عنوان

Diffusion in the Mean for Markov Schrödinger Equations

Number

TL53041

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Diffusion in the Mean for Markov Schrödinger Equations

General Material Designation

[Thesis]

First Statement of Responsibility

Tilocco, Franklin Zakary

Subsequent Statement of Responsibility

Schenker, Jeffrey

Name of Publisher, Distributor, etc.

Michigan State University

Date of Publication, Distribution, etc.

2020

Text of Note

79 p.

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

Michigan State University

Text preceding or following the note

2020

Text of Note

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.

Subject Term

Mathematics

Subject Term

Physics

Tilocco, Franklin Zakary

Schenker, Jeffrey

Michigan State University

Electronic name

p

[Thesis]

276903

a

Y