Inverse Problems in Disordered Systems
Citation:
Mukim, Shardul Shashikant, Inverse Problems in Disordered Systems, Trinity College Dublin, School of Physics, Physics, 2023Download Item:
Abstract:
It is a simple Quantum Mechanics problem to find the electronic conductance of
a device by directly solving the Schrodinger Equation. Obviously, this is the case
if and only if the underlying Hamiltonian is known, i.e., if all scattering sources
are fully specified. Trying to perform the same task in reverse is significantly more
challenging. For example, assuming that the device conductance is known, how
can one infer about the Hamiltonian components from that information alone? To
make matters worse, what if the device is made of a heavily disordered material?
Questions of this type are generally labelled as Inverse Problems (IP) and are
classified as those which attempt to obtain from a set of observations the causal
factors that generated them in the first place. IP are integral parts of classical
visualization tools but far less common in the quantum realm. Materials Science
is ideal for applications of inverse problem since it involves studying structures
for which the underlying Hamiltonians are rarely known. Identifying the precise
Hamiltonian that generates a specific observable is a difficult process. In general,
it consists of solving the Schrodinger equation with a Hamiltonian containing one
(or more) parameter(s) that must be changed until the solution closely matches
the original observation. Because of the gigantic number of possibilities, finding
the exact configuration is computationally very demanding. Efficient codes and powerful computers alone are not sufficient to make this approach feasible and
alternative ways of probing the phase space of possibilities are needed.
In this thesis, I introduce a simple mathematically-transparent inversion technique
capable of extracting structural and compositional information from a disordered
quantum device and nanowire/nanosheet networks by looking at their electronic
signatures. We put forward an efficient way that can quantify the overall concentration of scatterers in a device. In addition, a sudoku style technique is also presented
which enables us not only to specify the total number of scatterers but also to
determine how they are spatially distributed.
Description:
APPROVED
Author: Mukim, Shardul Shashikant
Advisor:
Ferreira, MauroPublisher:
Trinity College Dublin. School of Physics. Discipline of PhysicsType of material:
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Full text availableKeywords:
inverse problem, quantum transportMetadata
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