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Dissertations / Theses on the topic 'Hamiltonian operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 March 2023

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1

Dejon, Alexander. "Stochastic image reconstruction as ground state of Hamiltonian operators." [S.l. : s.n.], 2006. http://madoc.bib.uni-mannheim.de/madoc/volltexte/2007/1394/.

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2

Savoldi, Andrea. "On Poisson structures of hydrodynamic type and their deformations." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20769.

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Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type systems, are one of the most important classes of nonlinear partial differential equations in the modern theory of integrable systems. They naturally arise in continuum mechanics and in a wide range of applications, both in pure and applied mathematics. Deep connections between the mathematical theory of hydrodynamic type systems with differential geometry, firstly revealed by Riemann in the nineteenth century, have been thoroughly investigated in the eighties by Dubrovin and Novikov. They intr

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3

Schäfer, Ingolf. "Representation theoretical construction of the classical limit and spectral statistics of generic Hamiltonian operators." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982122179.

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4

Musumbu, Dibwe Pierrot. "The metric for non-Hermitian Hamiltonians : a case study." Thesis, Stellenbosch : Stellenbosch University, 2006. http://hdl.handle.net/10019.1/17403.

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Thesis (MSc)--University of Stellenbosch, 2006.<br>ENGLISH ABSTRACT: We are studying a possible implementation of an appropriate framework for a proper non- Hermitian quantum theory. We present the case where for a non-Hermitian Hamiltonian with real eigenvalues, we define a new inner product on the Hilbert space with respect to which the non-Hermitian Hamiltonian is Quasi-Hermitian. The Quasi-hermiticity of the Hamiltonian introduces the bi-orthogonality between the left-hand eigenstates and the right-hand eigenstates, in which case the metric becomes a basis transformation. We use the n

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5

Rhind, Elian O. T. "Topics on Hamiltonian dynamics related to symbols of certain Schrodinger operators associated with generators of Levy processes." Thesis, Swansea University, 2018. https://cronfa.swan.ac.uk/Record/cronfa40877.

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L ́evy processes give rise to positivity preserving one-parameter operator semigroups, a source for many studies. They are completely characterised by their characteristic exponent which is continuous and negative definite. Using Fourier analysis it can be found that also characterises the corresponding semigroup and its generator. An interesting case is where e−tψ ∈ L1 (Rn) for all t > 0. This allows us to represent the semigroup as a convolution operator. Through this transition densities are introduced, who are greatly relevant in research associated with probability theory. As a continuous

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6

Pester, Cornelia. "Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601470.

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When the eigenvalues of a given eigenvalue problem are symmetric with respect to the real and the imaginary axes, we speak about a Hamiltonian eigenvalue symmetry or a Hamiltonian structure of the spectrum. This property can be exploited for an efficient computation of the eigenvalues. For some elliptic boundary value problems it is known that the derived eigenvalue problems have this Hamiltonian symmetry. Without having a specific application in mind, we trace the question, under which assumptions the spectrum of a given quadratic eigenvalue problem possesses the Hamiltonian structure.

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7

SILVA, VICTOR LOPES DA. "A PROJECTOR OPERATOR FORMALISM TO SOLVE THE ANDERSON HAMILTONIAN." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23245@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>Nesta dissertação propomos um formalismo de operadores de projeção para obter a energia do estado fundamental do Hamiltoniano da Impureza de Anderson com repulsão Coulombiana U infinita. Este formalismo consiste em projetar o espaço de Hilbert em um subespaço de uma unica função correspondente ao estado fundamental do mar de Fermi, onde uma versão renormalizada do Hamiltoniano opera. A energia do estado fundamental pode

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8

Hyder, Asif M. "Green's operator for Hamiltonians with Coulomb plus polynomial potentials." California State University, Long Beach, 2013.

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9

Ristow, Gerald H. "A quantum mechanical investigation of the Arnol'd cat map." Thesis, Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/27568.

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10

Yildirim, Yolcu Selma. "Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31649.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Harrell, Evans; Committee Member: Chow, Shui-Nee; Committee Member: Geronimo, Jeffrey; Committee Member: Kennedy, Brian; Committee Member: Loss, Michael. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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11

Senese, Frederick A. "A tensor product decomposition of the many-electron Hamiltonian." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54413.

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A new direct full variational approach is described. The approach exploits a tensor (Kronecker) product construction of the many-electron Hamiltonian and has a number of computational advantages. Explicit assembly and storage of the Hamiltonian matrix is avoided by using the Kronecker product structure to form matrix-vector products directly from the molecular integrals. Computation-intensive integral transformations and formula tapes are unnecessary. The wavefunction is expanded in terms of spin-free primitive kets rather than Slater determinants or configuration state functions and is equiva

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12

Gu, Xiang. "Hamiltonian structures and Riemann-Hilbert problems of integrable systems." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7677.

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We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation. In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarc

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13

Gaim, Wolfgang [Verfasser]. "Higher Order Semiclassical Approximations for Hamiltonians with Operator-Valued Symbols / Wolfgang Gaim." Tübingen : Universitätsbibliothek Tübingen, 2021. http://d-nb.info/1235399141/34.

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14

Marchetti, Iacopo. "Dal formalismo hamiltoniano ai fondamenti della meccanica quantistica." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19229/.

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In questa tesi, dopo aver ricordato l’equazione di Eulero-Lagrange e le equazioni di Hamilton-Jacobi, si cerca di descrivere un sistema fisico quantistico seguendo i postulati di Dirac e von Neumann, per enunciare al contempo qualche risultato classico. Vengono poi trattati gli operatori pseudo-differenziali per effettuare la siddetta quantizzazione di Weyl. Infine viene studiato il problema di trovare lo spettro dell’oscillatore armonico.

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15

Conte, Riccardo. "A dynamical approach to the calculation of thermal reaction rate constants." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85794.

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16

Sambou, Diomba. "Accumulation spectrale pour les Hamiltoniens quantiques magnétiques." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-01059664.

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Dans cette thèse on s'interesse à l'étude de phénomènes d'accumultation spectrale de certains opérateurs issus de la physique quantique à savoir les opérateurs de Schrödinger, de Pauli, et de Dirac. Typiquement, ces opérateurs apparaissent dans la modélisation de certains problèmes de physique sous forme d'équations d'évolution. Selon les contraintes du problème physique, ils peuvent être associés ou non à un champ magnétique pouvant être constant ou non constant. Le cadre où le champ magnétique est dit admissible est celui que nous allons considérer (en dimension 3). Ce dernier cadre inclut e

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17

Pasqua, Michael. "Analisi spettrale di operatori differenziali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12034/.

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L'elaborato è finalizzato a presentare l'analisi degli operatori differenziali agenti in meccanica quantistica e la teoria degli operatori di Sturm-Liouville. Nel primo capitolo vengono analizzati gli operatori differenziali e le relative proprietà. Viene studiata la loro autoaggiunzione su vari domini con diverse condizioni al contorno e vengono tratte delle conclusioni sul loro significato come osservabili. Nel secondo capitolo viene presentato il concetto di spettro e vengono studiate le sue proprietà.Vengono poi analizzati gli spettri degli operatori precedentemente introdotti. Nell'ut

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18

Cao, Zhenwei. "Quantum evolution: The case of weak localization for a 3D alloy-type Anderson model and application to Hamiltonian based quantum computation." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/19205.

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Over the years, people have found Quantum Mechanics to be extremely useful in explaining various physical phenomena from a microscopic point of view. Anderson localization, named after physicist P. W. Anderson, states that disorder in a crystal can cause non-spreading of wave packets, which is one possible mechanism (at single electron level) to explain metalinsulator transitions. The theory of quantum computation promises to bring greater computational power over classical computers by making use of some special features of Quantum Mechanics. The first part of this dissertation considers a 3D

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19

Bower, Peter Velling. "Solid state nuclear magnetic resonance techniques for determining structure in proteins and peptides /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/8663.

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20

Fassari, Silvestro. "Spectral properties of relativistic and non-relativistic Krönig- Penney Hamiltonians with short-range impurities." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54524.

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In this work, we investigate the spectrum of the non-relativistic Krönig-Penney Hamiltonian H<sub>α</sub>= -d²/dx² +αΣ<sub>m∈Z</sub>δ(-(2m+1)π) perturbed by a short-range potential λW and the spectrum of its relativistic counterpart obtained by replacing the Schrödinger Hamiltonian H<sub>α</sub> with its relativistic analogue H̅<sub>α</sub>. The interesting feature of both spectra is that they have gaps and that bound states may occur in such gaps as a consequence of the presence of the short-range potential representing the impurity. Such bound states, often called "impurity states" in the s

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21

Bressler, Barry Lee. "An application of the Liouville resolvent method to the study of fermion-boson couplings." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49994.

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The Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a Hilbert space and that represent transitions between many-particle states. These commutators produce linear combinations of stepping operators, so the results can be arrayed as matrix elements of the Liouville operator L̂ in the Hilbert space of stepping operators. The resulting L̂ matrix is usually of

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22

La, Fuente Gravy Laurent. "Automorphismes hamiltoniens d'un produit star et opérateurs de Dirac Symplectiques." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209411.

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Cette thèse est consacrée à l'étude de deux sujets de géométrie symplectique inspirés<p>de la physique mathématique. Les thèmes que nous développerons mettent en évidence certaines <p>connexions avec la topologie symplectique d'une part, la géométrie Riemannienne d'autre part.<p><p>Dans la partie 1, nous étudions la quantification par déformation formelle d'une variété <p>symplectique, à l'aide de produits star. Nous définissons le groupe des automorphimes<p>hamiltoniens d'un produit star formel. En nous inspirant d'idées de Banyaga, nous <p>identifions ce groupe comme étant le noyau d'un morp

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23

Holtz, Susan Lady. "Liouville resolvent methods applied to highly correlated systems." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49795.

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24

Junkermeier, Chad Everett. "Iteration Methods For Approximating The Lowest Order Energy Eigenstate of A Given Symmetry For One- and Two-Dimensional Systems." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/85.

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Using the idea that a quantum mechanical system drops to its ground state as its temperature goes to absolute zero several operators are devised to enable the approximation of the lowest order energy eigenstate of a given symmetry; as well as an approximation to the energy eigenvalue of the same order.

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25

INFERRERA, Guglielmo. "From classical to operatorial models." Doctoral thesis, Università degli Studi di Palermo, 2023. https://hdl.handle.net/10447/580046.

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Mathematical models for the collective dynamics of interacting and spatially distributed populations find applications in several contexts (biology, ecology, social sciences). Their formulation depends primarily on the (continuous or discrete) description of the space. Reaction-diffusion equations have been widely used in bioecology (morphogenesis, migration of biological species, tumor growth, neuro-degenerative diseases) and in the social sciences (diffusion of opinions or decisionmaking processes), and exhibit complex behaviors (propagation of oscillatory phenomena, pattern formation

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26

Barber, IV John Letherman. "Application of optimal prediction to molecular dynamics." Berkeley, Calif. : Oak Ridge, Tenn. : Lawrence Berkeley National Laboratory ; distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2004. http://www.osti.gov/servlets/purl/838987-xpCsPP/native/.

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Thesis (Ph.D.); Submitted to the University of California at Berkeley, Berkeley, CA 94720 (US); 1 Dec 2004.<br>Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56842" Barber IV, John Letherman. USDOE Director. Office of Science. Advanced Scientific Computing Research (US) 12/01/2004. Report is also available in paper and microfiche from NTIS.

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27

Fiala, Jan. "DNA výpočty a jejich aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-412902.

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This thesis focuses on the design and implementation of an application involving the principles of DNA computing simulation for solving some selected problems. DNA computing represents an unconventional computing paradigm that is totally different from the concept of electronic computers. The main idea of DNA computing is to interpret the DNA as a medium for performing computation. Despite the fact, that DNA reactions are slower than operations performed on computers, they may provide some promising features in the future. The DNA operations are based on two important aspects: massive parallel

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28

Ciavatta, Alessandro. "Teoria della superconduttività e soluzione numerica dell’equazione della gap BCS." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23633/.

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La superconduttività è uno stato della materia caratterizzato dall'assenza di resistività DC. Durante la transizione di fase il materiale espelle dall'interno il campo magnetico applicato, diventando un perfetto diamagnete; questo è noto come effetto Meissner-Ochsenfeld. La prima teoria presentata in questa tesi è la teoria di London, che spiega l'effetto Meissner all'interno delle due equazioni fenomenologiche di London. In seguito viene presentata la teoria di Ginzburg-Landau, che estende la teoria di Landau sulle transizioni di fase del secondo ordine e ricava una dipendenza della densità d

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29

Dejon, Alexander [Verfasser]. "Stochastic image reconstruction as ground state of hamiltonian operators / vorgelegt von Alexander Dejon." 2007. http://d-nb.info/983633266/34.

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30

Schäfer, Ingolf [Verfasser]. "Representation theoretical construction of the classical limit and spectral statistics of generic Hamiltonian operators / von Ingolf Schäfer." 2006. http://d-nb.info/982122179/34.

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31

Le, Roux Jaco. "Linear optical quantum computing, associated Hamilton operators and computer algebra implementations." Thesis, 2012. http://hdl.handle.net/10210/5000.

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M.Sc.<br>In this thesis we study the techniques used to calculate the Hamilton operators related to linear optical quantum computing. We also discuss the basic building blocks of linear optical quantum computing (LOQC) by looking at the logic gates and the physical instruments of which they are made.

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32

Assanioussi, Mehdi. "New dynamics for canonical loop quantum gravity." Doctoral thesis, 2016.

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Canonical loop quantum gravity (LQG) is a canonical quantization of general relativity in its Hamiltonian formulation, which has successfully completed the construction of a kinematical Hilbert space and the implementation of the Gauss constraints and the spatial diffeomorphism constraints. In the first part of this thesis I give a general introduction to the Ashtekar– Barbero Hamiltonian formulation of general relativity and a detailed overview of the LQG program. In the second part, I present a new approach for quantizing the Hamiltonians in various LQG models. The result allows to make a st

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33

Simmons, Jill. "Closure operations and Hamiltonian properties of independent and total domination critical graphs." 2005. http://hdl.handle.net/1828/658.

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34

Mäkinen, Ilkka. "Dynamics in Canonical Models of Loop Quantum Gravity." Doctoral thesis, 2019. https://depotuw.ceon.pl/handle/item/3489.

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Loop quantum gravity is a tentative but relatively well-developed attempt at a manifestly background independent theory of quantum gravity. The kinematical structure of loop quantum gravity is well understood, with the elementary kinematical states of the theory having a physically appealing interpretation as states describing quantized, discrete spatial geometries. However, formulating the dynamics of the theory in a fully satisfactory way has proven to be surprisingly challenging, and to a significant extent, the issue of dynamics still remains an open problem in loop quantum gravity. In th

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35

Scott, Derek Douglas. "An investigation of parity and time-reversal symmetry breaking in tight-binding lattices." Thesis, 2014. http://hdl.handle.net/1805/6106.

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Indiana University-Purdue University Indianapolis (IUPUI)<br>More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the ef

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36

Hume, Leigh Robert. "Return to equilibrium in the XY-model." Phd thesis, 1988. http://hdl.handle.net/1885/138524.

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37

Israelsson, Anders. "Mathematical Foundations of Quantum Mechanics." Thesis, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-210078.

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