Coherent states and wave packet dynamics for the Bogoliubov-de Gennes equations
Langham-Lopez, Jordan (2016) Coherent states and wave packet dynamics for the Bogoliubov-de Gennes equations. PhD thesis, University of Nottingham.
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.
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