Coherent states and wave packet dynamics for the Bogoliubov-de Gennes equations

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" Coherent states and wave packet dynamics for the Bogoliubov-de Gennes equations "
Langham-Lopez, Jordan

Document Type	:	Latin Dissertation
Record Number	:	1092440
Doc. No	:	TLets689993
Main Entry	:	Langham-Lopez, Jordan
Title & Author	:	Coherent states and wave packet dynamics for the Bogoliubov-de Gennes equations\ Langham-Lopez, Jordan
College	:	University of Nottingham
Date	:	2016
student score	:	2016
Degree	:	Ph.D.
Abstract	:	We investigate generalizations of coherent states as a means of representing the dynamics of excitations of the superconducting ground state. We also analyse the propagation of generalized coherent state wave packets under the Bogoliubov-de Gennes Hamiltonian. The excitations of the superconducting ground state are superpositions of electron and hole quasi-particles described by the Bogoliubov-de Gennes equations, that can only exist at energies outside the band gap. A natural generalization relevant to the excitations of the superconducting ground state is the tensor product of canonical and spin coherent states. This state will quickly become de-localized on phase space under evolution by the Bogoliubov-de Gennes Hamiltonian due to the opposite velocities of the quasi-spin components. We therefore define the electron-hole coherent states which remain localised on phase space over longer times. We show that the electron-hole coherent states though entangled retain many defining features of coherent states. We analyse the propagation of both product and electron hole coherent states in a superconductor with a spatially homogeneous superconducting band gap. The dispersion relation indicates that wavepackets defined on the band gap have a zero group velocity, but we will show that interference effects can create states on the band gap that propagate at the Fermi velocity. We also consider the two semiclassical, short wavelength regimes, hbar→0
Subject	:	QA611 Topology
	:	QC Physics
Added Entry	:	University of Nottingham