Full density matrix dynamics for large quantum systems: Interactions, Decoherence and Inelastic effects

Abstract

We develop analytical tools and numerical methods for time evolving the total density matrix of the finite-size Anderson model. The model is composed of two finite metal grains, each prepared in canonical states of differing chemical potential and connected through a single electronic level (quantum dot or impurity). Coulomb interactions are either excluded all together, or allowed on the dot only. We extend this basic model to emulate decoherring and inelastic scattering processes for the dot electrons with the probe technique. Three methods, originally developed to treat impurity dynamics, are augmented to yield global system dynamics: the quantum Langevin equation method, the well known fermionic trace formula, and an iterative path integral approach. The latter accommodates interactions on the dot in a numerically exact fashion. We apply the developed techniques to two open topics in nonequilibrium many-body physics: (i) We explore the role of many-body electron-electron repulsion effects on the dynamics of the system. Results, obtained using exact path integral simulations, are compared to mean-field quantum Langevin equation predictions. (ii) We analyze aspects of quantum equilibration and thermalization in large quantum systems using the probe technique, mimicking elastic-dephasing effects and inelastic interactions on the dot. Here, unitary simulations based on the fermionic trace formula are accompanied by quantum Langevin equation calculations.

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• Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions
• A note on the Full Counting Statistics of paired fermions
• The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution
• Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
• Qubit-mediated energy transfer between thermal reservoirs: beyond Markovian Master equation
• How long does it take to form the Andreev quasiparticles ?
• Finite coupling effects in double quantum dots near equilibrium
• Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads
• Non-interacting many-particle quantum transport between finite reservoirs
• Environment assisted superballistic scaling of conductance
• Nonreciprocal electrical transport in linear systems with balanced gain and loss in the bulk