Open Quantum Systems. An Introduction

2011/04/27 by Ángel Rivas, ́Angel Rivas, Susana F. Huelga · 2 voices · 57 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #cond-mat.quant-gas #cond-mat.stat-mech #math-ph #math.MP #physics.atom-ph #physics.chem-ph #quant-ph

paper · pdf · doi:10.1007/978-3-642-23354-8

100 pages, 3 figures. Updated version with typos corrected. Preprint version of the published book

arxiv published 2011/04/27 · openalex publication_date 2011/09/29 · arxiv created 2012/02/09 · arxiv updated 2013/07/29 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/04

Abstract

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.

Citations

• Master equation - tutorial approach
• One-parameter semigroups for linear evolution equations

Cited by

• Relaxation control of open quantum systems
• Quantum-to-Classical Transition via Single-Shot Generalized Measurements
• Learning the non-Markovian features of subsystem dynamics
• Magic Steady State Production: Non-Hermitian and Stochastic pathways
• A Fundamental Bound for Robust Quantum Gate Control
• Making Non-Markovian master equations accessible with approximate environments
• Optical signatures of quantum skyrmions
• Memory effects in a dynamical decoupling process
• Integrals of motion as slow modes in dissipative many-body operator dynamics
• Intrinsic Hamiltonian of Mean Force and Strong-Coupling Quantum Thermodynamics
• Parity-Time Symmetric Spin-1/2 Richardson-Gaudin Models
• Quantum Statistical Mechanics of Electronically Open Molecules: Reduced Density Operators
• Exact quantum noise deconvolution with partial knowledge of noise
• Statistical Characterization of Entanglement Degradation Under Markovian Noise in Composite Quantum Systems
• Divide-and-Conquer Simulation of Open Quantum Systems
• Entanglement Relativity in the Foundations of The Open Quantum Systems Theory
• Statistics of non-conserved observables in Lindblad master equations
• Vanishing quantum discord is not necessary for completely positive maps
• Stationary discrete solitons in a driven dissipative Bose-Hubbard chain
• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• Language Model for Large-Text Transmission in Noisy Quantum Communications
• Non-hermitian quantum thermodynamics
• Quantum Absorption Refrigerator
• The local approach to quantum transport may violate the second law of thermodynamics
• DAMPyF: a Python implementation of the DAMPF method for the simulation of open-system dynamics
• Cohering power of quantum operations
• Effect of Cross-Spectral Correlations on Qubit Dynamics: Coherence Revival and Relaxation Modulation
• Quantum Simulation of Dissipative Processes without Reservoir Engineering
• Quantum thermodynamics and quantum coherence engines
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Estimating the degree of non-Markovianity using machine learning
• Momentum coupling in non-Markovian quantum Brownian motion
• How Far do Lindbladians Go?
• Excitation energy transport with noise and disorder in a model of the selectivity filter of an ion channel
• Non-normality and dissipation in Markovian quantum dynamics: Implications for quantum simulation
• Bifurcation and chaos in nonlinear Lindblad equations
• Non-equilibrium quantum heat machines
• Extended convexity of quantum Fisher information in quantum metrology
• On the Lyapunov-Perron reducible Markovian Master Equation
• From Zeno to anti-Zeno regime: Decoherence-control dependence on the quantum statistics of the bath
• Correlation-Picture Approach to Open-Quantum-System Dynamics
• Self-consistent projection operator theory for quantum many-body systems
• Complete Positivity on the Subsystems Level
• Effects of initial system-environment correlations on open-quantum-system dynamics and state preparation
• Non-Markovianity of a quantum emitter in front of a mirror
• Quantum chaos, equilibration, and control in extremely short spin chains
• Efficient Simulation of Finite-Temperature Open Quantum Systems
• Non-Hermitian physics and master equations
• Point-gap topology with complete bulk-boundary correspondence and anomalous amplification in the Fock space of dissipative quantum systems
• Generalized Kraus Operators for the One-Qubit Depolarizing Quantum Channel
• Microwave photonics with Josephson junction arrays: Negative refraction index and entanglement through disorder
• Measurement-based cooling of a nonlinear mechanical resonator
• Local master equations may fail to describe dissipative critical behavior
• Rate Operator Unraveling for Open Quantum System Dynamics
• The effects of thermal and correlated noise on magnons in a quantum ferromagnet
• Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
• Dressed-state master equation for two strongly coupled two-level atoms with long-lived entanglement
• Spectral delineation of Markov Generators: Classical vs Quantum
• Controllable Non-Markovianity for a Spin Qubit in Diamond

Discussions

• We recently put a preprint on this issue, providing a direct algebraic proof of the non-positivity of $\mathcal{L}$ 's eigenvalues' real parts for finite-dimensional systems. Here is the arXiv link, h [stackexchange, 3 points]
• If a Lindblad equation is derived from a "microscopic" Hamiltonian that covers both the system and the environment, $$H_\text{tot} = H_\text{sys} + H_\text{env} + H_\text{sys-env},$$ (where $H_\text{s [stackexchange, 0 points]

Related

• An Operator-Based Exact Treatment of Open Quantum Systems
• General form of quantum evolution
• An introduction to Markovian open quantum systems
• Open environments for quantum open systems
• Dynamical maps beyond Markovian regime