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- All Subjects: Quantum Mechanics
- All Subjects: Physics--Data processing.
- Creators: Matyushov, Dmitry
- Resource Type: Text
- Status: Published
Advanced path-sampling methods exploit reduced physical models or biasing to produce plausible transitions while balancing accuracy and efficiency, but quantifying their accuracy relative to other numerical and experimental data has been challenging. Indeed, new horizons in elucidating protein function necessitate that present methodologies be revised to more seamlessly and quantitatively integrate a spectrum of methods, both numerical and experimental. In this dissertation, experimental and computational methods are put into perspective using the enzyme adenylate kinase (AdK) as an illustrative example. We introduce Path Similarity Analysis (PSA)—an integrative computational framework developed to quantify transition path similarity. PSA not only reliably distinguished AdK transitions by the originating method, but also traced pathway differences between two methods back to charge-charge interactions (neglected by the stereochemical model, but not the all-atom force field) in several conserved salt bridges. Cryo-electron microscopy maps of the transporter Bor1p are directly incorporated into EqMD simulations using MD flexible fitting to produce viable structural models and infer a plausible transport mechanism. Conforming to the theme of integration, a short compendium of an exploratory project—developing a hybrid atomistic-continuum method—is presented, including initial results and a novel fluctuating hydrodynamics model and corresponding numerical code.
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.