Inelastic Quantum Transport

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Abstract
We solve a Schrödinger equation for inelastic quantum transport that retains full quantum coherence, in contrast to previous rate or Boltzmann equation approaches. The model Hamiltonian is the zero temperature 1D Holstein model for an electron coupled to optical phonons (polaron), in a strong electric field. The Hilbert space grows exponentially with electron position, forming a nonstandard Bethe lattice. We calculate nonperturbatively the transport current, electron-phonon correlations, and quantum diffusion. This system is a toy model for the constantly branching “wave function of the universe.”
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