Дисертації з теми "Solvable models"
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de, Woul Jonas. "Fermions in two dimensions and exactly solvable models." Doctoral thesis, KTH, Matematisk fysik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-50471.
QC 20111207
Shum, Christopher. "Solvable Particle Models Related to the Beta-Ensemble." Thesis, University of Oregon, 2013. http://hdl.handle.net/1794/13302.
Brown, Jeffrey Michael. "Exactly Solvable Light-Matter Interaction Models for Studying Filamentation Dynamics." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/612844.
Dey, Sanjib. "Solvable models on noncommutative spaces with minimal length uncertainty relations." Thesis, City University London, 2014. http://openaccess.city.ac.uk/5917/.
Wagner, Fabian. "Exactly solvable models, Yang-Baxter algebras and the algebraic Bethe Ansatz." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621030.
Sinitsyn, Nikolai. "Generalizations of the Landau-Zener theory in the physics of nanoscale systems." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/216.
Downing, Charles Andrew. "Quantum confinement in low-dimensional Dirac materials." Thesis, University of Exeter, 2015. http://hdl.handle.net/10871/17215.
Himberg, Benjamin Evert. "Accelerating Quantum Monte Carlo via Graphics Processing Units." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/728.
Aldarak, Helal. "Spin chain with A and D-type algebra and Coderivative." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCK100.
This thesis is concerned with the study of specific integrable quantum system ``spin chains'' with different symmetries. These spin chains are considered toy models of some two-dimensional field theories when the size of these models is finite. In particular, some functional relations in these spin chains were generalized to field theories using a finite number of equations to find their spectrum.We start this thesis by describing the well-studied rational spin chain with GL(n) symmetry using the Coderivative operator to build a polynomial ``Q-operator'' that allows us to diagonalize the Hamiltonian. We show the equivalence with another construction relying on representations that are explicit in terms of harmonic oscillators.We then study a lesser-known spin chain with SO(2r) symmetry. We build the ``Q-operator'' for the known representations. Then we attempt several methods to build said operators for general representations. These attempts clearly show that, on the one hand, the attempts strongly suggest the Coderivative is not sufficient to describe general representations in auxiliary space. On the other hand, we hope they will help to find what additional tools may allow us to describe them
Thiery, Thimothée. "Analytical methods and field theory for disordered systems." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE017/document.
This thesis presents several aspects of the physics of disordered elastic systems and of the analytical methods used for their study.On one hand we will be interested in universal properties of avalanche processes in the statics and dynamics (at the depinning transition) of elastic interfaces of arbitrary dimension in disordered media at zero temperature. To study these questions we will use the functional renormalization group. After a review of these aspects we will more particularly present the results obtained during the thesis on (i) the spatial structure of avalanches and (ii) the correlations between avalanches.On the other hand we will be interested in static properties of directed polymers in 1+1 dimension, and in particular in observables related to the KPZ universality class. In this context the study of exactly solvable models has recently led to important progress. After a review of these aspects we will be more particularly interested in exactly solvable models of directed polymer on the square lattice and present the results obtained during the thesis in this direction: (i) classification ofBethe ansatz exactly solvable models of directed polymer at finite temperature on the square lattice; (ii) KPZ universality for the Log-Gamma and Inverse-Beta models; (iii) KPZ universality and non-universality for the Beta model; (iv) stationary measures of the Inverse- Beta model and of related zero temperature models
Lahtinen, Ville Tapani. "Interacting non-Abelian anyons in an exactly solvable lattice model." Thesis, University of Leeds, 2010. http://etheses.whiterose.ac.uk/1026/.
Moosavi, Per. "An Exactly Solvable Gauge Theory Model for Correlated Fermions in 3+1 Dimensions." Thesis, KTH, Teoretisk fysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-145032.
Takieddin, Khaled. "Prediction of hydrate and solvate formation using knowledge-based models." Thesis, University of East Anglia, 2016. https://ueaeprints.uea.ac.uk/62903/.
Krajenbrink, Alexandre. "Beyond the typical fluctuations : a journey to the large deviations in the Kardar-Parisi-Zhang growth model." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE021.
Throughout this Ph.D thesis, we will study the Kardar-Parisi-Zhang (KPZ) stochastic growth model in 1+1 dimensions and more particularly the equation which governs it. The goal of this thesis is two-fold. Firstly, it aims to review the state of the art and to provide a detailed picture of the search of exact solutions to the KPZ equation, of their properties in terms of large deviations and also of their applications to random matrix theory or stochastic calculus. Secondly, is it intended to express a certain number of open questions at the interface with integrability theory, random matrix theory and Coulomb gas theory.This thesis is divided in three distinct parts related to (i) the exact solutions to the KPZ equation, (ii) the short time solutions expressed by a Large Deviation Principle and the associated rate functions and (iii) the solutions at large time and their extensions to linear statistics at the edge of random matrices.We will present the new results of this thesis including (a) a new solution to the KPZ equation at all times in a half-space, (b) a general methodology to establish at short time a Large Deviation Principle for the solutions to the KPZ equation from their representation in terms of Fredholm determinant and (c) the unification of four methods allowing to obtain at large time a Large Deviation Principle for the solution to the KPZ equation and more generally to investigate linear statistics at the soft edge of random matrices
Alam, Imam Tashdid-Ul. "Discrete holomorphicity in solvable lattice models." Phd thesis, 2014. http://hdl.handle.net/1885/156195.
"Solvable Time-Dependent Models in Quantum Mechanics." Doctoral diss., 2011. http://hdl.handle.net/2286/R.I.8843.
Dissertation/Thesis
Ph.D. Applied Mathematics for the Life and Social Sciences 2011
Rychnovsky, Mark. "Some Exactly Solvable Models And Their Asymptotics." Thesis, 2021. https://doi.org/10.7916/d8-3pga-pm90.
Geojo, K. G. "Quantum Hamilton-Jacobi study of wave-functions and energy spectrum of solvable and quasi-exactly solvable models." Thesis, 2003. http://hdl.handle.net/2009/1000.
Wang, Zitao. "Topological Phases of Matter: Exactly Solvable Models and Classification." Thesis, 2019. https://thesis.library.caltech.edu/11488/14/Wang_Zitao_2019.pdf.
In this thesis, we study gapped topological phases of matter in systems with strong inter-particle interaction. They are challenging to analyze theoretically, because interaction not only gives rise to a plethora of phases that are otherwise absent, but also renders methods used to analyze non-interacting systems inadequate. By now, people have had a relatively systematic understanding of topological orders in two spatial dimensions. However, less is known about the higher dimensional cases. In Chapter 2, we will explore three dimensional long-range entangled topological orders in the framework of Walker-Wang models, which are a class of exactly solvable models for three-dimensional topological phases that are not known previously to be able to capture these phases. We find that they can represent a class of twisted discrete gauge theories, which were discovered using a different formalism. Meanwhile, a systematic theory of bosonic symmetry protected topological (SPT) phases in all spatial dimensions have been developed based on group cohomology. A generalization of the theory to group supercohomology has been proposed to classify and characterize fermionic SPT phases in all dimensions. However, it can only handle cases where the symmetry group of the system is a product of discrete unitary symmetries. Furthermore, the classification is known to be incomplete for certain symmetries. In Chapter 3, we will construct an exactly solvable model for the two-dimensional time-reversal-invariant topological superconductors, which could be valuable as a first attempt to a systematic understanding of strongly interacting fermionic SPT phases with anti-unitary symmetries in terms of exactly solvable models. In Chapter 4, we will propose an alternative classification of fermionic SPT phases using the spin cobordism theory, which hopefully can capture all the phases missing in the supercohomology classification. We test this proposal in the case of fermionic SPT phases with Z2 symmetry, where Z2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimensions less than or equal to 3.
Fridkin, Vladislav. "Reflection equations in exactly solvable models of statistical mechanics." Phd thesis, 1999. http://hdl.handle.net/1885/144940.
Caiazzo, Antonio. "Analytically solvable models for equilibrium and dynamical properties of glassy systems." Tesi di dottorato, 2002. http://www.fedoa.unina.it/50/1/Caiazzo.pdf.
Chua, Victor Kooi Ming. "Explorations into the role of topology and disorder in some exactly solvable Hamiltonians." 2013. http://hdl.handle.net/2152/21322.
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Ellem, Richard Mark. "The thermodynamic Bethe Ansatz approach to exactly solvable models in statistical mechanics and quantum field theory." Phd thesis, 1998. http://hdl.handle.net/1885/143945.
Palacios, Guillaume [Verfasser]. "Exactly solvable models of strongly correlated systems : application to one-dimensional cold gases and quantum impurity problems / von Guillaume Palacios." 2007. http://d-nb.info/987030949/34.
Ryabov, Artem. "Stochastická dynamika a energetika biomolekulárních systémů." Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-338023.
Lemay, Jean-Michel. "Polynômes orthogonaux : processus limites et modèles exactement résolubles." Thèse, 2019. http://hdl.handle.net/1866/23476.
This thesis is concerned with the study of families of orthogonal polynomials and their connection to exactly solvable models. It comprises two parts. In the first one, four novel families of orthogonal polynomials are caracterized through limit processes applied to families belonging to the Askey and Bannai-Ito schemes. Singular truncations of the Wilson and Askey-Wilson polynomials are considered. The first two bivariate extensions of families of the Bannai-Ito tableau are also introduced. The second part presents four exactly solvable models connected to the theory of orthogonal polynomials. The perfect transfer of quantum information and entanglement generation properties of an XX spin chain model whose couplings are linked to the para-Racah polynomials are examined. Two superintegrable models containing reflexion operators are proposed. Their solutions are obtained and their symmetries are encoded respectively in the rank two and arbitrary rank Bannai-Ito algebra which leads to conjecture the apparition of multivariate Bannai-Ito polynomials as overlaps. Finally, via the representation theory of the osp(1|2) Lie superalgebra, two convolution identities for families of orthogonal polynomials of the Bannai-Ito tableau are offered. Realizations in terms of Dunkl operators lead to a bilinear generating function for the Big −1 Jacobi polynomials.
Jinliang, Ren. "A complete structure of the three-layer Zamolodchikov model." Thesis, 2021. http://hdl.handle.net/1885/256026.