This thesis consists of research work in the broad area of soft condensed matter theory with a focus on active matter. The study of long wavelength, low frequency collective behavior of active particles (bacterial suspensions, fish schools, motor-microtubule extracts, active gels) forms an interesting modification to liquid-crystal hydrodynamics, in which the constituent particles carry permanent stresses that stir the fluid. Activity introduces novel instabilities and many novel aspects emerge. Our works focus on the dynamics, order, fluctuations and instabilities in these systems. In particular, we investigated the dynamics, order and fluctuation properties emerging from effective hydrodynamic descriptions of translationally ordered active matter and also studied those in microwave-driven quantum Hall nematics. We also investigated the rheological properties of active suspensions subjected to an applied orienting field. A summary of the works carried out is as follows. Translationally ordered active phases – active smectics and active cholesterics: Active or self-propelled particles consume and dissipate energy generating permanent stresses that stir the fluid around them. The collective behavior of systems of active particles, in systems with translational order, pose interesting questions and possibilities of new physics that differ strikingly from those in systems at thermal equilibrium with the same spatial symmetry. We developed the hydrodynamic equations of motion for (a) an active system with spontaneously broken translational symmetry in one direction, i.e., smectic and (b) the simplest uniaxially ordered phase of active chiral objects, namely, an active cholesteric. We analyze the fluctuation properties as well as the nature of characteristic instabilities that these systems can display and make a number of predictions. For example, in the case of an active smectic, we show that active stresses generate an effective active layer tension which, if positive, sup-presses the Landau-Peierls effect, leading to long-range smectic order in dimension d =3 and quasi-long-range in d =2, in sharp contrast with thermal equilibrium systems. Negative active layer tension in bulk systems, however, lead to a spontaneous Helfrich-Hurault undulation instability of the layers, accompanied by spontaneous flow. Also, active smectics, unlike orientationally ordered active systems, normally have finite concentration fluctuations. Similarly, for the case of cholesterics we show that cholesteric elasticity intervenes to suppress some of the instabilities present in active nematics. xi Numerical simulation of active smectics: We present results from a Brownian Dynamics simulation, with no hydrodynamic interaction, of a system of apolar active particles form-ing translational liquid-crystalline order in a suspension. The particles interact through a prolate-ellipsoidal Gay-Berne potential. We model activity minimally through different noise temperatures for movement along and normal to the orientation axis of each particle. We present preliminary results on the disruptive effect of activity on smectic order for the parameter values investigated. Future work will test the predictions of our theory [1] on active smectics. Rheology of active suspensions near field-induced critical points : Shear induces orientation of active stresses in a suspension, through flow alignment. Depending on the sign, activity then either enhances or reduces the viscosity. The change in viscosity, in the zero frequency limit, is proportional to the product of the magnitude of active stress and the system relaxation time. A strong enough orienting field can make the system approach a critical point and the relaxation time diverges. We show that, this results in the divergence of viscosity at zero frequency making the system strongly viscoelastic. Depending on the sign, activity strengthens or reduces the effect of the field. We also investigate the rheological property of an active suspension with mixed polar and nematic oreder. Active quantum Hall systems: We construct the hydrodynamic theory for a 2d charged active nematic with 3d electrostatics. We have investigated the interplay of the Coulomb interaction and activity in these systems. We show that activity competes to enhance the charge density fluctuations normally suppressed by long-ranged Coulomb interactions. The charge structure factor Sq of the corresponding passive charged nematic goes to zero as q, whereas in charged active nematics, activity leads to a nonvanishing charge structure factor at small wavenumber. We also show how the effect of an applied magnetic field can be incorporated into the dynamics of the system and leave scope for further studies on these effects.

No description available.

<p>The pi-striped, <em>d</em>-wave superconducting (SC) state, which is a type of pair density wave wherein the SC order is spatially modulated, has recently been shown to generate the key ingredients for quantum oscillations consistent with experimental observations (Zelli <em>et al.</em>, 2011, 2012). This was accomplished with a phenomenological approach using non-self-consistent Bogoliubov-de Gennes (BdG) theory. The objective of this thesis is to explore two aspects of this approach: the addition of a charge density wave (CDW) order to the previous non-self-consistent calculations, and an attempt at stabilizing the pi-striped state in fully self-consistent BdG theory. It was found that the CDW order had a minimal effect on the Fermi surface characteristics of the pi-striped state, but that a sufficiently strong CDW degrades the Landau levels which are essential for the formation of quantum oscillations. The self-consistent mean-field calculations were unable to stabilize the pi-striped state under a range of modifications to the Hamiltonian. Free energy calculations with the modulated SC order treated as a parameter demonstrate that the pi-striped state is always less energetically favourable than the normal state for the scenarios which were considered. The results of this study constitute a basis for future, more comprehensive studies, using the BdG approach, of the stability of possible pi-striped SC phases.</p> / Master of Science (MSc)

In this thesis I discuss the nature of ‘measurement’ in quantum theory. ‘Measurement’ is associated with several different processes: the gradual imprinting of information about one system onto another, which is well understood; the collapse of the wavefunction, which is ill-defined and troublesome; and finally, the means by which inferences about unknown experimental parameters are made. I present a theoretical extension to an experimental proposal from Leggett and Garg, who suggested that the quantum-or-classical reality of a macroscopic system may be probed with successive measurements arrayed in time. The extension allows for a finite level of imperfection in the protocol, and makes use of Leggett’s ‘null result’ measurement scheme. I present the results of an experiment conducted in Oxford that, up to certain loopholes, defies a non-quantum interpretation of the dynamics of phosphorous nuclei embedded in silicon. I also present the theory of statistical parameter estimation, and discover that a recent trend to employ time symmetric ‘postselected’ measurements offers no true advantage over standard methods. The technique, known as weak-value amplification, combines a weak transfer of quantum information from system to meter with conditional data rejection, to surprising effect. The Fisher information is a powerful tool for evaluating the performance of any parameter estimation model, and it reveals the technique to be worse than ordinary, preselected only measurements. That this is true despite the presence of noise (including magnetic field fluctuations causing deco- herence, poor resolution detection, and random displacements), casts serious doubt on the utility of the method.

We study correlated two-level quantum impurity models coupled to a metallic conduction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-1 impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liquid state. By employing physical arguments and the numerical renormalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz-Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A `Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the $T=0$ zero-bias conductance --- it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt to resolve some points of contention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the differential conductance) is not linear in the applied field, showing a more complicated form than a simple `Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC state is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity-host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.

In this thesis we review the gauge/gravity duality and how it can be used to compute the thermodynamic properties and low-energy excitations of holographic quantum liquids - strongly-interacting field theories with a non-zero density of matter. We then study in detail the charge density excitations of two such liquids, the D3/D7 theory and the RN-AdS₄ theory, by computing the poles of their charge density Green's functions, and their charge density spectral functions. Although it is not a Landau Fermi liquid, the charge density excitations of the D3/D7 theory display many of the same properties as one, including a collisionless/hydrodynamic crossover as the temperature is increased. In contrast to this, the charge density (and energy density) excitations of the RN-AdS₄ theory do not share these properties but behave in a way that cannot be explained by Landau's theory of interacting fermionic quasiparticles. This is consistent with other results which indicate that this is not a Landau Fermi liquid.

Silicon nitride is a bulk and a coating material exhibiting excellent mechanical properties. The understanding of the complex processes at the nanometre scale gained through experimental research will be enhanced by the existence of a computationally efficient and accurate model that is able to describe the mechanical properties of silicon nitride. Such a model has yet to be proposed. In this thesis we present a transferable reduced tight-binding (TB) model for the silicon nitride system. More precisely, this model consists of a reduced TB model for elemental silicon, a reduced TB model for elemental nitrogen, and a reduced TB model for silicon nitride. These models are developed within the framework of coarse-graining the electronic structure from density functional theory (DFT) to tight binding (TB) to bond-order potentials (BOPs), and can therefore be used in the future as the stepping stone to develop BOPs for the application in large scale simulations. The bond integrals employed in the reduced TB models are obtained directly from mixed-basis DFT projections of wave functions onto a minimal basis of atom-centred orbitals. This approach reduces the number of overall parameters to be fitted and provides models which are transferable through the different coarse-graining levels. We provide an example by using the same bond integrals in the reduced TB model for silicon and the preliminary bond-based BOP for silicon. DFT binding energies of ground state and metastable crystal structures are used as the benchmark to which the TB and BOP repulsive parameters are fitted. In addition to model development, we present an improved methodology when going from TB to reduced TB. By weighting all four &sigma; TB bond integrals equally, we provide a new parameterisation (Eqs. (2.73) and (2.74)) and show that the quality of the silicon reduced TB model can be increased by choosing one of the reduced TB parameters to be distance invariant. The ingredients, the development methodology, and the quality of each of the four models are discussed in a separate chapter. The quality of the reduced TB models and BOP is demonstrated by comparing their predictions for the binding energies, heats of formation, elastic constants, and defect energies with DFT and experimental values.

This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.

We investigate systems comprising chains and rings of quantum dots, coupled to two metallic leads. Such systems allow to study the competition between orbital and spin degrees of freedom in a nanodevice, and the effect this subtle interplay has on two-channel Kondo (2CK) physics. We demonstrate that a rich range of strongly correlated electron behaviour results, with non-Fermi liquid 2CK phases and non-trivial phase transitions accessible. We employ physical arguments and the numerical renormalization group (NRG) technique to analyse these systems in detail, examining in particular both thermodynamic and dynamical properties. When leads are coupled to either end of a chain of dots, we show that the resulting behaviour on low temperature/energy scales can be understood in terms of simpler paradigmatic quantum `impurity' models. An effective low-energy single-spin 2CK model is derived for all odd-length chains, while the behaviour of even-length chains is related fundamentally to that of the classic `two-impurity Kondo' model. In particular, for small interdot coupling, we show that an effective coupling mediated though incipient single-channel Kondo states drives all odd chains to the 2CK fixed point (FP) on the lowest temperature/energy scales. A theory is also developed to describe a phase transition in even chains. We derive an effective channel-anisotropic 2CK model, which indicates that the critical FP of such models must be the 2CK FP. This physical picture is confirmed using NRG for various chain systems. We also examine the effect of local frustration on 2CK physics in mirror-symmetric ring systems. The importance of geometry and symmetry is demonstrated clearly in the markedly different physical behaviour that arises in systems where two leads are either connected to the same dot, or to neighbouring dots. In the latter case, we show for all odd-membered rings that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot couplings. A frustration-induced phase transition thus occurs, the 2CK phases being separated by a novel critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasidegenerate local trimer states acts to destabilise the 2CK FPs, and the critical FP is shown to consist of a free pseudospin together with effective single-channel spin quenching. While connecting both leads to the same dot again results in two parity-distinct phases, a simple level-crossing transition now results due to the symmetry of the setup. The proposed geometry also allows access to a novel ferromagnetically-coupled two-channel local moment phase. Driven by varying the interdot couplings and occurring at the point of inherent magnetic frustration, such transitions in ring structures provide a striking example of the subtle interplay between internal spin and orbital degrees of freedom in coupled quantum dot systems, and the resulting effect on Kondo physics.

La physique de la matière condensée, et notamment les systèmes fortement corrélés, amènent à des problèmes parmi les plus stimulants et difficiles de la physique moderne. Dans ces systèmes, les interactions à plusieurs corps et les corrélations entre les particules quantiques ne peuvent être négligées, sinon, les modèles échoueraient simplement à capturer les mécanismes physiques en jeu et les phénomènes qui en découlent. En particulier, le travail présenté dans ce manuscrit traite du magnétisme quantique et aborde plusieurs questions distinctes à l'aide d'approches computationnelles et méthodes numériques à l'état de l'art. Les effets conjoints du désordre (i.e. impuretés) et des interactions sont étudiés concernant un matériau magnétique spécifique : plutôt qu'une phase de la matière dite localisée, attendue à fort champ magnétique, une phase ordonnée induite par le désordre lui-même est mise en lumière, avec une réapparition inattendue de la cohérence quantique dans ledit composé. Par ailleurs, la réponse dynamique d'aimants quantiques à une perturbation externe, comme celle mesurée dans des expériences de résonance magnétique nucléaire ou de diffusion inélastique de neutrons est étudiée. / Condensed matter physics, and especially strongly correlated systems provide some of the most challenging problems of modern physics. In these systems, the many-body interactions and correlations between quantum particles cannot be neglected; otherwise, the models would simply fail to capture the relevant physics at play and phenomena ensuing. In particular, the work presented in this manuscript deals with quantum magnetism and addresses several distinct questions through computational approaches and state-of-the-art numerical methods. The interplay between disorder (i.e. impurities) and interactions is studied regarding a specific magnetic compound, where instead of the expected many-body localized phase at high magnetic fields, a novel disorder-induced ordered state of matter is found, with a resurgence of quantum coherence. Furthermore, the dynamical response of quantum magnets to an external perturbation, such as it is accessed and measured in nuclear magnetic resonance and inelastic neutron scattering experiments is investigated.