Phonon dynamics in correlated quantum systems driven away from equilibrium

Abstract

A general form of a many-body Hamiltonian is considered, which includes an interacting fermionic sub-system coupled to non-interacting extended fermionic and bosonic systems. We show that the exact dynamics of the extended bosonic system can be derived from the reduced density matrix of the sub-system alone, despite the fact that the latter contains information about the sub-system only. The advantage of the formalism is immediately clear: While the reduced density matrix of the sub-system is readily available, the formalism offers access to observables contained in the full density matrix, which is often difficult to obtain. As an example, we consider an extended Holstein model and study the nonequilibrium dynamics of the, so called, "reaction mode" for different model parameters. The effects of the phonon frequency, the strength of the electron-phonon couplings, and the source-drain bias voltage on the phonon dynamics across the bistability are discussed.

5 pages, 3 figures

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• Efficient simulation of non-Markovian system-environment interaction
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• Green's function methods for single molecule junctions
• Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities
• Sub-Ohmic to super-Ohmic crossover behavior in nonequilibrium quantum systems with electron-phonon interactions
• Optimized auxiliary representation of a non-Markovian environment by a Lindblad equation
• Exact Calculation of the Time Convolutionless Master Equation Generator: Application to the Nonequilibrium Resonant Level Model
• Many-body Green's function theory for electron-phonon interactions: the Kadanoff-Baym approach to spectral properties of the Holstein dimer
• Time-linear quantum transport simulations with correlated nonequilibrium Green's functions
• Lead Geometry and Transport Statistics in Molecular Junctions
• Transient dynamics in interacting nanojunctions within self-consistent perturbation theory
• Reduced Dynamics of Full Counting Statistics
• Controlling the conductance of molecular junctions using proton transfer reactions: A theoretical model study
• Transient currents of a single molecular junction with a vibrational mode
• A complete quasiclassical map for the dynamics of interacting fermions