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 81 for “"master equation"”.
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Numerical Methods for the Chemical Master Equation
The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene …
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A master equation approach to nonlinear optics and chemical reactions
… optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time …
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Decoherence, Master Equation for Open Quantum Systems, and the Subordination Theory
… of inphasing and dephasing generates a Markov master equation statistically equivalent to a random walker jumping from one state to the other. This model can be used to describe intermittent fluorescence, as a sequence of "light on" and "light off" states. The experiments on blinking quantum …
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Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference
… to modeling such problems is to find their master equation. In systems biology, the equation is called the chemical master equation (CME), and solving the CME is a difficult task, because of the curse of dimensionality. The goal of this dissertation is to alleviate this curse via the use of …
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Tensors and Stochastic Automata Networks with Application to Chemical Kinetics
… Many revolve around solving the chemical master equation that arises in the modeling of the underlying biochemical kinetics. Traditionally, the chemical master equation models states consisting of the population counts present of each molecular species. This work considers the case of …
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Noise in coulomb blockaded quantum dots and kondo systems
… work on this system, the emphasis have been on master equation approaches in the shot noise regime. In the vicinity of the peak of conductance it remained unclear if this classical approach is valid since we have two strongly interacting charging states and a full quantum treatment is necessary. …
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Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data
… and diffusion coefficients of a Fokker-Planck equation describing a vacancy hopping in inhomogeneous media in one dimension under a directed stress. The study used the general master equation as a basis for a physical model because of the mesoscopic view that the change in average concentration …
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Computational and Experimental Studies of Coherence and Energy Flow in Microscopic and Mesoscopic Systems
… approach is appropriate. Therefore, we adopt a master equation model previously applied to this problem, and propose resonant IR overtone excitation of the surface Si-H vibration as a method for enhancing desorption rates. Finally, we present findings of our experimental efforts at implementing …
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SDEs and MFGs towards Machine Learning applications
… is centred on Backward Stochastic Differential Equations (BSDEs) featuring time-delayed generators. Subsequently, we direct our interest towards Mean Field Games (MFGs) incorporating absorption aspects, with a focus on the corresponding Master Equation within a confined domain under the …
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Calibrating a Latent Order Book Model to Market Data
… as a reaction diffusion Partial Differential Equation (PDE) and its subsequent numerical solution through an explicit method based on discrete stochastic processes. The numerical solution is calibrated using likelihood-free methods, Approximate Bayesian Computation (ABC) and an iterative …
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Geometry and Light in Quantum Optical Systems
… couplings to the environment through a Lindblad master equation. We look at observables such as optical spectrum to see the complex eigenvalues of the non-Hermitian systems. We compare the difference between how the linear oscillator and the non-linear truncated system behave at the steady state …
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Many-body decoherence with cold atoms in optical lattices
… we provide a framework to derive a microscopic master equation and look at the regimes of strong interactions. The interplay between the atomic physics and many-body physics is found to give rise to interesting observations like suppression of the decoherence effect for magnetically ordered …
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Statistical mechanics of strongly driven Ising systems
… external driving field. A formalism based on the master equation to handle such nonequilibrium systems is introduced and applied to a mean field approximation, and one- and two-dimensional variants of the model. A novel type of phase transition related to spontaneous symmetry breaking and dynamic …
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Contribution to Entanglement Theory, Applications in Atomic Systems and Cavity QED
… a cavity by using perturbation theory and a full master equation approach. We unveil interesting features of blockade and transparency in such cavity QED systems.
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A theoretical study of surface kinetic processes in the Mbe growth of compound semiconductors
… using a stochastic model which is based on the master equation approach and random distribution approximation. The kinetic processes included in the model are: adsorption, surface migration and evaporation. In the study of surface roughening kinetics in GaAs (100), a transition temperature at …
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Accelerating Finite State Projection through General Purpose Graphics Processing
… a new way of directly solving the chemical master equation. The algorithm utilizes the matrix exponential function, and so the algorithm’s performance suffers when it is applied to large problems. Other work has been done to reduce the size of the exponentiation through mathematical …
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Entanglement in a Bipartite Gaussian State
… to an environment and use the Non-Rotating Wave master equation to study the system's dynamics. We also present a derivation of this equation. We consider two di�fferent types of evolution. Under free evolution we �and that entanglement is lost quickly between the particles. When a harmonic …
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First Exit Time Analysis for the Stochastic Reaction Diffusion Process in a One Dimensional Domain
… (RD) process have focused on particle-based and master equation formulations. While these models offer strong theoretical foundation, a practical challenge remains: how does the choice of spatial discretization affect the accuracy and computational efficiency of simulation results, particularly …
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High-precision electron-spin sensing with ensembles of nitrogen-vacancy centers in diamond
… of the ESR spectrum. Using the Lindblad master equation, we model ESR line-shape and for the first time consider the influence of infrared driving on the ESR contrast. Both continuous-wave and pulsed sensing protocols are described, and a novel reference-free temperature sensing scheme is …
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Experimental Demonstration of Lindblad Tomography on a Superconducting Quantum Device
… more fully with a Lindbladian operator in the master equation formalism. In this thesis, I outline and present the results of the first experimental demonstration of Lindblad Tomography, a novel technique for tomographically reconstructing the Hamiltonian and Lindbladian operators of an …
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