Theoretical Analysis of Single Molecule Spectroscopy Lineshapes of Conjugated Polymers

Conjugated Polymers(CPs) exhibit a wide range of highly tunable optical properties. Quantitative and detailed understanding of the nature of excitons responsible for such a rich optical behavior has significant implications for better utilization of CPs for more efficient plastic solar cells and other novel optoelectronic devices. In general, samples of CPs are plagued with substantial inhomogeneous broadening due to various sources of disorder. Single molecule emission spectroscopy (SMES) offers a unique opportunity to investigate the energetics and dynamics of excitons and their interactions with phonon modes. The major subject of the present thesis is to analyze and understand room temperature SMES lineshapes for a particular CP, called poly(2,5-di-(2\u27-ethylhexyloxy)-1,4-phenylenevinylene)(DEH-PPV). A minimal quantum mechanical model of a two-level system coupled to a Brownian oscillator bath is utilized. The main objective is to identify the set of model parameters best fitting a SMES lineshape for each of about 200 samples of DEH-PPV, from which new insight into the nature of exciton-bath coupling can be gained. This project also entails developing a reliable computational methodology for quantum mechanical modeling of spectral lineshapes in general. Well-known optimization techniques such as gradient descent, genetic algorithms, and heuristic searches have been tested, employing an $L^2$ measure between theoretical and experimental lineshapes for guiding the optimization. However, all of these tend to result in theoretical lineshapes qualitatively different from experimental ones. This is attributed to the ruggedness of the parameter space and inadequateness of the $L^2$ measure. On the other hand, when the dynamic reduction of the original parameter space to a 2-parameter space through feature searching and visualization of the search space paths using directed acyclic graphs(DAGs), the qualitative nature of the fitting improved significantly. For a more satisfactory fitting, it is shown that the inclusion of an additional energetic disorder is essential, representing the effect of quasi-static disorder accumulated during the SMES of each polymer. Various technical details, ambiguous issues, and implication of the present work are discussed

International Symposium on Mathematics, Quantum Theory, and Cryptography

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography

International Symposium on Mathematics, Quantum Theory, and Cryptography

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography

An Algorithmic Interpretation of Quantum Probability

The Everett (or relative-state, or many-worlds) interpretation of quantum mechanics has come under fire for inadequately dealing with the Born rule (the formula for calculating quantum probabilities). Numerous attempts have been made to derive this rule from the perspective of observers within the quantum wavefunction. These are not really analytic proofs, but are rather attempts to derive the Born rule as a synthetic a priori necessity, given the nature of human observers (a fact not fully appreciated even by all of those who have attempted such proofs). I show why existing attempts are unsuccessful or only partly successful, and postulate that Solomonoff's algorithmic approach to the interpretation of probability theory could clarify the problems with these approaches. The Sleeping Beauty probability puzzle is used as a springboard from which to deduce an objectivist, yet synthetic a priori framework for quantum probabilities, that properly frames the role of self-location and self-selection (anthropic) principles in probability theory. I call this framework "algorithmic synthetic unity" (or ASU). I offer no new formal proof of the Born rule, largely because I feel that existing proofs (particularly that of Gleason) are already adequate, and as close to being a formal proof as one should expect or want. Gleason's one unjustified assumption--known as noncontextuality--is, I will argue, completely benign when considered within the algorithmic framework that I propose. I will also argue that, to the extent the Born rule can be derived within ASU, there is no reason to suppose that we could not also derive all the other fundamental postulates of quantum theory, as well. There is nothing special here about the Born rule, and I suggest that a completely successful Born rule proof might only be possible once all the other postulates become part of the derivation. As a start towards this end, I show how we can already derive the essential content of the fundamental postulates of quantum mechanics, at least in outline, and especially if we allow some educated and well-motivated guesswork along the way. The result is some steps towards a coherent and consistent algorithmic interpretation of quantum mechanics