Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 36 for “"Integrable systems"”.
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Quantum intertwiners and integrable systems
… quantum groups and eigenfunctions for quantum integrable systems. First, we study the Etingof-Kirillov Jr. expression of Macdonald polynomials as traces of intertwiners of quantum groups in the Gelfand-Tsetlin basis. In the quasiclassical limit, we obtain a new Harish-Chandra type integral …
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Soliton solutions of noncommutative integrable systems
… is concerned with solutions of noncommutative integrable systems where the noncommutativity arises through the dependent variables in either the hierarchy or Lax pair generating the equation. Both Chapters 1 and 2 are entirely made up of background material and contain no new material. …
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Cluster algebras and discrete integrable systems
… between cluster algebras and discrete integrable systems, especially T-systems and their specializations/generalizations. We give connections between the T-system or the octahedron relation, and the pentagram map and its various generalizations. A solution to the T-system with …
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Local conservation laws in quantum integrable systems
One of the phenomena associated with quantum integrable systems is the possibility of persistent currents, i.e. currents which do not decay away entirely, but have some portion that continues to flow undiminished and indefinitely. These residual currents are shown to be the conserved part of the …
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On orthogonal polynomials and related discrete integrable systems
… polynomial community after their connection with integrable systems was found. This thesis is concerned with the different ways these connections can occur. We approach the problem from both perspectives, by looking for integrable structures in orthogonal polynomials and by using an integrable …
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Anomalous quantum dynamics in scarred and integrable systems
Generic quantum systems are expected to reach local thermal equilibrium under their unitary dynamics starting from any initial state. This thesis presents scenarios in which such thermalization does not occur. Firstly, we establish the quantum integrability of the central spin-1 XX model by …
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Rational matrix differential operators and integrable systems of PDEs
A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra …
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Poisson structures and degenerations of integrable systems related to y (gl2)
… dynamical system studied in the theory of integrable systems. It is known that the Toda lattice is related to other integrable systems: the DST system and the XXX model. We will generalize these three systems by attaching a Hamiltonian system to a nonincreasing sequence ▁k=(k_0,k_1,...,k_N) …
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Stochastically Perturbed Dynamics of Hamiltonian Systems Near 1:1-Resonance
… stochastically perturbed two-degrees of freedom integrable systems is emphasized throughout the study. The extension of the method of stochastic averaging on graphs to 1:1-resonant Hamiltonian systems forms the other major aspect of this work.
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Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad
… sistemas hamiltonianos clásicos completamente integrables N dimensionales, construidos mediante la técnica de simetría de coálgebra. Primeramente se ha obtenido la condición necesaria de integrabilidad para una representación simpléctica de cualquier coálgebra de Poisson. Esta condición ha sido …
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Whitham Equations, Dispersionless KP Theory and Seiberg-Witten Variables
… Briefly, a Riemann surface gives rise to integrable systems via the BA function. The averaging process gives modulation parameters Tn, ai and Whitham equations which describe the deformation of moduli such as branch points. We outline and give a detailed development of the theory with a …
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On trigonometric and elliptic Cherednik algebras
… operators, we construct a new family of quantum integrable systems.
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Non-Hermitian Hamiltonians in Field Theory
… fashion metrics and isospectral partners for systems of physical interest. Classically, our efforts were concentrated on integrable models presenting PT - symmetry. Because the latter can also establish the reality of energies in classical systems described by Hamiltonian functions, we search …
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Integrability from Chern-Simons theories
… details my work exploring connections between integrable systems and Chern-Simons theories. It is divided into two parts. The first concerns the application of 4d Chern-Simons theory to describe integrable models with boundary, while the second concerns relations between holomorphic …
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Geometric structures on the target space of Hamiltonian evolution equations
… is concerned with the relationship between integrable Hamiltonian partial differential equations and geometric structures on the manifold in which the dependent variables take their values. Chapters 1 and 2 are introductory chapters, and as such contain no original material. Chapter 1 covers …
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Dynamical Tunneling in Systems with a Mixed Phase Space
… While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated …
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Logarithmic Gromov-Witten theory and double ramification cycles
… double ramification cycle is then solved using integrable systems methods due to Buryak-Rossi.
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Quantum Simulation of Many-body Systems with Superconducting Qubits
The study of interacting many-body quantum systems is central to the understanding of wide a range of physical phenomena in condensed-matter systems, quantum gravity, and quantum circuits. However, quantum systems are often hard to study analytically, and the classical computing resources required …
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Lagrangian structures and multidimensional consistency
… a key integrability property of certain discrete systems; it implies that we are dealing with infinite hierarchies of compatible equations rather than with one single equation. Requiring the property of multidimensional consistency to be reflected also in the Lagrangian formulation of such …
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Integrable Evolution Partial Differential Equations: Multidimensions and Dirichlet-to-Neumann Maps
This thesis is about integrable Partial Differential Equations (PDEs). Here "integrable" means that the given PDE or system of PDEs can be written as the compatibility condition of a set of linear equations, the so-called Lax pair, and can be solved via a method related to the Inverse Scattering …
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