Decoherence of quantum kinematical correlations: Elastic scattering of identical particles

We include the dynamics of the angular straggling process in the angular distributions of Mott scattering of heavy ions. We model the passage of an incoming nucleus through a target as a diffusion process. It is then possible to derive a simple and physically transparent expression for the angular dispersion due to the straggling. The angular dispersion should be folded with the theoretical Mott cross section to see its effect on the amplitude of the Mott oscillations. Our results agree very well with data of Pb-208 + Pb-208 scattering. We define the "classical" limit as the limit when the angular dispersion due to straggling becomes comparable with the Mott oscillation period and get the disappearance of quantum interference occurring at the limit 0.050 root xi Z(4)/E-3/2 >= 1, where xi stands for the target thickness, Z is the system's charge, and E is the center-of-mass energy. The experiments on lead are very close to this limit. We show that the kinematical correlations due to the identity of the particles is maintained, as it should be, and the action of the environment is to reduce the fringe visibility.

Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

Measurement-based quantum computation is an efficient model to perform universal computation. Nevertheless, theoretical questions have been raised, mainly with respect to realistic noise conditions. In order to shed some light on this issue, we evaluate the exact dynamics of some single-qubit-gate fidelities using the measurement-based quantum computation scheme when the qubits which are used as a resource interact with a common dephasing environment. We report a necessary condition for the fidelity dynamics of a general pure N-qubit state, interacting with this type of error channel, to present an oscillatory behavior, and we show that for the initial canonical cluster state, the fidelity oscillates as a function of time. This state fidelity oscillatory behavior brings significant variations to the values of the computational results of a generic gate acting on that state depending on the instants we choose to apply our set of projective measurements. As we shall see, considering some specific gates that are frequently found in the literature, the fast application of the set of projective measurements does not necessarily imply high gate fidelity, and likewise the slow application thereof does not necessarily imply low gate fidelity. Our condition for the occurrence of the fidelity oscillatory behavior shows that the oscillation presented by the cluster state is due exclusively to its initial geometry. Other states that can be used as resources for measurement-based quantum computation can present the same initial geometrical condition. Therefore, it is very important for the present scheme to know when the fidelity of a particular resource state will oscillate in time and, if this is the case, what are the best times to perform the measurements.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Molecular dynamics simulations of silicate and borate glasses and melts : structure, diffusion dynamics and vibrational properties

Molecular dynamics simulations of silicate and borate glasses and melts: Structure, diffusion dynamics and vibrational properties. In this work computer simulations of the model glass formers SiO2 and B2O3 are presented, using the techniques of classical molecular dynamics (MD) simulations and quantum mechanical calculations, based on density functional theory (DFT). The latter limits the system size to about 100−200 atoms. SiO2 and B2O3 are the two most important network formers for industrial applications of oxide glasses. Glass samples are generated by means of a quench from the melt with classical MD simulations and a subsequent structural relaxation with DFT forces. In addition, full ab initio quenches are carried out with a significantly faster cooling rate. In principle, the structural properties are in good agreement with experimental results from neutron and X-ray scattering, in all cases. A special focus is on the study of vibrational properties, as they give access to low-temperature thermodynamic properties. The vibrational spectra are calculated by the so-called ”frozen phonon” method. In all cases, the DFT curves show an acceptable agreement with experimental results of inelastic neutron scattering. In case of the model glass former B2O3, a new classical interaction potential is parametrized, based on the liquid trajectory of an ab initio MD simulation at 2300 K. In this course, a structural fitting routine is used. The inclusion of 3-body angular interactions leads to a significantly improved agreement of the liquid properties of the classical MD and ab initio MD simulations. However, the generated glass structures, in all cases, show a significantly lower fraction of 3-membered planar boroxol rings as predicted by experimental results (f=60%-80%). The largest boroxol ring fraction of f=15±5% is observed in the full ab initio quenches from 2300 K. In case of SiO2, the glass structures after the quantum mechanical relaxation are the basis for calculations of the linear thermal expansion coefficient αL(T), employing the quasi-harmonic approximation. The striking observation is a change change of sign of αL(T) going along with a temperature range of negative αL(T) at low temperatures, which is in good agreement with experimental results.

Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

Atomic Quantum Simulation of U(N) and SU(N) Abelian Lattice Gauge Theories

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.