Dissertations / Theses: 'Classical physics'

1

Chambers, Chris M. "Classical aspects of black hole physics." Thesis, University of Newcastle Upon Tyne, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294892.

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2

Beamond, Eleanor. "Quantum and classical localisation." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249185.

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3

Di, Criscienzo Roberto. "Semi-classical aspect of black hole physics." Doctoral thesis, Università degli studi di Trento, 2011. https://hdl.handle.net/11572/367865.

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4

Di, Criscienzo Roberto. "Semi-classical aspect of black hole physics." Doctoral thesis, University of Trento, 2011. http://eprints-phd.biblio.unitn.it/627/1/PhD_v2.pdf.

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5

Vrinceanu, Daniel. "Quantal-classical correspondence in atomic collisions." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28035.

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Sylvester, Igor Andrade. "Efficient classical simulation of spin networks." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/36112.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
Includes bibliographical references (p. 45).
In general, quantum systems are believed to be exponentially hard to simulate using classical computers. It is in these hard cases where we hope to find quantum algorithms that provide speed up over classical algorithms. In the paradigm of quantum adiabatic computation, instances of spin networks with 2-local interactions could hopefully efficiently compute certain problems in NP-complete. Thus, we are interested in the adiabatic evolution of spin networks. There are analytical solutions to specific Hamiltonians for 1D spin chains. However, analytical solutions to networks of higher dimensionality are unknown. The dynamics of Cayley trees (three binary trees connected at the root) at zero temperature are unknown. The running time of the adiabatic evolution of Cayley trees could provide an insight into the dynamics of more complicated spin networks. Matrix Product States (MPS) define a wavefunction anzatz that approximates slightly entangled quantum systems using poly(n) parameters. The MPS representation is exponentially smaller than the exact representation, which involves 0(2n) parameters. The MPS Algorithm evolves states in the MPS representation.
(cont.) We present an extension to the DMRG algorithm that computes an approximation to the adiabatic evolution of Cayley trees with rotationally-symmetric 2-local Hamiltonians in time polynomial in the depth of the tree. This algorithm takes advantage of the symmetry of the Hamiltonian to evolve the state of a Cayley tree exponentially faster than using the standard DMRG algorithm. In this thesis, we study the time-evolution of two local Hamiltonians in a spin chain and a Cayley tree. The numerical results of the modified MPS algorithm can provide an estimate on the entropy of entanglement present in ground states of Cayley trees. Furthermore, the study of the Cayley tree explores the dynamics of fractional-dimensional spin networks.
by Igor Andrade Sylvester.
S.B.

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Rudner, Mark S. (Mark Spencer). "Classical and quantum control in nanosystems." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/45443.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.
Includes bibliographical references (p. 189-202).
The central claim of this thesis is that nanoscale devices offer a platform to study and demonstrate new forms of control over both quantum and classical degrees of freedom in solid-state systems. To support this claim, I present a series of theoretical discussions that demonstrate how static and/or time-varying fields can be used to control spin degrees of freedom in GaAs quantum dots. This work is motivated by recent experiments in single and double quantum dots that have demonstrated many interesting phenomena arising from the coupled dynamics of electron and nuclear spins. In addition, I will present some results on the control of superconducting flux qubits, obtained in collaboration with the Orlando group at MIT. The control techniques discussed in this thesis may help provide new directions for experimental research on nuclear spin dynamics in solids, and may be applied to help enable future spintronics or quantum information processing tasks.
by Mark S. Rudner.
Ph.D.

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8

Saizar, Pedro. "Multiwavelength studies of classical nova shells /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487780865408208.

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9

Klales, Anna. "A Classical Perspective on Non-Diffractive Disorder." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:26718765.

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The unifying themes connecting the chapters in this dissertation are the profound and often surprising effects of disorder in classical and quantum systems and the tremendous insight gained from a classical perspective, even in quantum systems. In particular, we investigate disorder in the form of weak, spatially correlated random potentials, i.e. far from the Anderson Localization regime. We present a new scar-like phenomenon in quantum wells. With the introduction of local impurities to the oscillator, the eigenstates localize onto classical periodic orbits of the unperturbed system. Compared to traditional scars in chaotic billiards, these scars are both more common and stronger. Though the unperturbed system has circular symmetry, the random perturbation selects a small number of orientations which are shared by many scarred states -- dozens or even hundreds -- over a range of energies. We show, via degenerate perturbation theory, that the cause of the new scars is the combination of an underlying classical resonance of the unperturbed system and a perturbation induced coupling that is strongly local in action space. Next we examine the same type of local perturbation applied to an open system: branched flow. Caustics in the manifold of trajectories have been implicated in the formation of strong branches. We show that caustic formation is intimately tied to compression of manifolds of trajectories in phase space, which has important implications for the position space density. We introduce the "Kick and Drift" model, a generalization of the standard map. The model is a good approximation to the full two dimensional dynamics of a wave propagating over a weak random potential, but it provides a simpler framework for studying branched flow. Next we develop a classical model for electrons executing cyclotron motion in a graphene flake and implement it numerically. We derive classical equations of motion for electrons moving through the graphene flake with a position dependent effective mass due to fluctuations in the background carrier density. I apply these methods to an experiment performed by the Westervelt group. They imaged the flow of electrons in a graphene flake by measuring the transresistance as they rastered a charged scanning probe microscope tip over the surface. My simulations show that the regions with the greatest change in transresistance do always coincide with the regions with the highest current density. Furthermore I show that the experimental results can qualitatively reproduced by treating the system classically. Finally, we extend Heller's thawed Gaussian approximation from second order in the classical action to third order, in order to capture curvature in phase space. Such phase space dynamics are ubiquitous in systems with weak random potentials, such as those discussed above. We derive a closed form solution, but find that more work needs to be done to make it numerically tractable and competitive with other methods. A semiclassical method capturing phase space curvature could provide insight into the behavior of scars away from the hbar goes to zero limit.
Physics

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10

Cotton, Stephen Joshua. "Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations." Thesis, University of California, Berkeley, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3686249.

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An approach has been developed for extracting approximate quantum state-to-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible.

To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H₂ reactive scattering calculations were performed [S.J. Cotton and W.H. Miller, J. Phys. Chem. A 117, 7190 (2013)] with SQC-quantization applied to the H₂ vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1/2-unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasi-classical procedure.

The SQC approach was then applied [S.J. Cotton and W.H. Miller, J. Chem. Phys. 139, 234112 (2013)] to the much more interesting and challenging problem of incorporating non-adiabatic effects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model—representing the occupations of the electronic states—in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for a range of standard benchmark models of electronically non-adiabatic processes, including applications where "quantum" coherence effects are significant. Notably, among these benchmarks was the well-studied "spin-boson" model of condensed phase non-adiabatic dynamics, in both its symmetric and asymmetric forms—the latter of which many classical approaches fail to treat successfully.

The SQC/MM approach to the treatment of non-adiabatic dynamics was next applied [S.J. Cotton, K. Igumenshchev, and W.H. Miller, J. Chem. Phys., 141, 084104 (2014)] to several recently proposed models of condensed phase electron transfer (ET) processes. For these problems, a flux-side correlation function framework modified for consistency with the SQC approach was developed for the calculation of thermal ET rate constants, and excellent accuracy was seen over wide ranges of non-adiabatic coupling strength and energetic bias/exothermicity. Significantly, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory was reproduced quantitatively for these models—representing the successful treatment of another regime that classical approaches generally have difficulty in correctly describing. Relatedly, a model of photoinduced proton coupled electron transfer (PCET) was also addressed, and it was shown that the SQC/MM approach could reasonably model the explicit population dynamics of the photoexcited electron donor and acceptor states over the four parameter regimes considered.

The potential utility of the SQC/MM technique lies in its stunning simplicity and the ease by which it may readily be incorporated into "ordinary" molecular dynamics (MD) simulations. In short, a typical MD simulation may be augmented to take non-adiabatic effects into account simply by introducing an auxiliary pair of classical "electronic" action-angle variables for each energetically viable Born-Oppenheimer surface, and time-evolving these auxiliary variables via Hamilton's equations (using the MM electronic Hamiltonian) in the same manner that the other classical variables—i.e., the coordinates of all the nuclei—are evolved forward in time. In a complex molecular system involving many hundreds or thousands of nuclear DOFs, the propagation of these extra "electronic" variables represents a modest increase in computational effort, and yet, the examples presented herein suggest that in many instances the SQC/MM approach will describe the true non-adiabatic quantum dynamics to a reasonable and useful degree of quantitative accuracy.

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11

Wang, Yao-Ting. "Novel wave phenomena in classical vibrations." Thesis, University of Birmingham, 2017. http://etheses.bham.ac.uk//id/eprint/7952/.

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In this thesis, from discrete spring-mass systems to continuous elastic solids, the possibility of achieving topological phases and elastic spin-Hall effect are analytically and numerically discussed. Originating from time-reversal symmetry breaking via applying external fields, a unidirectional and backscattering-immune edge state arises owing to the topological protection. Caused by the effective spin-orbit coupling, the elastic counterpart of spin-Hall effect arises at certain area of the momentum space. Also, the proposed arguments are verified by numerical calculation of practical mechanical crystals and elastic composites. We believe these studies pave the way for the future researches in topological elasticity. On the other hand, PT symmetry, which is a weaker restriction than Hermicity, allows real eigenvalues in a non-Hermitian Hamiltonian. However, it is challenging to introduce the PT condition into quantum mechanical systems. In this thesis, we consider an acoustic metamaterial made of periodically arranged spinning cylinders. By virtue of the rotational Doppler effects, the dispersion relation around the rotating speed of rods is significantly influenced by the rotation. The frequency shifts cause a PT symmetric Hamiltonian so that, at specific points, the spontaneous PT symmetry breaking emerges and exceptional points arise. Lastly a possible setup is discussed for the future experimental realisation.

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12

Luna, Godoy Andres. "The double copy and classical solutions." Thesis, University of Glasgow, 2018. http://theses.gla.ac.uk/8716/.

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The Bern-Carrasco-Johansson (BCJ) double copy, which relates the scattering amplitudes of gauge and gravity theories has been an active area of research for a few years now. In this thesis, we extend the formalism of BCJ to consider classical solutions to the field equations of motion, rather than scattering amplitudes. One first approach relies on a family of solutions to the Einstein equations, namely Kerr-Schild metrics, which linearise the Ricci tensor. Using them we propose a simple ansatz to construct a gauge theory vector field which, in a stationary limit, satisfies linearised Yang-Mills equations. Using such ansatz, that we call the Kerr-Schild double copy, we are able to relate, for example, colour charges in Yang-Mills with the Schwarzschild and Kerr black holes. We extend this formalism to describe the Taub-NUT solution (which is dual to an electromagnetic dyon), perturbations over curved backgrounds and accelerating particles, both in gauge and gravity theories. A second, more utilitarian approach consists on using the relative simplicity of gauge theory to efficiently compute relevant quantities in a theory of perturbative gravity. Working along this lines, we review an exercise by Duff to obtain a spacetime metric using tree-level graphs of a quantum theory of perturbative gravity, and repeat it using a BCJ inspired gravity Lagrangian. We find that the computation is notably simplified, but a new formalism must be developed to remove the unwanted dilaton information, that naturally appears in the double copy.

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13

Chism, William Wesley. "Nonlinear classical dynamics in intense laser-atom physics /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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14

Chen, Chen. "Quantum and Classical Manifestation of Hamiltonian Monodromy." W&M ScholarWorks, 2017. https://scholarworks.wm.edu/etd/1516639669.

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Integrable Hamiltonian systems are said to display nontrivial monodromy if fundamental action-angle loops defined on phase-space tori change their topological structure when the system is carried around a circuit. It was shown in earlier work that this topological change can be seen in families of trajectories of noninteracting particles; however, that work required use of a very abstract flow in phase space. In this dissertation, we show that the same topological change can occur as a result of application of ordinary forces. We also show how this dynamical phenomenon could be observed experimentally in cold atom systems. Almost everything that happens in classical mechanics also shows up in quantum mechanics when we know where to look for it. In the latter half of the dissertation, we show a corresponding change in quantum wave functions: these wave functions change their topological structure in the same way that the action and angle loops change. Also the probability current associated with this wave function follows the angle loop, changing its winding number from 0 to -1.

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15

Breuer, Thomas. "Classical observables, measurement, and quantum mechanics." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339726.

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16

Pittman, Suzanne Michelle. "The Classical-Quantum Correspondence of Polyatomic Molecules." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493526.

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In this thesis, we study the classical-quantum correspondence of polyatomic molecules to further understand their rotational and vibrational behavior. More specifically, we focus on two different scenarios: (1) completely rigid asymmetric top molecules and (2) molecules with purely vibrational behavior. In the first part, we study the dynamics of the two asymmetric top molecules ortho-aminobenzonitrile (OABN) and para-aminobenzonitrile (PABN) in a static electric field. These structural isomers feature differing asymmetries and dipole moments. We show that the dynamics of each molecule depends on the region of phase space of the initial rotational state, the asymmetry of the molecule, and the direction of the dipole. We also show that the ergodicity of the system varies gradually with energy, except where the rotational energy of the initial state is much less than the Stark interaction. We find that both molecules are far from full chaos for total angular momentum quanta $J\in[0,45]$, which counters the results presented in reference 1. However, the initial rotational states in OABN access much more of the available phase space than in PABN, which is a strong cause for the experimental discrepancies observed in the molecular beam deflection experiment of reference 1. In the second part, we address the 0.01-0.1 cm$^{-1}$ peak splittings found in high-resolution IR spectra of polyatomic molecules. Narrow splittings lead to energy flow on extremely long time scales. For polyatomics molecules, there are two main competing mechanisms that occur over such time scales: (1) dynamical tunneling, which connects classically disconnected regions of phase space by tunneling through dynamical barriers, and (2) Arnol'd Diffusion, which describes diffusion in phase space along a resonance network called the Arnol'd web. As a result of the ubiquitous numerical errors that accumulate during numerical studies of Arnol'd Diffusion, we use a physically motivated non-convex Hamiltonian that features fast diffusion along the Arnol'd web. Fast diffusion is a worst case scenario as a competitor to dynamical tunneling. We show how dynamical tunneling dominates fast diffusion, suggesting that dynamical tunneling is the prime culprit of the narrow peak splittings in high-resolution IR spectra of polyatomic molecules.
Physics

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17

Andreev, Anton. "Random matrices, quantum chaos and irreversible classical dynamics." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/36086.

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18

Schmidt, Jan Hendrik. "From perfect predictability to causal indeterminism in classical physics." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624807.

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19

Gundlach, C. "Classical and quantum scalar fields in cosmology." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240140.

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20

Benassi, Costanza. "On classical and quantum lattice spin systems." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/108566/.

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This thesis focuses on some results about quantum and classical lattice spin systems. We study a wide class of two-dimensional quantum models which enjoy a U(1) symmetry. Using the so called complex rotation method we show that the decay of the relevant correlation functions is at least algebraically fast. We provide some examples of relevant models which belong to our class. We review some results present in the literature concerning the so called GriffthsGinibre inequalities for the classical XY model and propose a generalisation to its quantum counterpart. Correlation inequalities indeed hold for the quantum XY model with spin- 1 2 and for the ground state of the spin-1 system. We propose some applications of these results, namely that the infinite volume limit of some correlation functions exists and that it is possible to compare quenched and annealed averages for a quantum XY model with random couplings. We investigate loop representations for O(n) classical spin systems. We propose a generalised random current representation and show its relationship with the Brydges-Fröhlich-Spencer one. We review some conjectures regarding the expected behaviour of these loop models { namely that macroscopic loops appear and their lengths are distributed according to a Poisson-Dirichlet distribution. We propose some arguments in favour of these conjectures for O(n) loop models, using a mix of exact results and heuristic considerations. In order to do so we de ne a stochastic process which is an effective split-merge process for macroscopic loops and we reformulate some correlation functions for the O(2) spin system in terms of loop properties.

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21

Han, Pin 1967. "Chaotic dynamics in classical and quantum mechanical systems." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/282102.

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This dissertation describes mainly researches on the chaotic properties of some classical and quantum mechanical systems. New phenomena like the three-dimensional uniform stochastic web and multiply riddled behavior are presented with numerical results. In the introduction, a short history and basic principles about chaotic dynamical systems are reviewed, which include the concepts of Lyapunov exponents and Poincare sections. In Chapter 2, we first discuss the Hamiltonian system, followed by the perturbation and KAM theory, then introduce Arnold diffusion and the existence of stochastic webs. We close this chapter with a system which can generate a three-dimensional uniform stochastic web. In Chapter 3, the relationship between deterministic chaos and quantum mechanics is studied. A quantum mechanical system called the tetrahedral array of Josephson junctions in which the deterministic chaos can exist is presented. At the end, we generalize such systems to any dimension and expect that chaos should survive in a higher dimensional case. In Chapter 4, in addition to the introduction of the riddled behavior, three examples in which multiply riddled behavior can occur are given and illustrated by graphs. The generalization of these systems is also made and we still expect that multiply riddled behavior will exist in these generalized systems containing more degrees of freedom.

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22

Tuohino, S. (Sasu). "Analysis of nonlinear dynamics in a classical transmon circuit." Bachelor's thesis, University of Oulu, 2017. http://urn.fi/URN:NBN:fi:oulu-201711223138.

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The focus of this thesis is on classical dynamics of a transmon qubit. First, we introduce the basic concepts of the classical circuit analysis and use this knowledge to derive the Lagrangians and Hamiltonians of an LC circuit, a Cooper-pair box, and ultimately we derive Hamiltonian for a transmon qubit. The transmon Hamiltonian is used to derive the equations of motion and also the meaning of these equations is discussed. Finally, the thesis is ended with some numerical results for the transmon equations of motion with a brief interpretation included.

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23

Almaas, Eivind. "Topics in the theory of quantum and classical networks /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486402957195756.

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24

Dellow, Mark Winston. "Quantum and classical transport in semiconductor nanostructures." Thesis, University of Nottingham, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334765.

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Johnson, Mark R. "Molecular rotation and the quantum-classical transition." Thesis, University of Nottingham, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334785.

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26

Dewald, Andrew S. "Semi-Classical Analysis of One-Dimensional Power- Plus Inverse-Power-Law Potentials." Ohio University Honors Tutorial College / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1461689832.

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27

Romero-Rochin, Victor Manuel. "Brownian motion and weak coupling in classical and quantum systems." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14383.

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Lue, Arthur. "Topological structure in classical and quantum SU(2)-Higgs theories." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10373.

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Gallego, Juan. "Two specific applications of semi-classical theories in nuclear physics." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41592.

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Two problems in nuclear physics are investigated using microscopic semi-classical models. The first model, developed to study heavy ion collisions, is based on the Boltzmann-Uehling-Uhlenbeck theory and has been extended to include one-body fluctuations. It has been successfully applied at low and intermediate energies and a comparison between simulations and an experiment done at the Michigan State University cyclotron facility has yielded very good agreement. The second is a nuclear structure model based on the Thomas-Fermi theory and describes nuclear rotations. It has been used to calculate nuclear shapes and limiting angular momenta across the periodic table. It has been found that it breaches the gap between classical Liquid Drop calculations and quantum Hartree-Fock calculations. Agreement with experimental results is satisfactory.

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30

Oreborn, Ulf. "IR spectroscopy for vibrational modes : A semi-classical approach based on classical electrodynamicsand modern quantum mechanics." Thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-78144.

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The atoms of a molecule are always restless and are constantly moving in one way or another.Apart from rotations and translations, they may vibrate in many different modes. They may moveradially toward or from each other, so called stretching. This can be done symmetrically or asymmetrically.The angels between a pair of atoms may change seen from a common atom, so calledbending. This may be done in a common plane like scissoring or rocking, or out of plane like waggingor twisting.Anyhow, it is of interest to study these movements — since they work as a fingerprint of themolecule. Two methods for studying these behavior are Raman- and IR-spectroscopy. Some vibrations,such as symmetric stretching, are mainly seen using Raman spectroscopy (Raman active); whilebending and asymmetric stretching are primarily detected by IR spectroscopy (IR active) However,all types of combinations exist, so there are no watertight compartments between them. Instead, themethods are complementary to each other.In this article, I build up a semi-classical model of the vibrations for the case of IR-spectroscopy,and implement it in Mathematica to test the model. It is based on classical physics such as vibratingspringmechanics and Maxwell’s electrodynamics, but the vibrations are computed using modernphysics quantum mechanics. Since there are several atoms involved (say N) and the vibrations betweenthese atoms are in 3 dimensions, this may be described by 3N coupled 1-dimensional harmonicoscillators. By suitable transformations these oscillators are uncoupled, but results in a wave functionwhich is the product of 3N eigenfunctions, one for each oscillator’s eigenfunction of a given mode.Adding a time varying electric field (the IR-illumination), we need the time dependent SchrödingerEquation, where the potential is time varying sinusoidally. Necessary perturbation theory for suchtime dependency is described in some details, and an expression for the dipole moment needed forthe estimation of the IR absorption by the molecule is given. However, the model also depend onthe electrons’ orbitals and the total bond energy within the molecule. These are given by a DFT(Density Functional Theory) computer code, which serve as input to my calculations.The standard approach to do IR-spectrum calculations is to use DFT also to move the atoms inthe directions of the vibrations and compute how the dipole moments for the molecules change. Mymethod is instead to use SE directly for the many vibrating particle problem based on the knownexact solutions to the one dimensional harmonic oscillator. This is followed by perturbation theoryfor the time dependency of the IR-field to get the dipole moments.The drawback with my approach is that the electron clouds around the atoms are not affectedat all by the vibrations, they just follow the nuclei. The DFT approach takes care of the changingelectron density functions. However, my approach solves the vibrational problem more directly withthe SE and takes care of the time dependent potential using perturbation theory.Computational results for seven molecules containing between 2 and 11 atoms are shown andcompared with spectroscopic parameters and measurements compiled by established references. Theconclusion is that my model and computational output are well in accordance with these references,and some shortcomings and possible enhancements are pointed out. The drawback with the electronclouds might affect the absorption levels of the vibrations rather than their energies and are possiblein future work to take into account.

Till minne av Ulf Oreborn (1957-2018)

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31

Bromley, Thomas R. "Navigating the quantum-classical frontier." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/43333/.

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The description of a quantum system follows a fundamentally different paradigm to that of a classical system, leading to unique yet counter-intuitive properties. In this thesis we consider some of these unique properties, here termed simply the quantum. We focus on understanding some important types of the quantum: quantum coherence and quantum correlations, as well as quantum entanglement as an important subclass of quantum correlations. Our objective is to investigate how to quantify the quantum, what it can be used for, and how it can be preserved in the adverse presence of noise. These findings help to clarify the frontier between quantum and classical systems, a crucial endeavour for understanding the applications and advantageous features of the quantum world.

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32

Cornell, Brennan. "An introduction to classical gauge theory in mathematics and physics." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/27583.

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We describe some aspects of classical gauge theory from the perspective of connections on vector bundles. We begin by examining classical electromagnetism, and use it to motivate the development of gauge theory on vector bundles. If G is a Lie group, we review some of the theory of vector G-bundles, their associated principal G-bundles, and the related theory of connections. We then discuss the idea of gauge transformations on principal and vector G-bundles, and view electromagnetism as an example of an abelian gauge theory. We briefly review the action principle in order to describe non-abelian gauge theories such as the Yang-Mills equation. Finally, we present the main results from an article by John Baez entitled "Higher Yang-Mills Theory" where he attempts to abstract Yang-Mills theory using some concepts from category theory.

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33

Lundberg, Erik. "Problems in Classical Potential Theory with Applications to Mathematical Physics." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3220.

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In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters. Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem). Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is analytic continuability of the solution outside its natural domain. Chapter 4 concerns certain complex-valued harmonic functions and their zeros. The special cases we consider apply directly in astrophysics to the study of multiple-image gravitational lenses.

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34

Gravanis, Elias. "Topics in D-membrane physics and membrane inspired classical gravity." Thesis, King's College London (University of London), 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441973.

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35

Atkins, Keith Michael. "Non-linearity and chaos in simple classical quantum systems." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302809.

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36

Smart, Sheila Ann. "The interaction between non-classical light and atomic systems." Thesis, Queen's University Belfast, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317525.

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37

Kimpton, Ian. "Classical and quantum modifications of gravity." Thesis, University of Nottingham, 2013. http://eprints.nottingham.ac.uk/13430/.

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Einstein’s General Relativity has been our best theory of gravity for nearly a century, yet we know it cannot be the final word. In this thesis, we consider modifications to General Relativity, motivated by both high and low energy physics. In the quantum realm, we focus on Horava gravity, a theory which breaks Lorentz invariance in order to obtain good ultraviolet physics by adding higher spatial derivatives to the action (improving propagator behaviour in loops) but not temporal (avoiding Ostrogradski ghosts). By using the Stückelberg trick, we demonstrate the necessity of introducing a Lorentz violating scale into the theory, far below the Planck scale, to evade strong coupling concerns. Using this formalism we then show explicitly that Horava gravity breaks the Weak Equivalence Principle, for which there are very strict experimental bounds. Moving on to considering matter in such theories, we construct DiffF(M) invariant actions for both scalar and gauge fields at a classical level, before demonstrating that they are only consistent with the Equivalence Principle in the case that they reduce to their covariant form. This motivates us to consider the size of Lorentz violating effects induced by loop corrections of Horava gravity coupled to a Lorentz invariant matter sector. Our analysis reveals potential light cone fine tuning problems, in addition to evidence that troublesome higher order time derivatives may be generated. At low energies, we demonstrate a class of theories which modify gravity to solve the cosmological constant problem. The mechanism involves a composite metric with the square root of its determinant a total derivative or topological invariant, thus ensuring pieces of the action proportional to the volume element do not contribute to the dynamics. After demonstrating general properties of the proposal, we work through a specific example, demonstrating freedom from Ostrogradski ghosts at quadratic order (in the action) on maximally symmetric backgrounds. We go on to demonstrate sufficient conditions for a theory in this class to share a solution space equal to that of Einstein’s equations plus a cosmological constant, before determining the cosmology these extra solutions may have when present.

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38

Schoellmann, Volker. "Quantum classical interactions of a superconducting quantum interference device." Thesis, University of Sussex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264634.

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39

Lin, Joseph Xiao. "Quantum blackjack : quantum strategies and advantages in games with limited classical communication." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120220.

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Thesis: S.B., Massachusetts Institute of Technology, Department of Physics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-60).
In this thesis, we examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we particularly focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed from the first-mover to the late-mover. Within this setting, optimal usage of quantum entanglement is explored, and conditions of quantum advantage over classical strategies are examined. Furthermore, theoretical, computational, and experimental techniques are presented that can be useful in the analysis and implementation of quantum strategies in these types of games.
by Joseph Xiao Lin.
S.B.

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40

Magill, Peter David. "Classical resonance in vibrationally inelastic collisions of diatomic molecules : experiments and modeling." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14727.

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41

Spellmeyer, Neal W. (Neal Warren) 1970. "Rydberg atoms in an oscillating field : extracting classical motion from quantum spectra." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47410.

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42

Dalzell, Alexander M. "Lower bounds on the classical simulation of quantum circuits for quantum supremacy." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/111859.

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Thesis: S.B., Massachusetts Institute of Technology, Department of Physics, 2017.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 91-93).
Despite continued experimental progress, no task has yet been performed on quantum technology that could not also have been performed quickly on today's classical computers. One proposed path toward achieving this milestone, which is often referred to as quantum supremacy, is to perform specific types of quantum circuits for which it is guaranteed, under plausible complexity theoretic conjectures, that any classical approximate weak simulation algorithm for these circuits must take more than polynomial time. Instantaneous quantum (IQP) circuits and Quantum Approximate Optimization Algorithm (QAOA) circuits are examples of circuits with this guarantee under the assumption that the polynomial hierarchy (PH) does not collapse. However, these arguments do not communicate how large these quantum circuits must be built before simulating them is hard in practice. We show how a fine-grained version of this assumption involving the PH leads to a fine-grained lower bound on the simulation time for IQP and QAOA circuits. Using the lower bound, we conclude that IQP circuits must contain roughly 1700 qubits, and QAOA circuits must contain roughly 7100 qubits before their simulation would be guaranteed to be intractable on today's fastest supercomputers. Additionally, we apply the same logic to find an asymptotic lower bound on the classical weak simulation of Clifford + T circuits with n qubits, m Clifford gates, and t T gates, concluding that any simulation with runtime of the form poly(n;m)2[gamma]t must have [gamma] > 1/135 [approximately equal] 0:0074. The best existing algorithm of this form [gamma] [approximately equal] 0:228.
by Alexander M. Dalzell.
S.B.

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43

Marshall, Richard John. "Semi classical description of a finite temperature Bose Einstein condensate." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249508.

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44

Yu, Lin-Yu. "Aspects of deterministic chaos in classical and quantum mechanical systems." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186219.

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We have found some fresh and important results in both classical and quantum dynamical systems. The understanding of the order within Hamiltonian chaos is enhanced particularly by the studies of novel systems that generate the stochastic web, both in classical and quantum systems. The most significant result in this dissertation is established by our counter examples to the common belief in the absence of deterministic chaos in quantum systems. Our examples deal with a periodically kicked quantum spin (PKQS) and with the superconducting systems described by a time-dependent Hamiltonian and a time-independent one. The asymptotic property of the Lyapunov exponents in Hamiltonian systems is also intensively investigated.

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45

Qubain, Edward George. "A quantum phase space with classical time evolution /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008424.

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46

Harrow, Aram (Aram Wettroth) 1980. "Applications of coherent classical communication and the Schur transform to quantum information theory." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/34973.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 167-176).
Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information not only yields new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory-coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half. The first part of this thesis (Chapters 1-4) is in fact built around two loosely overlapping themes. One is quantum Shannon theory, a broad class of coding theorems that includes Shannon and Schumacher data compression, channel coding, entanglement distillation and many others. The second, more specic, theme is the concept of using unitary quantum interactions to communicate between two parties. We begin by presenting new formalism: a general framework for Shannon theory that describes communication tasks in terms of fundamental information processing resources, such as entanglement and classical communication. Then we discuss communication with unitary gates and introduce the concept of coherent classical communication, in which classical messages are sent via some nearly unitary process. We find that coherent classical communication can be used to derive several new quantum protocols and unify them both conceptually and operationally with old ones.
(cont.) Finally, we use these new protocols to prove optimal trade-o curves for a wide variety of coding problems in which a noisy channel or state is consumed and two noiseless resources are either consumed or generated at some rate. The second half of the thesis (Chapters 5-8) is based on the Schur transform, which maps between the computational basis of (Cd)n and a basis (known as the Schur basis) which simultaneously diagonalizes the commuting actions of the symmetric group Sn and the unitary group Ud. The Schur transform is used as a subroutine in many quantum communication protocols (which we review and further develop), but previously no polynomial-time quantum circuit for the Schur transform was known. We give such a polynomial-time quantum circuit based on the Clebsch-Gordan transform and then give algorithmic connections between the Schur transform and the quantum Fourier transform on Sn.
by Aram Wettroth Harrow.
Ph.D.

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47

Kobayashi, Kohjiro. "Topics in classical and quantum phase transitions." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1199254396.

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48

Smith, Mark James. "Quasi-classical theory of weakly anisotropic superconductors." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3297/.

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This thesis starts by reviewing superconductivity in one-dimension where fluctuations cause a loss of supercurrent due to an intrinsic resistance. Solved via the Ginzburg-Landau equations, the theory of thermally activated phase slips given by Langer and Ambegaokar is outlined. In turn this leads to the investigation of superconductivity via a microscopic approach, in particular the quasi-classic green’s functions of Eilenberger. The Eilenberger equations are derived and considered in the dirty and weakly anisotropic limits which provides a simple derivation of the Ginzburg-Landau equations near the transition temperature. This prompts an extended derivation which includes the non-linear terms normally removed in deriving the Ginzburg-Landau equations. This is required for calculating effects at temperatures below the transition temperature. These quasi-classic equations of weakly anisotropic superconductors are first written for arbitrary temperature and impurity concentration then limited to the pure and dirty cases. The latter being simplified to zero temperature and solved in the context of thermally activated phase slips.

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Godskesen, Simon. "Geometric Phases in Classical and Quantum Systems." Thesis, Uppsala universitet, Teoretisk fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388414.

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We are accustomed to think the phase of single particle states does not matter. After all, the phase cancels out when calculating physical observables. However, the geometric phase can cause interference even in single particle states and can be measured. Berry’s phase is a geometric phase the system accumulates as its time-dependent Hamiltonian is subjected to closed adiabatic excursion in parameter space. In this report, we explore how Berry’s phase manifests itself in various fields of physics, both classical and quantum mechanical. The Hannay angle is a classical analogue to Berry’s phase and they are related by a derivative. The Aharonov-Bohm effect is a manifestation of Berry’s phase. Net rotation of deformable bodies in the language of gauge theory can be translated as a Berry phase. The well-known BornOppenheimer approximation is a molecular Aharonov-Bohm effect and is another manifestation of Berry’s Phase.

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Tanaka, Kaori. "Shell structure and classical orbits in mesoscopic systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ30172.pdf.

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Dissertations / Theses on the topic 'Classical physics'

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