98 research outputs found
Electron-hole coherent states for the Bogoliubov-de Gennes equation
We construct a new set of generalized coherent states, the electron-hole
coherent states, for a (quasi-)spin particle on the infinite line. The
definition is inspired by applications to the Bogoliubov-de Gennes equations
where the quasi-spin refers to electron- and hole-like components of electronic
excitations in a superconductor. Electron-hole coherent states generally
entangle the space and the quasi-spin degrees of freedom. We show that the
electron-hole coherent states allow obtaining a resolution of unity and form
minimum uncertainty states for position and velocity where the velocity
operator is defined using the Bogoliubov-de Gennes Hamiltonian. The usefulness
and the limitations of electron-hole coherent states and the phase space
representations built from them are discussed in terms of basic applications to
the Bogoliubov-de Gennes equation such as Andreev reflection.Comment: 18 page
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