This licentiate thesis in theoretical physics focuses on the existence of quantum features in physical systems such as axion dark matter and gravity. Our focus is mostly on effects which appear at low energies, a regime in which our models can be confronted with current experiments or within the foreseeable future. In our first project, we focus on squeezing of axion dark matter, a quantum mechanical effect which accompanies the standard mean field description of axions. We have showed that within a reasonable set of assumptions, the quantum state of axions is highly squeezed. This theoretical finding suggests that the mean field description of axion dark matter is incomplete, since the latter conceals many interesting and possibly experimentally relevant phenomena, and paves the way for axion dark matter studies beyond the mean field approximation. Moreover, in this thesis, some ongoing work on axion dark matter decoherence is presented. Our goal is to test whether axion dark matter squeezing is robust against decoherence. Preliminary results indicate that squeezing is not diminished in presence of environmental interactions. Our results stem from an interdisciplinary approach at the intersection between cosmology, quantum optics, quantum open systems and cold atoms. Our second work focuses on quantum features of gravity. An almost century old question is how gravity can be reconciled with the laws of quantum mechanics. This question remains still open and part of the reason is the lack of experimental evidence. However, in recent years, the rapid progress of experimental techniques allows for quantum control and manipulation of larger and larger quantum systems. These new experimental routes have sparkled an interest in testing such fundamental questions with tabletop experiments. One particularly interesting proposal aims to test whether gravity can mediate entanglement between two spatially superposed mesoscopic masses. This proposal, in order to deduce the existence of quantized gravitational mediators, relies on a quantum-information-theoretic argument, the so-called LOCC (Local Operations and Classical Communication). In our work, we critically assess this proposal, its underlying assumptions and what teaches about quantum gravity. We conclude that the LOCC argument is not useful and by invoking it, one cannot unambiguously infer the existence of quantum mediators unless the principle oflocality is elevated to a fundamental principle of nature. We support our claim by explicitly showing that well known relativistic field theories, apart from local formulations can also admit non-local ones. Therefore, the entanglement generating quantum channel can be either local or non-local.

In this thesis I present a derivation of statistical mechanics starting from a closed, isolated quantum many body system. I first establish under what conditions we expect static equilibrium to emerge. It is found that the purity of the diagonal ensemble is a sufficient criteria for equilibration to occur and avoid short time recurrences. I next derive the usual ensembles of statistical mechanics using the principle of maximum entropy. These ensembles are then connected to the diagonal ensemble through the strong and the weak eigenstate thermalization hypothesis (ETH). Counter examples to ETH are discussed along with the process of scrambling. The thesis contains three contributed articles relevant to this introductory chapter studying early time relaxation, recurrences and scrambling. / Thesis / Doctor of Philosophy (PhD)

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Indiana University-Purdue University Indianapolis (IUPUI) / Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semi-classical models with mode selective losses, and lossy quantum systems. The rapidly growing research on these systems has mainly focused on the wide range of novel functionalities they demonstrate. In this thesis, I intend to present some intriguing properties of a class of open systems which possess parity (P) and time-reversal (T) symmetry with a theoretical background, accompanied by the experimental platform these are realized on. These systems show distinct regions of broken and unbroken symmetries separated by a special phase boundary in the parameter space. This separating boundary is called the PT-breaking threshold or the PT transition threshold. We investigate non-Hermitian systems in two settings: tight binding lattice models, and electrical circuits, with the help of theoretical and numerical techniques. With lattice models, we explore the PT-symmetry breaking threshold in discrete realizations of systems with balanced gain and loss which is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. These results provide a surprising way to engineer the PT threshold in experimentally accessible samples. In another example, we investigate the PT-threshold for a one-dimensional, finite Kitaev chain—a prototype for a p-wave superconductor— in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, onsite potential, and the distance between the gain and loss sites. In addition to a robust, non-local threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev model. Finally, with electrical circuits, we propose a protocol to study the properties of a PT-symmetric system in a single LC oscillator circuit which is contrary to the notion that these systems require a pair of spatially separated balanced gain and loss elements. With a dynamically tunable LC oscillator with synthetically constructed circuit elements, we demonstrate static and Floquet PT breaking transitions by tracking the energy of the circuit. Distinct from traditional mechanisms to implement gain and loss, our protocol enables parity-time symmetry in a minimal classical system.

Yes / The Desargues property is well known in the context of projective geometry. An analogous property is presented in the context of both classical and Quantum Physics. In a classical context, the Desargues property implies that two logical circuits with the same input, show in their outputs selective correlations. In general their outputs are uncorrelated, but if the output of one has a particular value, then the output of the other has another particular value. In a quantum context, the Desargues property implies that two experiments each of which involves two successive projective measurements, have selective correlations. For a particular set of projectors, if in one experiment the second measurement does not change the output of the rst measurement, then the same is true in the other experiment.

This dissertation explores the properties of sulfonated poly(arylene ether sulfone)s for desalination membrane applications. A multi-scale approach is used to understand the relationships between the chemical structure of the polymer, the equilibrium water content, and the bulk properties. The polysulfones investigated here are aromatic polymers with relatively high ion contenremain in the glassy state at room temperature even when fully hydrated. In order to better understand the effects of water on these ionic polysulfones molecular dynamics (MD) simulation is used to investigate ion aggregation and hydration at the atomic scale. MD simulations show that the sulfonate and sodium ions are not simply paired. Instead, they form an ionic network. The molecular nature of melting water within sulfonated polysulfones is also examined by combining differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR), and MD simulation. Experimental evidence shows that at high ion contents, the spacing between the ionic groups impacts the amount of melting water present in the polymer. We conclude that the amount of melting water in the polymer is more closely related to geometric clustering effects than electrostatic effects. Finally, molecular-scale insight is used to understand the trends in hydrated tensile modulus and hydrated glass transition (Tg) temperatures in sulfonated polysulfones. Polymers with a more rigid backbone show different trends compared to those with a more flexible backbone. The modulus and Tg trends for the more flexible backbone are qualitatively consistent with the increase in intra-chain ionic associations (loops) predicted by the sticky Rouse model. / Doctor of Philosophy / This dissertation investigates new materials that could be used to make better membranes that can remove ions (salt) from water. Existing materials are too soft or too brittle when they are fully immersed in water. Consequently, they must be combined with more durable materials in order to make useful membranes. We would like to design durable ionic polymers (large chain-like molecules with ions attached) that interact with water and other ions in a very specific way in order to make membranes that can remove salt efficiently. The goal of this research is to create tools that can describe how changes to the chemical structure of the polymer impact how the polymer, water, and ions interact with each other so that we can improve membrane properties. We find that the ions on the polymer chain interact with each other to form threads, which can form a network inside of the polymer under the right conditions. When the ions are located far apart on the polymer chain, the ion threads link one polymer chain to another polymer chain. These ionic links strengthen the polymer network. However, when the ions are located closer together on the polymer chain, the chain starts to form loops between neighboring ions. As the number of loops increases, the polymer quickly becomes softer and more gel-like. We also find that water molecules are distributed within the polymer and are not always located next to the ions. When there is more water inside the polymer, the water molecules begin to group together to form clusters. At low temperatures, water molecules that have fewer than four neighboring molecules cannot freeze. However, water in a cluster of five molecules or more can freeze into an ice crystal. The insights gained from this research will help the community to design better polymers for desalination membrane applications.

The nuclear spin response to a rotating field H has been theoretically investigated from the 1930s to the 1950s. Building upon Majorana's probability theory, the behavior of spin 1/2 is well-illustrated in the joint review by Rabi, Ramsey, andSchwinger, and their spin wave function ψ is succinctly restated by Gottfried: ψ(t) = e-iIzωt/ℏe-i[Iz(ω0-ω)+Ixω1]t/ℏψ(0). However, the complexity involved in evaluating the wave function ψ in terms of probability amplitudes Cm attributed to the noncommutative nature of spin operators [Ix, Iz] ≠0, hinders the application of this well-established theory to spins with arbitrary values I > 1/2. In a recent study by Hall and Klemm, a conjectural form of the spin wave function was suggested. Here, we present an alternative formulation of the wave function ψ by controlling doubly rotating coordinates: ψ(t) = e-iIzωt/ℏ e-iIyθ/ℏ e-iIzΩt/ℏ eiIyθ/ℏ ψ(0). This formulation facilitates the computation of general state transitions from an initial state ψ(0)=∑mCm(0)ψm(0) to ψ(t)=∑m'Cm'(t)ψm'(t). Moreover, by assuming an analogous form of the total electron spin J to that of the nucleus I, we can explore hyperfine structures in atoms and/or molecules traversing in the magnetic field H in terms of the nuclear-electronic spin interaction (I·J). Through this approach, we not only formulate wave functions more effectively but also bridge quantum mechanics and algebraic perspectives.

No / Budesonide is a mixture of 22R and 22S epimers. The epimeric content of budesonide was reported in both British and European pharmacopoeias to be within the range of 60-49/40-51 for R and S epimers, respectively. In this work, contribution of the two epimers to the overall infrared spectrum of budesonide has been investigated by quantum chemical calculations.

Usando as Regras de Soma da QCD, testamos se a nova estrutura estreita, X(4350) recentemente observada pela Colaboração Belle, pode ser descrita como um estado molecular D8D80 exótico JPC = 1+. Consideramos as contribuições dos condensados de dimensão oito, trabalhamos com os termos dominantes em 8 mantendo os termos lineares na massa do quark estranho m8. A massa obtida é igual a mD8D80 = (5.05±0.19) GeV. Consideramos também uma corrente molecular 1+, DD0 e obtemos mDD0 = (4.92 ± 0.08) GeV. Concluímos que não é possível descrever a estrutura X(4350) como um estado molecular 1+ D8D80. / Using the QCD sum rules we test if the new narrow structure, the X(4350) recently observed by the Belle Collaboration, can be described as a JPC = 1+ exotic D8D80 molecular state. We consider the contributions of condensates up to dimension eight, we work at leading order in s and we keep terms which are linear in the strange quark mass ms. The mass obtained for such state is mD8D80 =(5.05 ± 0.19) GeV. We also consider a molecular 1+, DD0 current and we obtain mDD0 = (4.92 ± 0.08) GeV. We conclude that it is not possible to describe the X(4350) structure as a 1+ D8D80 molecular state.

Usando as Regras de Soma da QCD, testamos se a nova estrutura estreita, X(4350) recentemente observada pela Colaboração Belle, pode ser descrita como um estado molecular D8D80 exótico JPC = 1+. Consideramos as contribuições dos condensados de dimensão oito, trabalhamos com os termos dominantes em 8 mantendo os termos lineares na massa do quark estranho m8. A massa obtida é igual a mD8D80 = (5.05±0.19) GeV. Consideramos também uma corrente molecular 1+, DD0 e obtemos mDD0 = (4.92 ± 0.08) GeV. Concluímos que não é possível descrever a estrutura X(4350) como um estado molecular 1+ D8D80. / Using the QCD sum rules we test if the new narrow structure, the X(4350) recently observed by the Belle Collaboration, can be described as a JPC = 1+ exotic D8D80 molecular state. We consider the contributions of condensates up to dimension eight, we work at leading order in s and we keep terms which are linear in the strange quark mass ms. The mass obtained for such state is mD8D80 =(5.05 ± 0.19) GeV. We also consider a molecular 1+, DD0 current and we obtain mDD0 = (4.92 ± 0.08) GeV. We conclude that it is not possible to describe the X(4350) structure as a 1+ D8D80 molecular state.