Diffusion in the Mean for Markov Schrödinger Equations

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" Diffusion in the Mean for Markov Schrödinger Equations "
Tilocco, Franklin Zakary Schenker, Jeffrey

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1053924
Doc. No	:	TL53041
Main Entry	:	Tilocco, Franklin Zakary
Title & Author	:	Diffusion in the Mean for Markov Schrödinger Equations\ Tilocco, Franklin ZakarySchenker, Jeffrey
College	:	Michigan State University
Date	:	2020
Degree	:	Ph.D.
student score	:	2020
Note	:	79 p.
Abstract	:	We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves according to a stationary Markov process, we obtain diffusive scaling for moments of the position displacement, with a diffusion constant that grows as the inverse square of the disorder strength at weak coupling. More generally, we show that a central limit theorem holds such that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation. We also consider how the addition of a random, stochastically evolving, potential leads to diffusive propagation in the random dimer and trimmed Anderson models.
Descriptor	:	Mathematics
	:	Physics
Added Entry	:	Schenker, Jeffrey
Added Entry	:	Michigan State University