Non-Markovian dynamics under time-translation symmetry

Abstract

A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator form. The kinetic coefficients are generally time-dependent and incorporate information on the kinematics and memory effects, while the operators manifest the dynamical symmetry. Specifically, we focus on time-translation symmetric dynamics, where the Lindblad jump operators constitute the eigenoperators of the free dynamics. This symmetry is motivated by thermodynamic microscopic considerations, where strict energy conservation between system and environment imposes the time-translation symmetry. The construction is generalized to other symmetries, and to driven quantum systems. The formalism is illustrated by three exactly solvable non-Markovian models, where the exact reduced description exhibits a dynamical symmetric structure. The formal structure of the master equation leads to a first principle calculation of the exact kinetic coefficients. This opens the possibility to simulate in a modular fashion non-Markovian dynamics.

References in corpus (20)

• Quantum Computing
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum coherence, time-translation symmetry and thermodynamics
• Bloch vectors for qudits
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Markovian master equations for quantum thermal machines: local vs global approach
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Markovian Master Equations: A Critical Study
• Finding the Kraus decomposition from a master equation and vice versa
• Preservation of Positivity by Dynamical Coarse-Graining
• Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• Nonperturbative master equation solution of central spin dephasing dynamics
• Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
• The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Non-Markovianity-assisted high-fidelity Deutsch-Jozsa algorithm in diamond
• Open system dynamics from thermodynamic compatibility
• How general are time-local master equations?
• Non-Markovianity, information backflow and system-environment correlation for open-quantum-system processes

Cited by in corpus (12)

• Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions
• Unification of the first law of quantum thermodynamics
• Classifying the non-time-local and entangling dynamics of an open qubit system
• Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources
• Complete positivity, positivity and long-time asymptotic behavior in a two-level open quantum system
• Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations
• Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Increasing extractable work in small qubit landscapes
• Integral fluctuation theorems and trace-preserving map
• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach
• Making Non-Markovian master equations accessible with approximate environments