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

By Tomaz Prosen. 2008

482 citations recorded by the source corpus.

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 magnetic field.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6e185613596db868a41f86e7ca312e12331908fb

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Matrix product simulations of non-equilibrium steady states of quantum spin chains (2008, background): “ult can be claimed for thermal states [18]. The deﬁning equation for NESS of an open-quantum system can be written as “right ground state” of a certain non-Hermitian quantum Liouville master operator [13], hence NESS can be thought of as a kind of non-normal ground state in the Liouville space. This”
Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos (2019, background): “[1] T.”
Spectral theorem for the Lindblad equation for quadratic open fermionic systems (2010, methodology): “This model is fermionized in terms of Majorana operators w1,2,3,4 [6] using Jordan-Wigner transformation H = − i 2Jw2w3 and the key matrices read”
Geometry of quantum phase transitions (2019, unknown): “[387, 388, 389, 177] using a formalism called “third quantisation”.”
Topology by dissipation in atomic quantum wires (2011, background): “Writing , the approach to steady state is governed by ∂ t δΓ=−l X ,δΓr, that is, the eigenvalues of the positive semi-definite matrix X (refs&nbs”
A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains (2012, methodology): “However, the approach of open-quantum-system has only quite recently been applied to the non-equilibrium problems of condensed matter physics [8, 9, 10, 11, 12, 13, 14, 15], such as the controversial quantum transport problem in one-dimension [16, 17, 18].”
Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “l dynamics is equivalent to that of a classical probability vector; this point is illustrated below. For a small sample of applications of this formalism to problems in open quantum dynamics see e.g. [108, 16, 19, 109, 110, 111, 112, 113, 114, 115, 116, 117]. 4.1.1. Example: 2-level system at T= 0 C”