Level-resolved quantum statistical theory of electron capture into many-electron compound resonances in highly charged ions

The strong mixing of many-electron basis states in excited atoms and ions with open f shells results in very large numbers of complex, chaotic eigenstates that cannot be computed to any degree of accuracy. Describing the processes which involve such states requires the use of a statistical theory. Electron capture into these “compound resonances” leads to electron-ion recombination rates that are orders of magnitude greater than those of direct, radiative recombination and cannot be described by standard theories of dielectronic recombination. Previous statistical theories considered this as a two-electron capture process which populates a pair of single-particle orbitals, followed by “spreading” of the two-electron states into chaotically mixed eigenstates. This method is similar to a configuration-average approach because it neglects potentially important effects of spectator electrons and conservation of total angular momentum. In this work we develop a statistical theory which considers electron capture into “doorway” states with definite angular momentum obtained by the configuration interaction method. We apply this approach to electron recombination with W²⁰⁺, considering 2×10⁶ doorway states. Despite strong effects from the spectator electrons, we find that the results of the earlier theories largely hold. Finally, we extract the fluorescence yield (the probability of photoemission and hence recombination) by comparison with experiment.

Optics-Based Quantum Information and Sensing Platforms Utilizing the Nitrogen-Vacancy Center in Diamond

Thesis (Ph.D.)--University of Washington, 2016-08

Non-Perturbative Methods in Quantum Field Theory and Quantum Gravity

This thesis considers non-perturbative methods in quantum field theory with applications to gravity and cosmology. In particular, there are chapters on black hole holography, inflationary model building, and the conformal bootstrap.

Capital structure, risk and asymmetric information : theory and evidence

This paper proposes a principal-agent model between banks and firms with risk and asymmetric information. A mixed form of finance to firms is assumed. The capital structure of firms is a relevant cause for the final aggregate level of investment in the economy. In the model analyzed, there may be a separating equilibrium, which is not economically efficient, because aggregate investments fall short of the first-best level. Based on European firm-level data, an empirical model is presented which validates the result of the relevance of the capital structure of firms. The relative magnitude of equity in the capital structure makes a real difference to the profits obtained by firms in the economy.

Black hole scattering from Worldline Quantum Field Theory and the Classical Double Copy of Spinning particles

This PhD thesis focuses on studying the classical scattering of massive/massless particles toward black holes, and investigating double copy relations between classical observables in gauge theories and gravity. This is done in the Post-Minkowskian approximation i.e. a perturbative expansion of observables controlled by the gravitational coupling constant κ = 32πGN, with GN being the Newtonian coupling constant. The investigation is performed by using the Worldline Quantum Field Theory (WQFT), displaying a worldline path integral describing the scattering objects and a QFT path integral in the Born approximation, describing the intermediate bosons exchanged in the scattering event by the massive/massless particles. We introduce the WQFT, by deriving a relation between the Kosower- Maybee-O’Connell (KMOC) limit of amplitudes and worldline path integrals, then, we use that to study the classical Compton amplitude and higher point amplitudes. We also present a nice application of our formulation to the case of Hard Thermal Loops (HTL), by explicitly evaluating hard thermal currents in gauge theory and gravity. Next we move to the investigation of the classical double copy (CDC), which is a powerful tool to generate integrands for classical observables related to the binary inspiralling problem in General Relativity. In order to use a Bern-Carrasco-Johansson (BCJ) like prescription, straight at the classical level, one has to identify a double copy (DC) kernel, encoding the locality structure of the classical amplitude. Such kernel is evaluated by using a theory where scalar particles interacts through bi-adjoint scalars. We show here how to push forward the classical double copy so to account for spinning particles, in the framework of the WQFT. Here the quantization procedure on the worldline allows us to fully reconstruct the quantum theory on the gravitational side. Next we investigate how to describe the scattering of massless particles off black holes in the WQFT.

Philosophy of quantum field theory: an introduction with interviews and comments

In this thesis, I address quantum theories and specifically quantum field theories in their interpretive aspects, with the aim of capturing some of the most controversial and challenging issues, also in relation to possible future developments of physics. To do so, I rely on and review some of the discussions carried on in philosophy of physics, highlighting methodologies and goals. This makes the thesis an introduction to these discussions. Based on these arguments, I built and conducted 7 face-to-face interviews with physics professors and an online survey (which received 88 responses from master's and PhD students and postdoctoral researchers in physics), with the aim of understanding how physicists make sense of concepts related to quantum theories and to find out what they can add to the discussion. Of the data collected, I report a qualitative analysis through three constructed themes.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Three-party entanglement from positronium

The decay of orthopositronium into three photons produces a physical realization of a pure state with three-party entanglement. Its quantum correlations are analyzed using recent results on quantum information theory, looking for the final state that has the maximal amount of Greenberger, Horne, and Zeilinger like correlations. This state allows for a statistical dismissal of local realism stronger than the one obtained using any entangled state of two spin one-half particles.

Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an N-2-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.

Why entanglement of formation is not generally monogamous

Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if one system A is maximally entangled with another system B, it cannot be entangled at all with a third system C. This concept, known as the monogamy of entanglement, is manifest when the entanglement of A with a pair BC can be divided as contributions of the entanglement between A and B and A and C, plus a term τABC involving genuine tripartite entanglement and so expected to be always positive. A very important measure in quantum information theory, the entanglement of formation (EOF), fails to satisfy this last requirement. Here we present the reasons for that and show a set of conditions that an arbitrary pure tripartite state must satisfy for the EOF to become a monogamous measure, i.e., for τABC≥0. The relation derived is connected to the discrepancy between quantum and classical correlations, τABC being negative whenever the quantum correlation prevails over the classical one. This result is employed to elucidate features of the distribution of entanglement during a dynamical evolution. It also helps to relate all monogamous instances of the EOF to the squashed sntanglement, an entanglement measure that is always monogamous. © 2013 American Physical Society.

Aspectos relativísticos da teoria da informação quântica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Informação quântica e relatividade

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.