This dissertation introduces some new properties of both superfluid phases of fermions with spin-orbit coupling (SOC) and superradiant phases of photons in an optical cavity. The effects of SOC on the phase transition between normal and superfluid phase are revealed; an unconventional crossover driven by SOC from the Bardeen-Cooper-Schrieffer (BCS) state to the Bose-Einstein condensate (BEC) state is verified in three different systems; and two kinds of excitations, a Goldstone mode and a Higgs mode, are demonstrated to occur in a quantum optical system. We investigate the BCS superfluid state of two-component atomic Fermi gases in the presence of three kinds of SOCs. We find that SOC drives a class of BCS to BEC crossover that is different from the conventional one without SOC. Here, we extend the concepts of the coherence length and Cooper-pair size in the absence of SOC to Fermi systems with SOC. We study the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length in three dimensions (3D) (or the twobody binding energy in two dimensions (2D)) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC respectively. By adding a population imbalance to a Fermi gas with Rashba-type SOC, we also map out the finite-temperature phase diagram. Due to a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large variety of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. We find that the tricritical point moves toward a regime of low temperature, high magnetic field, and high polarization as the SOC strength increases. Besides Fermi fluids, this dissertation also gives a new angle of view on the superradiant phase in the Dicke model. Here, we demonstrate that Goldstone and Higgs modes can be observed in an optical system with only a few atoms inside a cavity. The model we study is the U(1)/Z2 Dicke model with N qubits (two-level atoms) coupled to a single photon mode.

<p>The dissolved concentration of an active pharmaceutical ingredient in biological fluids is of significant importance for establishing a therapeutic effect in patients. However, the current pharmaceutical landscape is abundant in poorly soluble drugs that require solubility enhancing techniques to enable their administration. A promising technique, with increasing commercial success, is to molecularly mix drug and polymer to create an amorphous solid dispersion (ASD). While these mixtures provide enhanced drug solubility and dissolution in aqueous solutions, the mechanistic processes by which they release drug into solution are not well understood. Some unexplained behaviors include rapid drug release even at the maximum supersaturated concentration and spontaneous formation of drug-rich nanoparticles. These are beneficial for rapidly achieving and maintaining a highly supersaturated drug concentration during absorption, if crystallization is inhibited. However, the phenomena occur at typically low drug loading and are abruptly lost above a certain threshold termed the ‘limit of congruency’ (LoC), which has been reported to vary based on the drug-polymer system. In this research, the mechanisms underpinning ASD release at low and high drug loading were studied, and the factors affecting LoC were mechanistically explored by performing dissolution experiments and utilizing imaging, separation, thermal analysis, and spectroscopy methods to characterize the materials in the presence and absence of water. The results show that ASDs developed a gel layer on the surface when exposed to aqueous solution. This water-rich environment was thermodynamically unstable and phase separated into hydrophilic and hydrophobic phases. The morphology of the hydrophobic phase was directly related to the ASD release behavior, where ASDs below the LoC exhibited a dispersed and stable hydrophobic phase morphology, and ASDs above the LoC displayed a continuous or aggregated morphology. In cases where thermodynamic factors were rate limiting, LoC was inferred from features on the ternary phase diagram. Moreover, drug-polymer interactions and polymer molecular weight were demonstrated to affect the morphology of the hydrophobic phase and ultimately the LoC. The conclusions from this work provide the basis of a theoretical framework for rationally designing ASDs and optimizing their release. </p>

Curcumin is the major phenolic diarylheptane derivative in Curcuma longa and has been reported to possess pharmacological activities. Unfortunately this compound suffers from poor bioavailability and rapid neutral-alkaline degradation. Co-crystal of curcumin is one option under exploration, motivated by the fact that a number of active pharmaceutical ingredient (API) co-crystals with improved dissolution have recently been synthesized. Hence, co-crystallization technique highlights an alternative means to improve the performance of curcumin. Within our work evidences for a co-crystal was ascertained from DSC, Kofler hot stage screening and PXRD, and all confirmed a new crystal phase could have been formed between curcumin and a co-crystallizing agent, nicotinamide. We report that re-crystallization step essentially aids the purification of commercial curcumin, a herbal based actives. Otherwise the prevalence of a new crystal phase in solvent-mediated co-crystallization will be significantly reduced. Besides, phase diagram is an effective tool for the study of solubility behaviours in co-crystal system. In order to acquire related techniques, fenbufen, a poorly water soluble drug, was selected. The result showed the huge difference in solubility between fenbufen and nicotinamide lead to difficulty in the construction of phase diagram.

There has been very little research into the bioanalytical application of Microemulsion High Performance Liquid Chromatography (MELC), a recently established technique for separating an active pharmaceutical ingredient from its related substances and for determining the quantity of active drug in a dose. Also, the technique is not good at separating hydrophilic drugs of very similar chemical structures. Different phase diagrams of oil (octane or ethyl acetate), co-surfactant (butanol), surfactant (sodium dodecyl sulphate (SDS) or Brij-35) and buffer (Phosphate pH 3) were developed and several nanoemulsion mobile phases identified. Nanoemulsion mobile phase that is, prepared with SDS, octane, butanol and a phosphate buffer, failed to separate hydrophilic compounds with a very close chemical structure, such as terbutaline and salbutamol. A nanoemulsion mobile phase containing a non-ionic surfactant (Brij-35) with ethyl acetate, butanol and a phosphate buffer, was, however, successful in achieving a base line separation, and the method was validated for simultaneous determination of terbutaline and salbutamol in aqueous and urine samples. An oil-in-water (O/W) NELC method was developed and validated for the determination of formoterol in an Oxis® Turbuhaler® using pre-column fluorescence derivatisation. Although the same mobile phase was extended for separation of formoterol in urine, the formoterol peak¿s overlap with endogenous peaks meant that fluorescence detection could not determine formoterol in urine samples. Solid phase extraction, concentrating the final analyte 40 times, enabled determination of a low concentration of formoterol in urine samples by UV detection. The method was validated and an acceptable assay precision %CV <4.89 inter-day and %CV <2.33 intra-day was achieved. Then after the application of O/W nanoemulsion mobile phase for HPLC was extended for the separation of lipophilic drugs. The nanoemulsion liquid chromatography (NELC) method was optimised for the determination of salmeterol and fluticasone propionate in good validation data was achieved. This thesis shows that, in general, the performance of O/W NELC is superior to that of conventional High Performance Liquid Chromatography (HPLC) for the analysis of both hydrophilic and lipophilic drugs in inhaled dosage formulations and urine samples. It has been shown that NELC uses cheaper solvents and that analysis time is faster for aqueous and urine samples. This considerable saving in both cost and time will potentially improve efficiency within quality control.

Crystal Engineering is the design of crystalline material using non-covalent synthesis. Co-crystals are multi-component crystals which are constructed from complementary intermolecular interactions, they are also known as supramolecular complexes. Design of such materials utilises the synthon approach, this involves the understanding of common intermolecular interactions which occur in the crystal packing and is used to design new solids with desired physical properties and chemical properties. Primary amides form supramolecular heterosynthons, these synthons represent an opportunity for a design of multi-component crystals in which one molecule contains a primary amide and a second molecule which is complimentary to the primary amide, usually carboxylic acids. The progress with regards to the screening process for the determination of co-crystals is evident in the literature, In particular, high throughput solution growth methods and solvent drop grinding. The comparison of Isonicotinamide and Benzamide as a co-crystal component has been presented. This study was motivated by the observation that the CSD contains 24 Isonicotinamide and 1 Benzamide co-crystal. The interaction with carboxylic acids is the focus of the work, in particular those which form Isonicotinamide co-crystal are being screened with Benzamide. Our work utilises a ReactArray Microvate to carry out the low throughput solution growth on a matrix of carboxylic acid with Benzamide, this study has been coupled with the Kofler hot stage microscope method which visually aids to screen and view co-crystal phase formation. Crystallisation screens have resulted in the identification of known co-crystal phases of Isonicotinamide and Benzamide, additionally new co-crystal phases have also been identified with Fumaric, 3-hydroxybenzoic acid, Mandelic Acid, 4-Nitrobenzoic Acid and Tartaric Acid. Single crystal structures of the Fumaric and 4-Nitrobenzoic acid have been obtained. In order to develop an understanding of co-crystal formation in Isonicotinamide and Benzamide with our supramolecular library, packing landscape analysis is being undertaken using both the CSD and crystal structures we have obtained. This is undertaken as collaboration with Dr Andy Parkin and Professor Gilmore (University of Glasgow), we have identified that the dSNAP analysis is a way forward for the analysis of how co-crystals pack. The analysis highlighted the subtleties that were present in the packing motifs of the Isonicotinamide co-crystals. In particular the cis and trans orientation of the amide and acid carbonyl to each other and the planar and off planar layer assemblies. All of which are required to maximise the hydrogen bond usage of the components comprising the co-crystals. Further investigations have led to the collaborative project with Syngenta Ltd in the design of a co-crystal screen using a high through-put robot, Crissy® -Automation Platform by Zinsser Analytical, using an extended screen of 16 acid coformers with Isonicotinamide, Benzamide and Nicotinamide the sample have been characterised using a reflectance diffraction method, GADDS. Further analysis of this data involves the use of polySNAP, which has led to further collaboration with Professor Gilmore¿s group. / Syngenta

Phase transitions are fundamental phenomena in (quantum) many-body systems. They are associated with changes in the macroscopic physical properties of the system in response to the alteration in the conditions controlled by one or more parameters, like temperature or coupling constants. Quantum phase transitions are particularly intriguing as they reveal new insights into the fundamental nature of matter and the laws of physics. The study of phase transitions in such systems is crucial in aiding our understanding of how materials behave in extreme conditions, which are difficult to replicate in laboratory, and also the behavior of exotic states of matter with unique and potentially useful properties like superconductors and superfluids. Moreover, this understanding has other practical applications and can lead to the development of new materials with specific properties or more efficient technologies, such as quantum computers. Hence, detecting the transition point from one phase of matter to another and constructing the corresponding phase diagram is of great importance for examining many-body systems and predicting their response to external perturbations. Traditionally, phase transitions have been identified either through analytical methods like mean field theory or numerical simulations. The pinpointing of the critical value normally involves the measure of specific quantities such as local observables, correlation functions, energy gaps, etc. reflecting the changes in the physics through the transition. However, the latter approach requires prior knowledge of the system to calculate the order parameter of the transition, which is uniquely associated to its universality class. Recently, another method has gained more and more attention in the physics community. By using raw and very general representative data of the system, one can resort to machine learning techniques to distinguish among patterns within the data belonging to different phases. The relevance of these techniques is rooted in the ability of a properly trained machine to efficiently process complex data for the sake of pursuing classification tasks, pattern recognition, generating brand new data and even developing decision processes. The aim of this thesis is to explore phase transitions from this new and promising data-centric perspective. On the one hand, our work is focused on the developement of new machine learning architectures using state-of-the-art and interpretable models. On the other hand, we are interested in the study of the various possible data which can be fed to the artificial intelligence model for the mapping of a quantum many-body system phase diagram. Our analysis is supported by numerical examples obtained via matrix-product-states (MPS) simulations for several one-dimensional zero-temperature systems on a lattice such as the XXZ model, the Extended Bose-Hubbard model (EBH) and the two-species Bose Hubbard model (BH2S). In Part I, we provide a general introduction to the background concepts for the understanding of the physics and the numerical methods used for the simulations and the analysis with deep learning. In Part II, we first present the models of the quantum many-body systems that we study. Then, we discuss the machine learning protocol to identify phase transitions, namely anomaly detection technique, that involves the training of a model on a dataset of normal behavior and use it to recognize deviations from this behavior on test data. The latter can be applied for our purpose by training in a known phase so that, at test-time, all the other phases of the system are marked as anomalies. Our method is based on Generative Adversarial Networks (GANs) and improves the networks adopted by the previous works in the literature for the anomaly detection scheme taking advantage of the adversarial training procedure. Specifically, we train the GAN on a dataset composed of bipartite entanglement spectra (ES) obtained from Tensor Network simulations for the three aforementioned quantum systems. We focus our study on the detection of the elusive Berezinskii-Kosterlitz-Thouless (BKT) transition that have been object of intense theoretical and experimental studies since its first prediction for the classical two-dimensional XY model. The absence of an explicit symmetry breaking and its gappless-to-gapped nature which characterize such a transition make the latter very subtle to be detected, hence providing a challenging testing ground for the machine-driven method. We train the GAN architecture on the ES data in the gapless side of BKT transition and we show that the GAN is able to automatically distinguish between data from the same phase and beyond the BKT. The protocol that we develop is not supposed to become a substitute to the traditional methods for the phase transitions detection but allows to obtain a qualitative map of a phase diagram with almost no prior knowledge about the nature and the arrangement of the phases -- in this sense we refer to it as agnostic -- in an automatic fashion. Furthermore, it is very general and it can be applied in principle to all kind of representative data of the system coming both from experiments and numerics, as long as they have different patterns (even hidden to the eye) in different phases. Since the kind of data is crucially linked with the success of the detection, together with the ES we investigate another candidate: the probability density function (PDF) of a globally U(1) conserved charge in an extensive sub-portion of the system. The full PDF is one of the possible reductions of the ES which is known to exhibit relations and degeneracies reflecting very peculiar aspects of the physics and the symmetries of the system. Its patterns are often used to tell different kinds of phases apart and embed information about non-local quantum correlations. However, the PDF is measurable, e.g. in quantum gas microscopes experiments, and it is quite general so that it can be considered not only in the cases of the study but also in other systems with different symmetries and dimensionalities. Both the ES and the PDF can be extracted from the simulation of the ground state by dividing the one-dimensional chain into two complementary subportions. For the EBH we calculate the PDF of the bosonic occupation number in a wide range of values of the couplings and we are able to reproduce the very rich phase diagram containing several phases (superfluid, Mott insulator, charge density wave, phase separation of supersolid and superfluid and the topological Haldane insulator) just with an educated gaussian fit of the PDF. Even without resorting to machine learning, this analysis is instrumental to show the importance of the experimentally accessible PDF for the task. Moreover, we highlight some of its properties according to the gapless and gapped nature of the ground state which require a further investigation and extension beyond zero-temperature regimes and one-dimensional systems. The last chapter of the results contains the description of another architecture, namely the Concrete Autoencoder (CAE) which can be used for detecting phase transitions with the anomaly detection scheme while being able to automatically learn what the most relevant components of the input data are. We show that the CAE can recognize the important eigenvalues out of the entire ES for the EBH model in order to characterize the gapless phase. Therefore the latter architecture can be used to provide not only a more compact version of the input data (dimensionality reduction) -- which can improve the training -- but also some meaningful insights in the spirit of machine learning interpretability. In conclusion, in this thesis we describe two advances in the solution to the problem of phase recognition in quantum many-body systems. On one side, we improve the literature standard anomaly detection protocol for an automatic and agnostic identification of the phases by employing the GAN network. Moreover, we implement and test an explainable model which can make the interpretation of the results easier. On the other side we put the focus on the PDF as a new candidate quantity for the scope of discerning phases of matter. We show that it contains a lot of information about the many-body state being very general and experimentally accessible.

No description available.

No description available.

No description available.

The work presented in this thesis was broadly focussed on the investigation of the magnetic behaviour of different superconducting materials in the form of bulk (singe crystals and pellets) and thin films (nanomagnetic devices like superconducting spin valves etc). Neutrons and muons were extensively used to probe the structural and magnetic behaviour of these systems at the nanoscale along with bulk characterisation techniques like high-sensitive magnetic property measurements, scanning probe microscopy and magneto-transport measurements etc. The nanoscale interplay of Superconductivity and Ferromagnetism was studied in the thin film structures using a combination of Polarised Neutron Reflectivity (PNR) and Low Energy Muon Spin Rotation (LE-µSR) techniques while bulk Muon Spin Rotation (µSR) technique was used for microscopic magnetic investigation in the bulk materials. In the Fe/Pb heterostructure, evidence of the Proximity Effect was observed in the form of an enhancement of the superconducting penetration depth (λs) with an increase in the ferromagnetic layer thickness (dF) in both the bilayered and the trilayered structures. The existence of an Inverted Magnetic Region was also detected at the Ferromagnet-Superconductor (F/S) interface in the normal state possibly originating from the induced spin polarisation within the Pb layer in the presence of the neighbouring Fe layer(s). The spatial size (height and width) of the Inverted Magnetic Region did not change much while cooling the sample below the superconducting transition temperature(Tc)and it also stayed unaffected by an increase in the Fe layer thickness and by a change of the applied magnetic field. In the superconducting spin valve structure containing Permalloy (Py) as ferromagnetic layer and Nb as the superconducting layer, LE-µSR measurements revealed the evidence of the decay of magnetic flux density (as a function of thickness) within the Nb layer symmetrically from the Py/Nb interfaces towards the centre of the Nb layer in the normal state. The thickness dependent magnetisation decay occurred over two characteristic length scales in the normal state that stayed of similar values in the superconducting state also. In the superconducting state, an additional contribution towards the magnetisation was found in the vicinity of the Py/Nb interfaces possibly originating from the spin polarisation of the singlet Cooper pairs in these areas. The nanoscale magnetic investigation on a highly engineered F/S/F structure (where each of the F blocks made of multiple Co/Pd layers with magnetic moments aligned perpendicular to the plane of these layers and neighbouring magnetic blocks separated by Ru layers giving rise to antiferromagnetic alignment) using LE-µSR showed an antisymmetric thickness dependent magnetic flux density profile with two characteristic length scales. In the superconducting state, the magnetic flux density profile got modified within the superconducting Nb₆₇Ti₃₃ layer near the F/S interfaces in a way similar to that of observed in the case of Py/Nb system, most likely because of the spin polarisation of the superconducting electron pairs. The vortex magnetic phase diagram of Bi₂Sr₂Ca₂Cu₃O10-δ was studied using the Muon Spin Rotation (µSR) technique to explore the effects of vortex lattice melting and rearrangements for vortex transitions and crossover as a function of magnetic field and temperatures. At low magnetic fields, the flux vortices undergo a first order melting transition from a vortex lattice to a vortex liquid state with increasing temperature while another transition also occurred with increasing field at fixed temperature to a vortex glass phase at the lowest temperatures. Evidence of a frozen liquid phase was found in the intermediate field region at low temperature in the form of a lagoon in the superconducting vortex state which is in agreement with earlier observations made in BiSCCO-2212. The magnetic behaviour of the unconventional superconductor Sr₂RuO₄ was investigated using µSR to find the evidence of normal state magnetism and the nature of the vortex state. In the normal state, a weak hysteretic magnetic signal was detected over a wide temperature and field range believed to be supporting the evidence of a chiral order parameter. The nature of the vortex lattice structure was obtained in different parts of the magnetic phase diagram and the evidence of magnetic field driven transition in the lattice structure was detected from a Triangular→Square structure while the vortex lattice stayed Triangular over the entire temperature region below Tc at low fields with a disappearance of pinning at higher temperatures.