Third quantization: a general method to solve master equations for quadratic open Fermi systems

@article{Prosen2008ThirdQA,
  title={Third quantization: a general method to solve master equations for quadratic open Fermi systems},
  author={Toma{\vz} Prosen},
  journal={New Journal of Physics},
  year={2008},
  volume={10},
  pages={043026}
}
  • T. Prosen
  • Published 8 January 2008
  • Physics
  • New Journal of Physics
The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n?4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method is applied to the explicit construction of non-equilibrium steady states (NESS) and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbour Heisenberg XY spin-1/2 chain in a transverse… 
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References

SHOWING 1-10 OF 107 REFERENCES
Fourier's Law confirmed for a class of small quantum systems
Abstract.Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the…
Modeling heat transport through completely positive maps.
TLDR
An alternative master equation is derived that is capable of describing a stationary energy current and, at the same time, leads to a completely positive dynamical map that paves the way for efficient numerical investigations of heat transport in larger systems based on Monte Carlo wave function techniques.
Theory of open quantum systems
A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary…
Heat transport in quantum spin chains
Abstract.We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe…
Strong evidence of normal heat conduction in a one-dimensional quantum system
We investigate how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system. The direct investigation of local energy distribution under thermal gradient…
Exact Time-Correlation Functions of Quantum Ising Chain in a Kicking Transversal Magnetic Field Spectral Analysis of the Adjoint Propagator in Heisenberg Picture
Spectral analysis of the adjoint propagator in a suitable Hilbert space (andLie algebra) of quantum observables in Heisenberg picture is discussed as an alternative approach to characterize infinite…
Heat Transport in Harmonic Lattices
We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic…
Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs
Abstract: We study the non-equilibrium statistical mechanics of a 2-level quantum system, ?, coupled to two independent free Fermi reservoirs ?1, ?2, which are in thermal equilibrium at inverse…
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…
Exactly Solvable Model of Quantum Diffusion
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band. The subsystem interacts with…
...
1
2
3
4
5
...