Disordered elastic systems: Fluctuations and AC-dynamics

Disordered elastic systems are studied in the quantum, classical, and dynamic regime in the present thesis. The thesis consists of two main parts: In the first part we study the low temperature phase diagram of one-dimensional weakly disordered quantum systems like charge or spin density waves and Luttinger liquids by a full finite temperature renormalization group (RG) calculation. In the classical region, for vanishing quantum fluctuations those results are supplemented by an exact solution of the model in the case of strong disorder, described by the ground state and the correlation function. Furthermore, by a mapping of the problem onto a Burgers equation with noise, in the case of weak disorder, we can derive an expression for the correlation length. At zero temperature we reproduce the (quantum) phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At finite temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram determined by the correlation functions. In particular we find four different scaling regions: a classical disordered, a quantum disordered, a quantum critical, and a thermal region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential, and for the case of density waves we discuss the influence of quantum phase-slips, which might lead to a new scenario for the unpinning (delocalization) transition at zero temperature. Additionally, we analyze the current noise in a classical one-dimensional charge density wave system in the weak pinning regime by solving the overdamped equation of motion numerically. At low temperatures and just above the zero temperature depinning threshold, the power spectrum of the current noise reveals the existence of 1/f or flicker noise. Our results are in agreement with experimental measurements in quasi-one-dimensional charge density wave systems. In part two, we examine the viscous motion of an interface driven by a periodically oscillating external field in a random medium. The velocity exhibits a smeared depinning transition showing a pronounced hysteresis, which is absent in the adiabatic case. Its width is determined by a new length scale, introduced by the frequency of the external drive and - in the low frequency regime - by the critical exponents of the zero frequency depinning transition. Scaling arguments and an approximate renormalization group treatment predict a power law behavior of the velocity as a function of frequency and field amplitude at the dc depinning threshold, which is confirmed numerically. Thermal fluctuations lead to an additional smearing of the transition. If the amplitude of the external driving force is smaller than the depinning field, the motion of the interface by avalanches has to be taken into account in order to describe the velocity hysteresis. To check the validity of our model with respect to experimental results, we calculate the complex susceptibilities using an adiabatic and non-adiabatic approach numerically for finite systems and compare it to measurements of a superferromagnetic granular multilayer system and find that the model of an ac driven interface in a disordered environment can describe the main features of the experimental results. Additionally, the influence of a strong surface potential on the critical depinning of an elastic system, driven in a random medium is considered. If the surface potential prevents depinning completely, the curvature of the displacement profile at zero temperature exhibits a pronounced rhombic hysteresis curve with width of two times the (bulk) depinning field. The hysteresis disappears at non-zero temperatures if the driving force is changed adiabatically. If the surface depinns by the applied force or thermal creep, the curvature is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, flux-line lattices, and charge-density waves. As addendum we examine low dimensional interacting, but clean Bose systems at low temperatures. The interaction leads to scattering events of the over-condensate particles for which we calculate the scattering times using Fermi's golden rule. With that we derive the thermal conductivity and the related weak localization corrections. This is done for short and long-range interactions

Displacement Profile of Charge Density Waves and Domain Walls at Critical Depinning

The influence of a strong surface potential on the critical depinning of an elastic system driven in a random medium is considered. If the surface potential prevents depinning completely the elastic system shows a parabolic displacement profile. Its curvature $\mathcal{C}$ exhibits at zero temperature a pronounced rhombic hysteresis curve of width $2f_c$ with the bulk depinning threshold $f_c$. The hysteresis disappears at non-zero temperatures if the driving force is changed adiabatically. If the surface depins by the applied force or thermal creep, $\mathcal{C}$ is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, flux-line lattices and charge-density waves.Comment: 4 pages, 2 figure

The influence of plasma treatment on the elasticity of the in situ oxidized gradient layer in PDMS: towards crack-free wrinkling

Controlled surface wrinkling is widely applied for structuring surfaces in the micro- and nano-range. The formation of cracks in the wrinkling process is however limiting applications, and developing approaches towards crack-free wrinkles is therefore vital. To understand crack-formation, we systematically characterized the thickness and mechanics of thin layers formed by O2-plasma-oxidation of polydimethyl siloxane (PDMS) as a function of plasma power and pressure using Atomic Force Microscopy Quantitative Nano-mechanical Mapping (AFM-QNM). We found a nearly constant layer thickness with simultaneously changing Young's moduli for both power and pressure screenings. We determined the respective crack densities, revealing conditions for crack-free wrinkling. Thus we could identify correlations between the intensity of plasma treatment and the cracking behavior. The primary cause for crack-suppression is a continuous elasticity gradient starting within the soft bulk PDMS, and rising up to several hundred MPa at the oxidized layer's surface. With mechanical simulations via the Finite Elements Method (FEM) we were able to demonstrate a noticeable difference in maximal stress intensity σmax between a comparable, but theoretical single layer and a gradient interface. A threshold in tensile stress of σcrit = 14 MPa distinguishes between intact and cracked layers

Characterisation and segmentation of basal ganglia mineralization in normal ageing with multimodal structural MRI

Iron is the most abundant trace metal in the brain and is essential for many biological processes, such as neurotransmitter synthesis and myelin formation. This thesis investigates small, multifocal hypointensities that are apparent on T2*- weighted (T2*w) MRI in the basal ganglia, where presumably most iron enters the brain via the blood-brain-barrier along the penetrating arteries. These basal ganglia T2*w hypointensities are believed to arise from iron-rich microvascular mineral deposits, which are frequently found in community-dwelling elderly subjects and are associated with age-related cognitive decline. This thesis documents the characteristic spatial distribution and morphology of basal ganglia T2*w hypointensities of 98 community-dwelling, elderly subjects in their seventies, as well as their imaging signatures on T1-weighted (T1w) and T2- weighted (T2w) MRI. A fully automated, novel method is introduced for the segmentation of basal ganglia T2*w hypointensities, which was developed to reduce the high intra- and inter-rater variability associated with current semi-automated segmentation methods and to facilitate the segmentation of these features in other single- and multi-centre studies. This thesis also presents a multi parametric quantitative MRI relaxometry methodology for conventional clinical MRI scanners that was developed and validated to improve the characterisation of brain iron. Lastly, this thesis describes the application of the developed methods in the segmentation of basal ganglia T2*w hypointensities of 243 community-dwelling participants of the Austrian Stroke Prevention Study Family (ASPS-Fam) and their analysis on R2* (=1/T2*) relaxation rate and Larmor frequency shift maps. This work confirms that basal ganglia T2*w hypointensities, especially in the globus pallidus, are potentially MRI markers of microvascular mineralization. Furthermore, the ASPS-Fam results show that basal ganglia mineral deposits mainly consist of paramagnetic particles, which presumably arise from an imbalance in the brain iron homeostasis. Hence, basal ganglia T2*w hypointensities are possibly an indicator of age-related microvascular dysfunction with iron accumulation, which might help to explain the variability of cognitive decline in normal ageing