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 10 of 10 for “"Liouville Equation"”.
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Quantum mechanics on phase space : geometry and motion of the Wigner distribution
… to propagate Wigner functions via the quantum Liouville equation. Using these methods we study the quantum mechanical phenomena of reflection, interference, and tunnelling and explain how these phenomena arise in phase space as a direct consequence of the first quantum correction to classical …
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Global existence in L1 for the square-well kinetic equation
… square-well is incorporated into the Enskog equation, in order to model the kinetic theory of a moderately dense gas with intermolecular potential. The existence of solutions to the Cauchy problem in <i>L</i>¹. global in time and for arbitrary initial data. is proved. A simple derivation of …
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Electronic Spin Coupled Nonadiabatic Dynamics
… and analyze a preconditioned quantum-classical Liouville equation (QCLE) theory that directly connects to the PD-PSSH algorithm and explains the latter's success in simulating complex-valued Hamiltonians. We expect that with the PD-PSSH algorithm, we can explore the coupled spin-nuclear …
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Model Abstraction in Dynamical Systems: Application to Mobile Robot Control
… law results in a partial differential equation known as the Liouville equation, for which a closed form solution is known. The solution provides the time evolution of the initial pdf which can be followed by the abstracted system.
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A novel state-space based method for direct numerical simulation of particle-laden turbulent flows
… of one-way coupling remains valid. The transport equation for the particle density function is derived from the governing equation of the particle dynamics described in a Lagrangian frame, by treating position and velocity of the particle as state-space variables and referring to the Liouville …
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Approaching magnetic field effects in biology using the radical pair mechanism
… pair mechanism: one based on the Schri::idinger Equation (see [4, 5] or Chapter 3), another based on the Liouville Equation (see [6] or Chapter 4), and two more mixed perturbation methods that bridge the gap between the Schri::idinger and Liouville formalisms (see Chapter 5). All of these …
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… problems of solutions to semilinear elliptic equations, with a particular focus on the study of symmetry and rigidity results. The thesis is divided into four chapters. In Chapter 1 we consider solutions to some semilinear elliptic equations on complete noncompact Riemannian manifolds and …
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Interfacing spin-based quantum sensors with complex systems
… at large optical excitation power. A stochastic Liouville equation model is used to model the spin diffusion process. In Chapter 4 and 5, nanodiamonds are used in thermometry to measure time-varying signal in biological cells. In this experiment, the theoretical temperature sensitivity is …
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On the parametrization of self-adjoint extensions of singular Sturm-Liouville operators
… extensions of a lower semi-bounded minimal Sturm–Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and …