Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices

@article{Li2015ResummationFN,
  title={Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices},
  author={Andy C. Y. Li and Francesco Petruccione and Jens Koch},
  journal={arXiv: Quantum Physics},
  year={2015}
}
Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a… 
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References

SHOWING 1-10 OF 83 REFERENCES
Synthetic gauge fields and homodyne transmission in Jaynes–Cummings lattices
Many-body physics is traditionally concerned with systems of interacting massive particles. Recent studies of effective interactions between photons, induced in the circuit quantum electrodynamics…
Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation
We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. Starting point is a microscopic description of the system…
Quantum Dynamical Semigroups and Applications
In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes…
Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases
We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of…
Dynamical phase transition in the open Dicke model
TLDR
In well-controlled sweeps across the Hepp–Lieb–Dicke phase transition, hysteretic dynamics showing power-law scaling with respect to the transition time suggests an interpretation in terms of a Kibble–Zurek mechanism, and indicates the possibility of universal behavior in the presence of dissipation.
Quantum correlations in the one-dimensional driven dissipative XY model
We study the non-equilibrium steady state (NESS) of a driven dissipative one-dimensional system near a critical point, and explore how the quantum correlations compare to the known critical behavior…
Circuit QED lattices: Towards quantum simulation with superconducting circuits
The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by…
Super-fermion representation of quantum kinetic equations for the electron transport problem.
TLDR
This work converts the problem of finding the nonequilibrium steady state to the many-body problem with non-hermitian liouvillian in super-Fock space, introduces nonequ equilibrium quasiparticles by a set of canonical nonunitary transformations and develops general many- body theory for the electron transport through the interacting region.
Perturbative approach to Markovian open quantum systems
TLDR
This work presents a perturbative treatment of Markovian open quantum systems which will be useful for an analytical understanding ofopen quantum systems and for numerical calculation of system observables which would otherwise be impractical.
Nonequilibrium-induced metal-superconductor quantum phase transition in graphene
We study the effects of dissipation and time-independent nonequilibrium drive on an open superconducting graphene. In particular, we investigate how dissipation and nonequilibrium effects modify the…
...
...