Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation. / Doctor of Philosophy / Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.

In this workshop we will discuss some fundamentals of equilibrium and non-equilibrium thermodynamics, in particular how concentration gradients are formed due to the Soret effect. At first we will pay attention to the analysis of fluctuations at macroscopic thermodynamic equilibrium for the determination of the Fick diffusion coefficient and the thermal diffusivity. Then, starting with the extended diffusion equation, we will derive solutions for the concentration field under common experimental geometries and introduce modern optical techniques for the measurement of the Fick diffusion, thermodiffusion and Soret coefficients.

There has been an increasing focus on using nanoscale devices for various applications ranging from computer components to biomechanical sensors. In order to effectively design devices of this size, it is important to understand the properties of materials at this length scale and their relevant transport equations. At everyday length scales, heat transport is governed by Fourier’s law, but at the nanoscale, it becomes increasingly inaccurate. Phonon kinetic theory can be used to develop more accurate governing equations. We present the moment method, which takes integral moments of the phonon Boltzmann kinetic equation to develop a set of equations based on macroscopic properties such as energy and heat flux. The advantage of using this method is that transport properties in nanodevices can be approximated analytically and efficiently. A number of simplifying assumptions are used in order to linearize the equations. Boundary conditions for the moment method are derived based on a microscopic model of phonons interacting with a surface by scattering, reflection or thermalization. Several simple, one dimensional problems are solved using the moment method equation. The results show the effects of phonon surface interactions and how they affect overal properties of a nanoscale device. Some of these effects were observed in a recent experiment and are replicated by other modeling techniques. Although the moment method has described some effects of nanoscale heat transfer, the model is limited by some of its simplifying assumptions. Several of these simplifying assumptions could be removed for greater accuracy, but it would introduce non-linearity into the moment method. / Graduate

Title from PDF of title page (University of Missouri--Columbia, viewed on February 23, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Sudarshan K. Loyalka and Dr. Robert V. Tompson. Vita. Includes bibliographical references.

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The standard approach to modelling mechanics of continuum based on bal- ances of mass, momentum, angular momentum and energy is a very powerful tool. However, there is no connection between that and the Hamiltonian mechanics, that superbly describes kinematics of isolated particles. Thus, the two topics are rather isolated. Nevertheless, there is another approach to continuum mechan- ics - a one, whose reversible part is based on Hamiltonian mechanics, while the irreversible is generated by a dissipation potential. This framework, called GENERIC, is thus an interesting bridge between con- tinuous and discrete systems. In this thesis, we present the GENERIC framework applied to a continuous body, derive the governing equations and compare them to the standard theory. Both analytical and numerical solutions to a decent range of model examples are presented and analysed.

Purpose of this work is to provide a comprehensive picture of thin film (interconnect) and solid droplet surface evolution under the several external applied forces with anisotropic physical properties so that one can eventually be able to predict main reasons and conditions under which stability of surface is defined. A systematic study based on the self-consistent dynamical simulations is presented for the spontaneous surface evolution of an thin film and isolated thin solid droplet on a rigid substrate, which is driven by the surface drift diffusion induced by the anisotropic diffusivity, the anisotropic capillary forces (surface stiffness) and mismatch stresses under electron winding. The effect of surface free energy anisotropies (weak and strong (anomalous)) on the development kinetics of the Stranski-Krastanow island type morphology are studied. Although, various tilt angles and anisotropy constants were considered during simulations, the main emphasis was given on the effect of rotational symmetries associated with the surface Helmholtz free energy topography in 2D space. The investigations of dynamics of surface roughness on concurrent actions of the appliedelasto- and electro- static fields clearly indicate that applied misfit stress level is highly important effect on resultant surface form which may be smooth wave like or crack like. The droplet simulations revealed the formation of an extremely thin wetting layer during the development of the bell-shaped Stranski-Krastanow island through the mass accumulation at the central region of the droplet via surface drift-diffusion. The developments in the peak height, in the extension of in the wetting layer beyond the domain boundaries, and the change in triple junction contact angle, one clearly observes that these quantities are reaching certain saturation limits or plateaus, when the growth mode turned-off. Islanding differences for weak anisotropy constant levels and the strong (anomalous) anisotropy constant domains are discussed.

It is well established that non-equilibrium flows cannot properly be described by traditional hydrodynamics, namely, the Navier-Stokes-Fourier (NSF) equations. Such flows occur, for example, in micro-electro-mechanical systems (MEMS), and ultra vacuum systems, where the dimensions of the devices are comparable to the mean free path of a gas molecule. Therefore, the study of non-equilibrium effects in gas flows is extremely important. The general interest of the present study is to explore boundary value problems for moderately rarefied gas flows, with an emphasis on numerical solutions of the regularized 13--moment equations (R13). Boundary conditions for the moment equations are derived based on either phenomenological principles or on microscopic gas-surface scattering models, e.g., Maxwell's accommodation model and the isotropic scattering model. Using asymptotic analysis, several non-linear terms in the R13 equations are transformed into algebraic terms. The reduced equations allow us to obtain numerical solutions for multidimensional boundary value problems, with the same set of boundary conditions for the linearized and fully non-linear equations. Some basic flow configurations are employed to investigate steady and unsteady rarefaction effects in rarefied gas flows, namely, planar and cylindrical Couette flow, stationary heat transfer between two plates, unsteady and oscillatory Couette flow. A comparison with the corresponding results obtained previously by the DSMC method is performed. The influence of rarefaction effects in the lid driven cavity problem is investigated. Solutions obtained from several macroscopic models, in particular the classical NSF equations with jump and slip boundary conditions, and the R13--moment equations are compared. The R13 results compare well with those obtained from more costly solvers for rarefied gas dynamics, such as the Direct Simulation Monte Carlo (DSMC) method. Flow and heat transfer in a bottom heated square cavity in a moderately rarefied gas are investigated using the R13 and NSF equations. The results obtained are compared with those from the DSMC method with emphasis on understanding thermal flow characteristics from the slip flow to the early transition regime. The R13 theory gives satisfying results including flow patterns in fair agreement with DSMC in the transition regime, which the conventional Navier-Stokes-Fourier equations are not able to capture. / Graduate / 0548 / anirudh@uvic.ca

This dissertation examines the motion of colloids in a temperature gradient, a non-equilibrium phenomenon also known as thermophoresis. Chapter 1 gives an introduction to the existing applications and basic concepts of thermophoresis and outlines some of the experimental and theoretical challenges that serve as a motivation for this PhD project. In Chapter 2, a general theoretical description for thermophoresis is formulated using the theory of non-equilibrium thermodynamics. The colloidal flux is split up into an interfacial single-colloid contribution and a bulk contribution, followed by a determination of transport coefficients based on Onsager’s reciprocal relations. It is further shown how the phenomenological expression of the thermophoretic flux can be recovered when the fluid is at steady-state. The results issuing from this description are then discussed and compared to other existing approaches, some of which are shown to neglect the hydrodynamic character of colloidal thermophoresis. Chapter 3 is dedicated to the validation of the introduced theoretical framework by means of computer simulations, using a simulation technique known as multi-particle collision dynamics. More specifically, the dependence of the thermophoretic force on different system parameters is examined and deviations from the theoretical prediction are explained by an advective distortion of interfacial fluid properties at the colloidal surface. Chapter 4 presents steady-state measurements of functionalised colloids in a temperature gradient, showing how the addition of molecular surface groups increases the experimental complexity of thermophoretic motion. The relaxation process behind this steady-state is also studied, to determine how the relaxation speed depends on the applied temperature gradient. In chapter 5, a general conclusion is drawn from the presented work and its implications are briefly discussed in relation to the current state of knowledge. Finally, the discussion is closed with an outlook on remaining challenges in understanding colloidal motion that could be the subject of future research.

Non-equilibrium thermodynamics, which serves as a framework for formulating evolution equations of macroscopic and mesoscopic systems, is briefly reviewed and further developed in this work. For example, the relation between the General Equation for the Nonequilibrium Reversible- Irreversible Coupling (GENERIC) and (ir)reversibility is elucidated, and Onsager-Casimir reciprocal relations are shown to be an implication of GENERIC. Non-equilibrium thermodynamics is then applied to describe fuel cells and related devices, and theoretical conclusions are compared to experimental data. Moreover, a generalization of standard exergy analysis is developed bringing a new method for revealing a map of useful work losses in electricity producing devices. This method requires a non-equilibrium thermodynamic model, and so the general theory of non- equilibrium thermodynamics and optimization of real power generating devices stand side by side.