Test particle motion in a Lorentz gas

This is a two-part thesis concerning the motion of a test particle in a bath. In part one we use an expansion of the operator PLe^it(1-P)LLP to shape the Zwanzig equation into a generalized Fokker-Planck equation which involves a diffusion tensor depending on the test particle's momentum and the time.

In part two the resultant equation is studied in some detail for the case of test particle motion in a weakly coupled Lorentz Gas. The diffusion tensor for this system is considered. Some of its properties are calculated; it is computed explicitly for the case of a Gaussian potential of interaction.

The equation for the test particle distribution function can be put into the form of an inhomogeneous Schroedinger equation. The term corresponding to the potential energy in the Schroedinger equation is considered. Its structure is studied, and some of its simplest features are used to find the Green's function in the limiting situations of low density and long time.

Suspension mechanics: I. Inertial and non-Newtonian migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows; II. The effect of viscoelasticity on the creeping motion of a train of neutrally buoyant Newtonian drops through a circular tube

The lateral migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows was studied theoretically. The cases of both inertia-induced migration in a Newtonian fluid and normal stress-induced migration in a second-order fluid were considered. Analytical results for the lateral velocities were obtained, and the equilibrium positions and trajectories of the spheres compared favorably with the experimental data available in the literature. The effective viscosity was obtained for a dilute suspension of spheres which were simultaneously undergoing inertia-induced migration and translational Brownian motion in a plane Poiseuille flow. The migration of spheres suspended in a second-order fluid inside a screw extruder was also considered.

The creeping motion of neutrally buoyant concentrically located Newtonian drops through a circular tube was studied experimentally for drops which have an undeformed radius comparable to that of the tube. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop due to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow were obtained for various viscosity ratios, total flow rates, and drop sizes. The results were compared with existing theoretical and experimental data.

Horizontal Bloch line motion in magnetic bubble materials

The purpose of this work is to extend experimental and theoretical understanding of horizontal Bloch line (HBL) motion in magnetic bubble materials. The present theory of HBL motion is reviewed, and then extended to include transient effects in which the internal domain wall structure changes with time. This is accomplished by numerically solving the equations of motion for the internal azimuthal angle ɸ and the wall position q as functions of z, the coordinate perpendicular to the thin-film material, and time. The effects of HBL's on domain wall motion are investigated by comparing results from wall oscillation experiments with those from the theory. In these experiments, a bias field pulse is used to make a step change in equilibrium position of either bubble or stripe domain walls, and the wall response is measured by using transient photography. During the initial response, the dynamic wall structure closely resembles the initial static structure. The wall accelerates to a relatively high velocity (≈20 m/sec), resulting in a short (≈22 nsec ) section of initial rapid motion. An HBL gradually forms near one of the film surfaces as a result of local dynamic properties, and moves along the wall surface toward the film center. The presence of this structure produces low-frequency, triangular-shaped oscillations in which the experimental wall velocity is nearly constant, v_s≈ 5-8 m/sec. If the HBL reaches the opposite surface, i.e., if the average internal angle reaches an integer multiple of π, the momentum stored in the HBL is lost, and the wall chirality is reversed. This results in abrupt transitions to overdamped motion and changes in wall chirality, which are observed as a function of bias pulse amplitude. The pulse amplitude at which the n^th punch- through occurs just as the wall reaches equilibrium is given within 0.2 0e by H_n = (2v_sH'/γ)^1/2 • (nπ)^1/2 + H_sv), where H' is the effective field gradient from the surrounding domains, and H_sv is a small (less than 0.03 0e), effective drag field. Observations of wall oscillation in the presence of in-plane fields parallel to the wall show that HBL formation is suppressed by fields greater than about 40 0e (≈2πM_s), resulting in the high-frequency, sinusoidal oscillations associated with a simple internal wall structure.

Quantum squeezing of motion in a mechanical resonator

Quantum mechanics places limits on the minimum energy of a harmonic oscillator via the ever-present "zero-point" fluctuations of the quantum ground state. Through squeezing, however, it is possible to decrease the noise of a single motional quadrature below the zero-point level as long as noise is added to the orthogonal quadrature. While squeezing below the quantum noise level was achieved decades ago with light, quantum squeezing of the motion of a mechanical resonator is a more difficult prospect due to the large thermal occupations of megahertz-frequency mechanical devices even at typical dilution refrigerator temperatures of ~ 10 mK.

Kronwald, Marquardt, and Clerk (2013) propose a method of squeezing a single quadrature of mechanical motion below the level of its zero-point fluctuations, even when the mechanics starts out with a large thermal occupation. The scheme operates under the framework of cavity optomechanics, where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion. In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in Kronwald et. al. to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies.

In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al.. We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1.09 +/- 0.06 times the quantum zero-point motion.

In the second experiment, we measure the spectral noise of the microwave cavity in the presence of the squeezing tones and fit a full model to the spectrum in order to deduce a quadrature variance of 0.80 +/- 0.03 times the zero-point level. These measurements provide the first evidence of quantum squeezing of motion in a mechanical resonator.