in addition to providing several applications in using this ground state method.

Dans ce travail de thèse, réalisé à l'IMFT, nous nous sommes intéressés aux écoulements turbulents diphasiques gaz-solides et plus particulièrement au phénomène de couplage inverse qui correspond à la modulation de la turbulence par la phase dispersée. Ce mécanisme est crucial pour les écoulements à forts chargements massiques. Dans cette thèse, nous avons considéré une turbulence homogène isotrope stationnaire sans gravité dans laquelle des particules sont suivies individuellement d'une façon Lagrangienne. La turbulence du fluide porteur est obtenue par des simulations directes (DNS). Les particules sont sphériques, rigides et d'une taille inférieure aux plus petites échelles de la turbulence. Leur densité est bien plus grande que la densité du fluide. Dans ce cadre, la force la plus importante agissant sur les particules est celle de traînée. Les interactions inter-particules ainsi que la gravité ne sont pas prises en compte. Pour modéliser ce type d'écoulement, une approche stochastique est utilisée pour laquelle l'accélération du fluide est modélisée par une équation de Langevin. L'originalité de ce travail est la prise en compte de l'effet de la modulation de la turbulence par un terme additionnel. Nous avons proposé deux modèles : une force de couplage moyenne qui est définie à partir des vitesses moyennes des phases, et une force instantanée qui est définie à l'aide du formalisme mésoscopique Eulérien. La fermeture des modèles s’appuie sur la fonction d’autocorrélation Lagrangienne et l’équation de transport de l’énergie cinétique. Les modèles sont testés en terme de prédiction de la vitesse de dérive et des corrélations fluide-particule. Les résultats montrent que le modèle moyen, plus simple, prend en compte les effets principaux du couplage inverse. Cependant, le problème de fermeture pratique est reporté sur la modélisation de l’échelle intégrale Lagrangienne et l’énergie cinétique de la turbulence du fluide vue par les particules. / In this thesis, performed in IMFT, we are interested in the turbulent gas-solid flows and more specifically, in the phenomenon of turbulence modulation which is the modification of the structure of the turbulence due to the solid particles. This mechanism is crucial in flows with high particle mass-loadings. In this work, we considered a homogeneous isotropic turbulence without gravity kept stationary with stochastic type forcing. Discrete particles are tracked individually in Lagrangian manner. Turbulence of the carrier phase is obtained by using DNS. The particles are spherical, rigid and of a diameter smaller than the smallest scales of turbulence. Their density is very large in comparison to the density of the fluid. In this configuration the only force acting on the particles is the drag force. Volume fraction of particles is very small and inter-particle interactions are not considered. To model this type of flow, a stochastic approach is used where the fluid element accel- eration is modeled using stochastic Langevin equation. The originality in this work is an additional term in the stochastic equation which integrates the effect of the particles on the trajectory of fluid elements. To model this term, we proposed two types of modeling: a mean drag model which is defined using the mean velocities from the mean transport equations of the both phases and an instantaneous drag term which is written with the help of the Mesoscopic Eulerian Approach. The closure of the models is based on the Lagrangian auto- correlation function of the fluid velocity and on the transport equation of the fluid kinetic energies. The models are tested in terms of the fluid-particle correlations and fluid-particle turbulent drift velocity. The results show that the mean model, simple, takes into account the principal physical mechanism of turbulence modulation. However, practical closure problem is brought forward to the Lagrangian integral scale and the fluid kinetic energy of the fluid turbulence viewed by the particles.

This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.

In this thesis, we investigate the quantum mechanical interaction of light with matter in the form of a gas of ultracold atoms: the atomic ensemble. We present a theoretical analysis of two problems, which involve the interaction of quantized electromagnetic fields (called signal and idler) with the atomic ensemble (i) cascade two-photon emission in an atomic ladder configuration, and (ii) photon frequency conversion in an atomic diamond configuration. The motivation of these studies comes from potential applications in long-distance quantum communication where it is desirable to generate quantum correlations between telecommunication wavelength light fields and ground level atomic coherences. In the two systems of interest, the light field produced in the upper arm of an atomic Rb level scheme is chosen to lie in the telecom window. The other field, resonant on a ground level transition, is in the near-infrared region of the spectrum. Telecom light is useful as it minimizes losses in the optical fiber transmission links of any two long-distance quantum communication device. We develop a theory of correlated signal-idler pair correlation. The analysis is complicated by the possible generation of multiple excitations in the atomic ensemble. An analytical treatment is given in the limit of a single excitation assuming adiabatic laser excitations. The analysis predicts superradiant timescales in the idler emission in agreement with experimental observation. To relax the restriction of a single excitation, we develop a different theory of cascade emission, which is solved by numerical simulation of classical stochastic differential equation using the theory of open quantum systems. The simulations are in good qualitative agreement with the analytical theory of superradiant timescales. We further analyze the feasibility of this two-photn source to realize the DLCZ protocol of the quantum repeater communication system. We provide a quantum theory of near-infrared to telecom wavelength conversion in the diamond configuration. The system provides a crucial part of a quantum-repeater memory element, which enables a "stored" near-infrared photon to be converted to a telecom wavelength for transmission without the destruction of light-atom quantum correlation. We calculate the theoretical conversion efficiency, analyzing the role of optical depth of the ensemble, pulse length, and quantum fluctuations on the process.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / É conhecido que derivações microscópicas obtidas através de métodos de teoria quântica de campos (TQC) podem conduzir a complicadas equações de movimento (EdM) que possuem um termo dissipativo com memória e um termo de ruído colorido. Um caso particularmente interessante é o modelo que escreve a interação entre um sistema e um banho térmico a temperatura T. Motivado por isso, usamos uma prescrição que nos permite reescrever EdMs não-markovianas semelhantes as obtidas em TQC em termos de um sistema de equações locais, para então confrontarmos a solução desse sistema com a solução aproximada usada correntemente na literatura, a chamada aproximação markoviana. A pergunta chave a qual se pretende responder aqui é: dado um conjunto de parâmetros que descrevem o modelo, a aproximação markoviana é suficientemente boa para descrever a dinâmica do sistema se comparada a dinâmica obtida atravéS da EdM não-markoviana? Além disso, consideramos uma versão linear da ELG de forma que pudéssemos determinar o nível de confiança da nossa metodologia numérica, procedimento este realizado comparando-se a solução analítica com a solução numérica. Como exemplo de aplicação prática do tema discutido aqui, comparamos a evolução não-markoviana do inflaton com a evolução markoviana do mesmo num modelo de universo primordial denominado inflação não-isentrópica (warm inflation). / It is known that microscopic derivations based on quantum field theory (QFT)methods can lead to quite complicated equations of motion (EoM) with a dissipation term with memory and a colored noise term. A very interesting particular case is the model that describes the interaction between a system and a thermal bath at some temperature T. Motivated by this, we use a prescription that allow us to rewrite similar non-Markovian EoMs to that obtained in QFT in terms of a set of local equations, so that we can contrast the solution of this system of equations with the approximated solution currently used in the literatury, the so-called Markovian approximation. The key question we want to address here is: given a set of parameters that characterizes the system and the bath, is the Markovian approximation good enough to represent the system's dynamics? We also have considered a linear version of the non-Markovian equation in order to check the confiability of our numerical approach. For that, we have compared the analytical solution with the numerical one. As an example of practical application of the theme discussed here, we contrast the non-Markovian and the Markovian evolution of the inflaton field in an early universe model called warm in inflation.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / É conhecido que derivações microscópicas obtidas através de métodos de teoria quântica de campos (TQC) podem conduzir a complicadas equações de movimento (EdM) que possuem um termo dissipativo com memória e um termo de ruído colorido. Um caso particularmente interessante é o modelo que escreve a interação entre um sistema e um banho térmico a temperatura T. Motivado por isso, usamos uma prescrição que nos permite reescrever EdMs não-markovianas semelhantes as obtidas em TQC em termos de um sistema de equações locais, para então confrontarmos a solução desse sistema com a solução aproximada usada correntemente na literatura, a chamada aproximação markoviana. A pergunta chave a qual se pretende responder aqui é: dado um conjunto de parâmetros que descrevem o modelo, a aproximação markoviana é suficientemente boa para descrever a dinâmica do sistema se comparada a dinâmica obtida atravéS da EdM não-markoviana? Além disso, consideramos uma versão linear da ELG de forma que pudéssemos determinar o nível de confiança da nossa metodologia numérica, procedimento este realizado comparando-se a solução analítica com a solução numérica. Como exemplo de aplicação prática do tema discutido aqui, comparamos a evolução não-markoviana do inflaton com a evolução markoviana do mesmo num modelo de universo primordial denominado inflação não-isentrópica (warm inflation). / It is known that microscopic derivations based on quantum field theory (QFT)methods can lead to quite complicated equations of motion (EoM) with a dissipation term with memory and a colored noise term. A very interesting particular case is the model that describes the interaction between a system and a thermal bath at some temperature T. Motivated by this, we use a prescription that allow us to rewrite similar non-Markovian EoMs to that obtained in QFT in terms of a set of local equations, so that we can contrast the solution of this system of equations with the approximated solution currently used in the literatury, the so-called Markovian approximation. The key question we want to address here is: given a set of parameters that characterizes the system and the bath, is the Markovian approximation good enough to represent the system's dynamics? We also have considered a linear version of the non-Markovian equation in order to check the confiability of our numerical approach. For that, we have compared the analytical solution with the numerical one. As an example of practical application of the theme discussed here, we contrast the non-Markovian and the Markovian evolution of the inflaton field in an early universe model called warm in inflation.