Dark solitons in holographic superfluids

We construct dark soliton solutions in a holographic model of a relativistic superfluid. We study the length scales associated with the condensate and the charge density depletion, and find that the two scales differ by a non-trivial function of the chemical potential. By adjusting the chemical potential, we study the variation of the depletion of charge density at the interface.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.

Corneal recovery after uncomplicated and complicated PRK and LASIK

Refractive errors, especially myopia, seem to increase worldwide. Concurrently, the number of surgical refractive corrections has increased rapidly, with several million procedures performed annually. However, excimer laser surgery was introduced after a limited number of studies done with animals and to date there still are only few long-term follow-up studies of the results. The present thesis aims to evaluate the safety and functional outcome of, as well as to quantify the cellular changes and remodelling in the human cornea after, photorefractive keratectomy (PRK) and laser assisted in situ keratomileusis (LASIK). These procedures are the two most common laser surgical refractive methods. In Study I, myopic ophthalmic residents at Helsinki University Eye Hospital underwent a refractive correction by PRK. Five patients were followed up for 6 months to assess their subjective experience in hospital work and their performance in car driving simulator and in other visuomotor functions. Corneal morphological changes were assessed by in vivo confocal microscopy (ivCM). Study II comprised 14 patients who had undergone a PRK operation in 1993-1994. Visual acuity was examined and ivCM examinations performed 5 years postoperatively. In Study III 15 patients received LASIK refractive correction for moderate to high myopia (-6 - -12 D). Their corneal recovery was followed by ivCM for 2 years. Diffuse lamellar keratitis (DLK) is a common but variable complication of LASIK. Yet, its aetiology remains unknown. In Study IV we examined six patients who had developed DLK as a consequence of formation of an intraoperative or post-LASIK epithelial defect, to assess the corneal and conjunctival inflammatory reaction. In the whole series, the mean refractive correction was -6.46 diopters. The best spectacle corrected visual acuity (BSCVA) improved in 30 % of patients, whereas in four patients BSCVA decreased slightly. The mean achieved refraction was 0.35 D undercorrected. After PRK, the stromal scar formation was highest at 2 to 3 months postoperatively and subsequently decreased. At 5 years increased reflectivity in the subepithelial stroma was observed in all patients. Interestingly, no Bowman s layer was detected in any patient. Subbasal nerve fiber bundle(snfb) regeneration could be observed already at 2 months in 2 patients after PRK. After 5 years, all corneas presented with snfb, the density of which, however, was still lower than in control corneas. LASIK induced a hypocellular area on both sides of the flap interface. A decrease of the most anterior keratocyte density was also observed. In the corneas that developed DLK, inflammatory cell-type objects were present in the flap interface in half of the patients. The other patients presented only with keratocyte activation and highly reflective extracellular matrix. These changes resolved completely with medication and time. Snfb regeneration was first detected at one month post-LASIK, but still after two years the density of snfb, however, was only 64 % of the preoperative values. The performance of ophthalmological examinations and microsurgery without spectacles was easier postoperatively, which was appreciated by the residents. Both PRK and LASIK showed moderate to good accuracy and high safety. In terms of visual perception and subjective evaluation, few patients stated any complaints in the whole series of studies. Instead, the majority of patients experienced a marked improvement in everyday life and work performance. PRK and LASIK have shown similar results, with good long term morphological healing. It seems evident that, even without the benefit of over-20-year follow-up results, these procedures are sufficiently safe and accurate for refractive corrections and corneal reshaping.

Inhomogeneous Structures in Holographic Superfluids I

We begin an investigation of inhomogeneous structures in holographic superfluids. As a first example, we study domain wall like defects in the 3+1 dimensional Einstein-Maxwell-Higgs theory, which was developed as a dual model for a holographic superconductor. In [1], we reported on such "dark solitons" in holographic superfluids. In this work, we present an extensive numerical study of their properties, working in the probe limit. We construct dark solitons for two possible condensing operators, and find that both of them share common features with their standard superfluid counterparts. However, both are characterized by two distinct coherence length scales (one for order parameter, one for charge condensate). We study the relative charge depletion factor and find that solitons in the two different condensates have very distinct depletion characteristics. We also study quasiparticle excitations above the holographic superfluid, and find that the scale of the excitations is comparable to the soliton coherence length scales.

Excimer laser refractive surgery : corneal wound healing and clinical results

Although the first procedure in a seeing human eye using excimer laser was reported in 1988 (McDonald et al. 1989, O'Connor et al. 2006) just three studies (Kymionis et al. 2007, O'Connor et al. 2006, Rajan et al. 2004) with a follow-up over ten years had been published when this thesis was started. The present thesis aims to investigate 1) the long-term outcomes of excimer laser refractive surgery performed for myopia and/or astigmatism by photorefractive keratectomy (PRK) and laser-in situ- keratomileusis (LASIK), 2) the possible differences in postoperative outcomes and complications when moderate-to-high astigmatism is treated with PRK or LASIK, 3) the presence of irregular astigmatism that depend exclusively on the corneal epithelium, and 4) the role of corneal nerve recovery in corneal wound healing in PRK enhancement. Our results revealed that in long-term the number of eyes that achieved uncorrected visual acuity (UCVA)≤0.0 and ≤0.5 (logMAR) was higher after PRK than after LASIK. Postoperative stability was slightly better after PRK than after LASIK. In LASIK treated eyes the incidence of myopic regression was more pronounced when the intended correction was over >6.0 D and in patients aged <30 years.Yet the intended corrections in our study were higher for LASIK than for PRK eyes. No differences were found in percentages of eyes with best corrected visual acuity (BCVA) or loss of two or more lines of visual acuity between PRK and LASIK in the long-term. The postoperative long-term outcomes of PRK with two different delivery systems broad beam and scanning laser were compared and revealed no differences. Postoperative outcomes of moderate-to-high astigmatism yielded better results in terms of UCVA and less compromise or loss of two more lines of BCVA after LASIK that after PRK.Similar stability for both procedures was revealed. Vector analysis showed that LASIK outcomes tended to be more accurate than PRK outcomes, yet no statistically differences were found. Irregular astigmatism secondary to recurrent corneal erosion due to map-dot-fingerprint was successfully treated with phototherapeutic keratectomy (PTK). Preoperative videokeratographies (VK) showed irregular astigmatism. However, postoperatively, all eyes showed a regular pattern. No correlation was found between pre- and postoperative VK patterns. Postoperative outcomes of late PRK in eyes originally subjected to LASIK showed that all (7/7) eyes achieved UCVA ≤0.5 at last follow-up (range 3 — 11 months), and no eye lost lines of BCVA. Postoperatively all eyes developed and initial mild haze (0.5 — 1) into the first month. Yet, at last follow-up 5/7 eyes showed a haze of 0.5 and this was no longer evident in 2/7 eyes. Based on these results, we demonstrated that the long-term outcomes after PRK and LASIK were safe and efficient, with similar stability for both procedures. The PRK outcomes were similar when treated by broad-beam or scanning slit laser. LASIK was better than PRK to correct moderate-to-high astigmatism, yet both procedures showed a tendency of undercorrection. Irregular astigmatism was proven to be able to depend exclusively from the corneal epithelium. If this kind of astigmatism is present in the cornea and a customized PRK/LASIK correction is done based on wavefront measurements an irregular astigmatism may be produced rather than treated. Corneal sensory nerve recovery should have an important role in the modulation of the corneal wound healing and post-operative anterior stromal scarring. PRK enhancement may be an option in eyes with previous LASIK after a sufficient time interval that in at least 2 years.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.