We consider two distinct, analytic models of quantum geometry that are both inspired by a desire to understand the dynamical space-time of non-perturbative quantum gravity.

The Unruh-DeWitt particle detector is a valuable tool for probing the physics of quantum fields when curved spacetimes or noninertial observers are involved. However, due to subtleties involving the regularisation of the Wightman distribution, a precise definition of the transition rate of such a detector in a general setting has proven elusive. Here the question is addressed within two different frameworks: the first one (originally introduced by Schlicht) involving a spatial smearing function and the second one involving smooth switching functions for turning on and off the interaction. It is shown that the two approaches lead to a same universal regularised expression for general detector trajectories in Minkowski space, and that the second approach is also valid in more general spacetimes. General properties of the transition rate are discussed, and several particular applications are considered, among them a detector with increasing acceleration in the Minkowski vacuum, an inertial detector in the Rindler vacuum and a detector at rest in a Newtonian gravitational field.

The polariton condensate is a highly interacting system with a macroscopically occupied state. Condensates may be formed either by non-resonant [1] or resonant (optical parametric oscillation) excitation [2] but the properties of the condensate are similar in bot.h cases. Due to the finite polariton lifetime, condensates are non-equilibrium. Nevertheless, they exhibit many of the same interesting phenomena as interacting Bose-Einstein condensates (BEC) in thermodynamic equilibrium, such as long-range spatial and temporal coherence and vortices. This thesis focusses on the coherence properties of polariton condensates within inorganic semiconductor microcavities. Condensates in CdTe microcavir ies excited using a non-resonant pump are shown to exhibit long coherence times of up to 250 ps, far longer than the polariton lifetime of "'" l.5 ps. This large slow-down in decay reveals intrinsic decohereuce properties which are confirmed by measuring the g(1) and g(2) correlation functions of single condensed modes. The characteristic lineshape of the 09(1) function is Gaussian. With increase of polaritons there is a "saturation" 3 in coherence time due to interactions, which has been predicted but not observed for equilibrium BEe. \Ye also demonstrate the existence of multiple, co-existing condensates which occur due to the non-equilibrium nature of the condensate. These condensates overlap in space and are shown to be truly independent of each other by correlation measurements. The condensates are triggered at momenta which are determined by the disorder of the polaritonic potential. Finally, the use of surface acoustic waves (SAW) to create a dynamic periodic potential is demonstrated. We study the effects of this potential on the condensate, such as the formation of condensate wires and corresponding reduction in spatial coherence due to reduced condensate dimensionality, We show that cont.rolled manipulation of coherence properties is possible, and discuss the potential for coherent transport. of the polariton condensate.

A relevant perturbation of a conformal field theory (CFT) on the half-plane, by both a bulk and boundary operator, often leads to a massive theory with a particle description in terms of the bulk S-matrix and boundary reflection factor R. The link between the particle basis and the CFT in the bulk is usually made with the thermodynamic Bethe ansatz effective central charge C(_eff). This allows a conjectured S-matrix to be identified with a specific perturbed CFT. Less is known about the links between the reflection factors and conformal boundary conditions, but it has been proposed that an exact, off-critical version of Affleck and Ludwig's g-function could be used, analogously to C(_eff), to identify the physically realised reflection factors and to match them with the corresponding boundary conditions. In the first part of this thesis, this exact g-function is tested for the purely elastic scattering theories related to the ADET Lie algebras. Minimal reflection factors are given, and a method to incorporate a boundary parameter is proposed. This enables the prediction of several new flows between conformal boundary conditions to be made. The second part of this thesis concerns the three-parameter family of PT-symmetric Hamiltonians H(M,o,1) = p(^2) – (ix) (^2M) – α(ix) The positions where the eigenvalues merge and become complex correspond to quadratic and cubic exceptional points. The quasi-exact solvability of the models for M = 3 is exploited to exploreaway from M = 3 is investigated using both numerical and perturbative approaches.

The dynamical structure factor (DSF) is an important quantity in the characterization and understanding of quantum magnets, both experimentally and theoretically. In this thesis the DSF is calculated for three different spin-1/2 systems with reduced spatial dimensions. These are: the bond alternating Heisenberg chain; the anisotropic Heisenberg, or XXZ, chain; and n a anisotropic triangular antiferromagnet with Dzyaloshinskii-Moriya interaction. All three cases are motivated by inelastic neutron scattering experiments on realistic manifestations of the models.

No description available.

This thesis is a review of the works and ideas I have been developing in my doctoral studies, and it is mainly based on Castro-Alvaredo & Levi [2011]; Castro-Alvaredo et al. [2011]; Levi [2012]; Levi et al. [2013]. The specific aims of these works were to explore the methods developed in Calabrese & Cardy [2004]; Cardy et al. [2008] with the purpose of quantifying entanglement in a quantum field theory, and have a deeper understanding of their predicting power on lattice systems. The first chapter is meant to be a review of quantum entanglement in many-body physics, and the methods we use to establish the link to QFT. In the second chapter, after a small introduction on conformal field theory, we collect the results of Calabrese & Cardy [2004], focusing in particular on the replica trick and the twist field. The third chapter is devoted to adapting these tools to massive QFT, as performed in Cardy et al. [2008]. In particular we focus on the form factor program for the twist field, by means of which we are able to outline the behavior of entanglement entropy in massive theories in a non perturbative way. We expand on the results found in Castro-Alvaredo & Levi [2011], where higher particle form factors were studied for the roaming trajectory model, and the SU(3)2-homogenous sine-Gordon model. We then carry out a numerical study of the Δ-function of the twist field for these two models. In the fourth chapter we focus on the connection between the Δ-function of the twist field and Zamolodchikov c-function, as performed in Castro-Alvaredo et al. [2011]. In addressing this issue we perform a thorough study of the two point function of the twist field and the trace of the stress-energy tensor. This allows us to introduce a class of composite twist fields, which were the main topic of Levi [2012]. In the fifth and last chapter we group the most common methods used to study the entanglement entropy of quantum spin chains. We start with the XY chain analysis, which is performed with a combination of analytical and numerical methods based on free fermion techniques. We then perform a numerical study of the XXZ chain by means of the density matrix renormalization group approach. Eventually we present the results obtained for these two models in Levi et al. [2013].

Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators without requiring or referring to a fictitious external observer is addressed, and this in turn rephrases and removes the traditional Measurement Problem inherent in the Copenhagen interpretation of quantum mechanics. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically, it is demonstrated that by considering the changing properties, separabilities and factorisations of both the state and the operators as the Universe proceeds though a sequence of discrete computations, familiar notions such as classical distinguishability, particle physics, space, time, special relativity and endo-physical experiments can all begin to emerge from the proposed picture. A pregeometric vision of cosmology is therefore discussed, with all of physics ultimately arising from the relationships occurring between the elements of the underlying mathematical structure. The possible origins of observable physics, including physical objects positioned at definite locations in an arena of apparently continuous space and time, are consequently investigated for a Universe that incorporates quantum theory as a fundamental feature. Overall, a framework for quantum cosmology is introduced and explored which attempts to account for the existence of time, space, matter and, eventually, everything else in the Universe, from a physically consistent perspective.

In this thesis, we develop a perturbative formulation of non-equilibrium thermal quantum field theory, capable of describing the evolution of both temporal and spatial inhomogeneities in relativistic, quantum-statistical ensembles. We begin with a review of the necessary prerequisites from classical thermodynamics, classical and quantum statistical mechanics, quantum field theory and equilibrium thermal field theory. Setting general boundary conditions on the ensemble expectation values of products of interaction-picture creation and annihilation operators, we derive free propagators in which space-time translational invariance is explicitly broken. By means of the Schwinger-Kelydsh, closed-time path formalism, we are then able to introduce a path-integral description that accounts consistently for these temporal and spatial inhomogeneities. Subsequently, we develop a time-dependent perturbation theory that is free of the pathologies previously thought to spoil such approaches to non-equilibrium dynamics. Following an unambiguous definition of the number density of particles, we derive from first principles perturbative, field-theoretic evolution equations for statistical distribution functions. These evolution equations do not rely on the gradient expansion of so-called Wigner functions, as is necessary in the alternative Kadanoff-Baym approach, and are consistent with the well-known Boltzmann equations in the classical limit. Finally, with reference to a simple toy model, we highlight the appearance of processes otherwise kinematically disallowed in existing approaches to thermal field theory. These evanescent contributions are a consequence of the microscopic violation of energy conservation and are shown to be significant to the early-time evolution of non-equilibrium systems. We observe that the spectral evolution oscillates with time-dependent frequencies, which is interpreted as a signal of non-Markovian, memory effects.

This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are be useful for quantum information. It draws from many well established physical theories such as quantum field theory in curved spacetimes, quantum optics and Gaussian state quantum information. The results are split between three chapters. For the first results, we set-up the basic framework for working with quantum fields confined to cavities. By considering the real Klein-Gordon field, we describe how to model the non-uniform motion of a rigid cavity through spacetime. We employ the use of Bogoliubov transformations to describe the effects of changing acceleration. We investigate how entanglement can be generated within a single cavity and the protocol of quantum teleportation is affected by non-uniform motion. The second set of results investigate how the Dirac field can be confined to a cavity for quantum information purposes. By again considering Bogoliubov transformations, we thoroughly investigate how the entanglement shared between two cavities is affected by non-uniform motion. In particular, we investigate the role of the Dirac fields charge in entanglement effects. We finally analyse a \one-way-trip" of one of the entangled cavities. It is shown that different types of Dirac field states are more robust against motion than others. The final results looks at using our second notion of localisation, Unruh-DeWitt detectors. We investigate how allowing for a \non-point-like" spatial profile of the Unruh-DeWitt detector affects how it interacts with a quantum field around it. By engineering suitable detector-field interactions, we use techniques from symplectic geometry to compute the dynamics of a quantum state beyond commonly used perturbation theory. Further, the use of Unruh-DeWitt detectors in generating entanglement between two distinct cavities will be investigated.