Third quantization: a general method to solve master equations for quadratic open Fermi systems
TLDR
In this paper, 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 bath operators are linear in the fermionic variables.Abstract:
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.read more
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Quantum trajectories and open many-body quantum systems
TL;DR: Open quantum systems as discussed by the authors describe quantum systems exhibiting quantum coherence that are coupled to their environment, where the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or project the system onto known states via feedback in quantum measurements.
Journal ArticleDOI
Topology by dissipation in atomic quantum wires
Sebastian Diehl,Sebastian Diehl,Enrique Rico,Enrique Rico,Mikhail A. Baranov,Mikhail A. Baranov,Mikhail A. Baranov,Peter Zoller,Peter Zoller +8 more
TL;DR: In this article, it was shown that topological features and phenomena occur not only in closed systems, but also in open quantum systems with appropriately engineered dissipation, which can make quantum systems robust to a wide class of microscopic perturbations.
Journal ArticleDOI
Quasilocal charges in integrable lattice systems
TL;DR: In this article, the concept of quasilocal conserved quantities has been studied in integrable quantum lattice systems, and two systematic procedures to rigorously construct families of conserved operators based on quantum transfer matrices are outlined, specializing on anisotropic Heisenberg XXZ spin 1/2 chain.
Book ChapterDOI
Engineered Open Systems and Quantum Simulations with Atoms and Ions
TL;DR: In this paper, the authors review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems of atoms and ions, and discuss a recent experiment demonstrating the basic building blocks of a full-fledged open-system quantum simulator.
Journal ArticleDOI
Finite-temperature transport in one-dimensional quantum lattice models
Bruno Bertini,Fabian Heidrich-Meisner,Christoph Karrasch,Tomaž Prosen,Robin Steinigeweg,Marko Žnidarič +5 more
TL;DR: In this paper, a review of the current understanding of transport in one-dimensional lattice models, in particular in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-theart theoretical methods, including both analytical and computational approaches.
References
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Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Journal ArticleDOI
On the Generators of Quantum Dynamical Semigroups
TL;DR: In this paper, the notion of a quantum dynamical semigroup is defined using the concept of a completely positive map and an explicit form of a bounded generator of such a semigroup onB(ℋ) is derived.
Book
The Theory of Open Quantum Systems
TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.
Journal ArticleDOI
Density matrix formulation for quantum renormalization groups
TL;DR: A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented and it is shown that this formulation is optimal in a certain sense.
Book
Mathematical Foundations of Quantum Mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.