Third quantization: a general method to solve master equations for quadratic open Fermi systems
arXiv:0801.1257 · doi:10.1088/1367-2630/10/4/043026
Abstract
The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 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 and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2 chain in a transverse magnetic field.
24 pages, with 8 eps figures - few minor corrections to the published version, e.g. anti-symmetrizing the matrix given by eq. (27)
References in corpus (10)
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- Heat transport in harmonic lattices
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Cited by in corpus (10)
- Quantum phase transition in a far from equilibrium steady state of XY spin chain
- Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
- Operator Space Entanglement Entropy in XY Spin Chains
- Dynamics of nonequilibrium thermal entanglement
- Complexity of thermal states in quantum spin chains
- Negative differential conductivity in far-from-equilibrium quantum spin chains
- Entanglement of two blocks of spins in the critical Ising model
- Reconstructing Fourier's law from disorder in quantum wires
- Nonequilibrium Fock space for the electron transport problem
- Markovian and Post-Markovian dynamics of nonequilibrium thermal entanglement