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This thesis deals with electron correlation effects within low-dimensional, mesoscopic systems. We study phenomena within two different types of system in which correlations play an important role. The first involves the spectra and spin structure of small symmetric quantum dots, or &quoteartificial atoms&quote. The second is the &quote0.7 structure&quote, a well-known but mysterious anomalous conductance plateau which occurs in the conductance profile of a quantum point contact. Artificial atoms are manufactured mesoscopic devices: quantum dots which resemble real atoms in that their symmetry gives them a &quoteshell structure&quote. We examine two-dimensional circular artificial atoms numerically, using restricted and unrestricted Hartree-Fock simulation. We go beyond the mean-field approximation by direct calculation of second-order correlation terms; a method which works well for real atoms but to our knowledge has not been used before for quantum dots. We examine the spectra and spin structure of such dots and find, contrary to previous theoretical mean-field studies, that Hund's rule is not followed. We also find, in agreement with previous numerical studies, that the shell structure is fragile with respect to a simple elliptical deformation. The 0.7 structure appears in the conductance of a quantum point contact. The conductance through a ballistic quantum point contact is quantised in units of 2e^2/h. On the lowest conductance step, an anomalous narrow conductance plateau at about G = 0.7 x 2e^2/h is known to exist, which cannot be explained in the non-interacting picture. Based on suggestive numerical results, we model conductance through the lowest channel of a quantum point contact analytically. The model is based on the screening of the electron-electron interaction outside the QPC, and our observation that the wavefunctions at the Fermi level are peaked within the QPC. We use a kinetic equation approach, with perturbative account of electron-electron backscattering, to demonstrate that these simple features lead to the existence of a 0.7-like structure in the conductance. The behaviour of this structure reproduces experimentally observed features of the 0.7 structure, including the temperature dependence and the behaviour under applied in-plane magnetic fields.

In ‘clean' confined conductors (the so-called mesoscopic systems), the electronic phase and momentum can be preserved over very long distances compared to the system dimensions. This gives rise to peculiar transport properties, bearing signatures of electron interferences, ballistic electron trajectories, electron-electron interactions, regular-chaotic electron dynamics and (in some cases) spin-orbit coupling. Examples of such effects are the Universal Conductance Fluctuations (UCFs) and the Weak Localization observed in the low-temperature magnetoconductance of many confined electronic systems. Of central importance, the electronic phase coherence time and the spin-orbit coupling time determine the amplitude of these quantum effects. In the first part of this thesis, we use UCFs to extract these characteristic timescales in open ballistic quantum dots (QDs) fabricated from InGaAs heterostructures. We observe an intrinsic saturation of the coherence time at low temperature in the InGaAs QDs. The origin of this phenomenon has been intensely debated during the last decade. Based on our observations and previous experimental data in QDs, we propose an explanation: the dwell time becomes the limiting factor for electron interferences in QDs at low temperature. Then, we report on magnetoconductance measurements in a bismuth ballistic nano-cavity. The cavity is found to be zero-dimensional for phase coherent processes at low temperature. We evidence an anomalous reduction of the phase coherence time in the cavity with respect to data obtained in thin Bi films, while the spin-orbit coupling time is similar in both systems. Finally, we examine the current-voltage characteristics of asymmetric InGaAs nano-junctions in the nonlinear regime. We observe a new tunable rectification effect, whose amplitude and sign are governed by the conductances of the junctions' channels. We show that the effect is ballistic and exhibits new features with respect to predictions of available models.

This work explores the effects of weak nonlinearity on harmonic oscillators.Two particular systems are studied experimentally: A superconductingresonator formed from a coplanar waveguide that oscillates at microwave frequencies,and the cantilever of an atomic force microscope (AFM) vibratingat ultrasonic frequencies. Both of these systems are described in the introduction,followed by a theory chapter giving a general theoretical framework for nonlinear oscillators. Basic properties of nonlinear oscillators, such asbifurcation and intermodulation, are explained using simple models. Experimental methods, including cryogenic and microwave measurement techniques,are described in some detail. The nonlinear superconducting resonator is studied for use as a parametric amplifier. A strong drive tone, called the pump, drives the oscillator nearthe point of bifurcation. A second, much weaker drive signal that is slightlydetuned from the pump, will cause energy to move from the pump to the signal, giving signal amplification. We have measured a signal gain greaterthan 22 dB in a bandwidth of 30 kHz, for a resonator pumped at 7.6 GHz.This type of amplifier is phase-sensitive, meaning that signals in phase withthe pump will be amplified, but signals in quadrature phase of the pump will be deamplified. Phase-sensitivity has important implications on the amplifier’snoise properties. With a parametric amplifier, a signal can be amplified without any additional noise being added by the amplifier, something that is fundamentally impossible for a standard amplifier. The vibrating AFM cantilever becomes a nonlinear oscillator when it is interacting with a surface. When driven with two frequencies, the amplitudeand phase of the cantilever’s response will develop mixing products, or intermodulation products, that are very sensitive to the exact form of the nonlinearity. Very small changes in the surface properties will be detectable when measuring the intermodulation products. Simultaneously measuring many intermodulation products, or acquiring an intermodulation spectrum,allows one to reconstruct the tip-surface interaction. Intermodulation AFM increases the sensitivity of the measurement or the contrast of the acquiredimages, and provides a means of rapidly measuring the nonlinear tip-surface interaction. The method promises to enhance the functionality of the AFM beyond simple topography measurement, towards quantitative analysis of the chemical or material properties of the surface. / <p>QC 20100812</p>

Mathematical models are now gaining in importance for descriptions of biological processes. In this thesis, such models have been used to identify and analyze principles that govern bacterial protein synthesis under amino acid limitation. New techniques, that are generally applicable for analysis of intrinsic fluctuations in systems of chemical reactions, are also presented. It is shown how multi-substrate reactions, such as protein synthesis, may display zero order kinetics below saturation, because an increase in one substrate pool is compensated by a decrease in another, so that the overall flow is unchanged. Under those conditions, metabolite pools display hyper sensitivity and large fluctuations, unless metabolite synthesis is carefully regulated. It is demonstrated that flow coupling in protein synthesis has consequences for transcriptional control of amino acid biosynthetic operons, accuracy of mRNA translation and the stringent response. Flow coupling also determines the choices of synonymous codons in a number of cases. The reason is that tRNA isoacceptors, cognate to the same amino acid, often read different codons and become deacylated to very different degrees when their amino acid is limiting for protein synthesis. This was demonstrated theoretically and used to successfully predict the choices of control codons in ribosome mediated transcriptional attenuation and codon bias in stress response genes. New tools for the analysis of internal fluctuations have been forged, most importantly, an efficient Monte Carlo algorithm for simulation of the Markov-process corresponding to the reaction-diffusion master equation. The algorithm makes it feasible to analyze stochastic kinetics in spatially extended systems. It was used to demonstrate that bi-stable chemical systems can display spontaneous domain separation also in three spatial dimensions. This analysis reveals geometrical constraints on biochemical memory circuits built from bistable systems. Further, biochemical applications of the Fokker-Planck equation and the Linear Noise Approximation have been explored.

In this dissertation, I have studied theoretical problems in statistical physics and electrodynamics of Bose particles, namely, mesoscopic effects in statistics of Bose- Einstein condensate (BEC) of atoms and electromagnetic waveguide effects of planar Bragg structures in Free Electron Lasers. A mesoscopic system of a trapped gas of Bose atoms is the most difficult for the theoretical analysis in quantum statistical physics since it cannot be studied by neither a quantum mechanics of the simple microscopic systems of one or very few atoms nor a standard statistical physics of the macroscopic systems that implies a thermodynamic limit. I present analytical formulas and numerical calculations for the moments and cumulants of BEC fluctuations in both ideal and weakly interacting gas. I analyze the universal scaling and structure of the BEC statistics in a mesoscopic ideal gas in the critical region. I present an exactly solvable Gaussian model of BEC in a degenerate interacting gas and its solution that confirms the universality and constraint-cut-off origin of the strongly non-Gaussian BEC statistics. I consider a two-energy-level trap with arbitrary degeneracy of an upper level and find an analytical solution for the condensate statistics in a mesoscopic ideal gas. I show how to model BEC in real traps by BEC in the two-level or three-level traps. I study wave propagation in the open oversized planar Bragg waveguides, in particular, in a planar metal waveguide with corrugation. I show that a step perturbation in a corrugation phase provides a high selectivity over transverse modes. I present a new Free Electron Laser (FEL) amplifier scheme, in which the radiation is guided by the planar Bragg structure with slightly corrugated walls and a sheet electron beam is traveling at a significant angle to the waveguide axis. By means of nonlinear analysis, I demonstrate that the proposed scheme provides an effective mode filtration and control over the structure of the output radiation and allows one to achieve amplification up to 30 dB in the existing FEL machines.

The low-energy properties of quantum dot systems are dominated by the Kondo effect. We study the dependence of the characteristic energy scale of the effect, the Kondo temperature, on the gate voltage, which controls the number of electrons in the strongly blockaded dot. We show that in order to obtain the correct Kondo temperature as a function of the gate voltage, it is crucial to take into account the presence of many energy levels in the dot. The dependence turns out to be very different from that in the conventional single-level Anderson impurity model. Unlike in the latter, the Kondo temperature cannot be characterized by a single parameter, such as the ratio of the tunneling-induced width of the energy levels in the dot and the charging energy.

The advent of microfluidic technology presents many difficulties but also many opportunities for separation science. Leveraging the potential of micro- and nanofluidic geometries is not only a matter of shrinking systems. Miniaturization can shift the relative importance of physical phenomena leading to separation. Theoretical and computational studies into the consequences of miniaturization are vital. Mesoscopic, multi-particle collision dynamics simulations are performed on polyelectrolytes and hard, colloidal solutes. Multiple variations of this simulation algorithm are implemented to achieve versatility for simulating non-equilibrium flows and dispersed solutes. The algorithm is extended to simulate the effects of finite Debye layers on the electro-hydrodynamics of electrophoresing macromolecules and used to study the electrophoresis of charged oligomers, polyelectrolytes and polyampholytes in both free-solution and confined geometries. Multi-particle collision dynamics simulations of hydrodynamic chromatography and field-flow fractionation are also performed to test the predictions of the derived unified, ideal retention theory. This unified, ideal retention predicts the transitions between multiple operational modes, including Faxén-mode FFF. Simulations and the theory show that increases in drag due to hydrodynamic interactions with microfluidic channel walls perturb the retention curves from the ideal predictions at large particle sizes. Further complications to field-flow fractionation including undesirable forces perpendicular to the flow direction, slip at channel walls and rectangular channel geometries are investigated. These theoretical studies lead to the proposal of several novel fractionation techniques, namely adverse-mode FFF, slip-mode FFF and polymer/depletant HC.

The purpose of this thesis is to report a theoretical investigation on the current-current correlation and noise in the tmnsient quantum transport regime. In particular, we calculate current correlations when the bias voltage of a LDL quantum device is suddenly turned off. Namely, we consider the situation that when time t < 0 the device is in a steady-state under bias Vb, when t > 0 the bias is turned off to zero. Under such a bias, the transport current l goes from a finite steady-state value 10 at t < 0 to zero at large times. When electronic structure of the leads as well as well as the device scattering region are to be taken into account, it is a difficult problem to calculate the time dependent current-current correlation. However, for the sharp step-down bias shape, we discover that the time-dependent problem can be solved exactly for non-interacting systems.

This thesis deals with electron correlation effects within low-dimensional, mesoscopic systems. We study phenomena within two different types of system in which correlations play an important role. The first involves the spectra and spin structure of small symmetric quantum dots, or &quoteartificial atoms&quote. The second is the &quote0.7 structure&quote, a well-known but mysterious anomalous conductance plateau which occurs in the conductance profile of a quantum point contact. Artificial atoms are manufactured mesoscopic devices: quantum dots which resemble real atoms in that their symmetry gives them a &quoteshell structure&quote. We examine two-dimensional circular artificial atoms numerically, using restricted and unrestricted Hartree-Fock simulation. We go beyond the mean-field approximation by direct calculation of second-order correlation terms; a method which works well for real atoms but to our knowledge has not been used before for quantum dots. We examine the spectra and spin structure of such dots and find, contrary to previous theoretical mean-field studies, that Hund's rule is not followed. We also find, in agreement with previous numerical studies, that the shell structure is fragile with respect to a simple elliptical deformation. The 0.7 structure appears in the conductance of a quantum point contact. The conductance through a ballistic quantum point contact is quantised in units of 2e^2/h. On the lowest conductance step, an anomalous narrow conductance plateau at about G = 0.7 x 2e^2/h is known to exist, which cannot be explained in the non-interacting picture. Based on suggestive numerical results, we model conductance through the lowest channel of a quantum point contact analytically. The model is based on the screening of the electron-electron interaction outside the QPC, and our observation that the wavefunctions at the Fermi level are peaked within the QPC. We use a kinetic equation approach, with perturbative account of electron-electron backscattering, to demonstrate that these simple features lead to the existence of a 0.7-like structure in the conductance. The behaviour of this structure reproduces experimentally observed features of the 0.7 structure, including the temperature dependence and the behaviour under applied in-plane magnetic fields.