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Showing 1 to 18 of 18 for “"Hamiltonian dynamics"”.
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Integral geometry, Hamiltonian dynamics, and Markov Chain Monte Carlo
… of Crofton's formula without introducing a bias. Hamiltonian Monte Carlo (HMC) algorithms are some the most widely-used MCMC algorithms. We use the symplectic properties of Hamiltonians to prove global Cheeger-type lower bounds for the mixing times of HMC algorithms, including Riemannian Manifold …
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Some applications of lie transformation groups to classical Hamiltonian dynamics
Recent work has established that a group theoretical viewpoint of completely integrable dynamical systems with N degrees of freedom yields an algorithm that provides new information concerning the symmetry transformation group structure of this class of dynamical systems. The work presented here …
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Investigating Hamiltonian dynamics by the method of covariant Lyapunov vectors
… use these objects to numerically investigate the dynamics of several autonomous Hamiltonian systems. The algorithm which we use for computing CLVs is the one developed by Ginelli and collaborators (G&C), which is quite efficient and has been used previously in many numerical investigations. Using …
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Classical Hamiltonian dynamics of a particle interacting with the vibrational modes of a one-dimensional medium
… behavior and underlying properties of polaron dynamics has been the focus of much research for many years. Since the exact quantum mechanical dynamics of the interacting particle/many-oscillator system remains computationally complex due to the enormous size of the man-body Hilbert space, it is …
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Mathematical Tools for Discontinuous Dynamical Systems
… Next, a new nonsmooth formulation of Hamiltonian dynamics for Hamiltonian systems with nonsmooth potential energy is developed, using lexicographic differentiation to derive a system of discontinuous differential equations, and theoretical results are developed. Using this nonsmooth …
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Beyond Geometry: Conceptual Foundations of a Force-Based Theory of Gravity
… this framework, the notions of Lagrangian and Hamiltonian dynamics are reformulated, leading naturally to a modified procedure for canonical quantization. The new definition reveals gravity as a genuine interaction rather than just a manifestation of spacetime geometry. On this basis, we …
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Explicit, Multi-Map Symplectic Integrator for Three -Body Classical Trajectory Studies in Hyperspherical Coordinates
… known for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. There is a general operator splitting method for developing explicit symplectic integration algorithms to any arbitrary even order for separable …
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Explicit, multi-map symplectic integrator for three-body classical trajectory studies in hyperspherical coordinates
… known for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. There is a general operator splitting method for developing explicit symplectic integration algorithms to any arbitrary even order for separable …
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Quantum Computation and Simulation using Fermion Pair Registers
… interaction, one can realize 2D quantum Ising Hamiltonians in a programmable geometry with tunable transverse and longitudinal fields. In addition, we present a sample-efficient protocol to characterize engineered gates and Hamiltonian dynamics by improving classical shadow process tomography …
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Coupled oscillators near resonance
We study the dynamics of two conservative librating oscillators with perturbations from a linear displacement coupling and non-Hamiltonian forces such as damping. We examine the dynamics of these systems when they are near a resonance using secular perturbation theory. We show that near resonance a …
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Computations in monotone Floer theory
… lie in estimating the numbers of equilibria in Hamiltonian dynamics, and more recently it has become a major component of the Homological Mirror Symmetry conjecture. This work presents several new computations in Floer theory which combine the use of geometric symmetries, naturally arising in …
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Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and transfer matrices
… kinds of dynamical systems described by Hamiltonian dynamics. The first part describes a computation of gauge anomalies and their macroscopic effects in a semiclassical picture. The geometric (symplectic) formulation of classical mechanics is used to describe the dynamics of Weyl fermions …
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Quantum information processing in continuous time
… quantum algorithms based on continuous-time Hamiltonian dynamics. In quantum computation by adiabatic evolution, the computer is prepared in the known ground state of a simple Hamiltonian, which is slowly modified so that its ground state encodes the solution to a problem. We argue that this …
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Algorithms for quantum simulation: design, analysis, implementation, and application
Simulating the Hamiltonian dynamics of quantum systems is one of the most promising applications of digital quantum computers. In this dissertation, we develop an understanding of quantum simulation algorithms concerning their design, analysis, implementation, and application. We implement three …
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General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions
<p>Hamiltonian Monte Carlo (HMC) is a state-of-the-art sampling algorithm for Bayesian computation. Popular probabilistic programming languages Stan and PyMC rely on HMC’s generality and efficiency to provide automatic Bayesian inference platforms for practitioners. Despite its wide-spread use and …
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Topics in Lattice Statistics: I. Systematics of Multilayer Adsorption Phenomena on Attractive Substrates II. Dynamical Critical Exponents for the Kinetic Ising Model: A Finite-Size Hamiltonian Calculation
Submitted by Carolyn Rauber (crauber2@illinois.edu) on 2011-06-02T17:26:09Z No. of bitstreams: 1 1982_pandit.pdf: 5769733 bytes, checksum: 3cf1cd189904f2a0b5ccbc3238ccdebc (MD5)
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Linear and non-linear collisionless many-particle systems
… many-particle systems, in which the Hamiltonian dynamics described by its particles are hyperbolic. Firstly, we study small data solutions for the Vlasov--Poisson system under the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flow. More …
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Calculations for charge-transfer in collisions of triply-ionized nitrogen and doubly-ionized sulphur with hydrogen atoms
Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-06-27T14:28:46Z No. of bitstreams: 1 1980_christensen.pdf: 4732068 bytes, checksum: 8660538e8ef435236d68b745f3b846da (MD5)