@phdthesis{oai:oist.repo.nii.ac.jp:00002912,
 author = {Campbell, Christopher},
 month = {2023-04-01, 2023-03-30},
 note = {In this thesis I present two studies that use ideas and concepts from supersymmetric quantum mechanics to understand and control the nonequilibrium dynamics of a quantum many-body system. The two protocols I study involve the quenching of a spin-polarized Fermi gas and the adiabatic control of single particle states during the expansion of an infinite square well over a finite time interval. In the first study, I explore the survival probability and the work probability distribution for quenches within a hierarchy of potentials created using supersymmetric factorization methods. I show that in this setting one can take advantage of the degeneracy between supersymmetric potentials in order to find simplified expressions for these quantities. I also show that many-body revivals in these systems exist and are robust even at finite temperatures.
For the second study I explore a shortcut to adiabaticity (STA) based on counterdiabatic driving for the single particle states of the supersymmetric partner potentials of the infinite square. By calculating the fidelity, quantum speed limit time and the cost of driving a system, I compare the efficiency of the shortcuts between the ground state wavefunctions of three supersymmetric potentials and three wavefunctions that are isospectral to one another. The use of a supersymmetric setting allows me to distinguish between the dynamical effects stemming from the energy spectrum and from the distance between the states in Hilbert space. I also show that in the isospectral case one can develop an intertwining relationship between the counterdiabatic driving terms using the operators of their single particle Hamiltonians.},
 school = {Okinawa Institute of Science and Technology Graduate University},
 title = {超対称性と非平衡量子動力学},
 year = {}
}