Open-quantum-system dynamics: Recovering positivity of the Redfield equation via the partial secular approximation

  title={Open-quantum-system dynamics: Recovering positivity of the Redfield equation via the partial secular approximation},
  author={D. Farina and Vittorio Giovannetti},
  journal={Physical Review A},
We show how to recover complete positivity (and hence positivity) of the Redfield equation via a coarse grain average technique. We derive general bounds for the coarse graining time scale above which the positivity of the Redfield equation is guaranteed. It turns out that a coarse grain time scale has strong impact on the characteristics of the Lamb shift term and implies in general non-commutation between the dissipating and the Hamiltonian components of the generator of the dynamical semi… 

Figures from this paper

Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation

Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini–Kossakowski–

A time-dependent regularization of the Redfield equation

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this

Higher-order Corrections to the Redfield Equation with Respect to the System-bath Coupling Based on the Hierarchical Equations of Motion

The Redfield equation describes the dynamics of a quantum system weakly coupled to one or more reservoirs and is widely used in theory of open quantum system. However, the assumption of weak

Going beyond local and global approaches for localized thermal dissipation

Identifying which master equation is preferable for the description of a multipartite open quantum system is not trivial and has led in the recent years to the local vs. global debate in the context

Thermodynamics of the Coarse-Graining Master Equation

It is shown that the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval generally leads to a Lindblad–Gorini–Kossakowski–Sudarshan generator.

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

A Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfields, and is adaptable between its time-independent, time-dependent, and Floquet form.

Open system dynamics from thermodynamic compatibility

The axiomatic approach sheds light on the validity of the secular approximation in microscopic derivations, the form of the steady state in heat transport phenomena, and indicates the lack of exceptional points in the dynamics of open quantum systems.

Response theory for nonequilibrium steady states of open quantum systems

We introduce a response theory for open quantum systems described by the Lindblad-Gorini-Kossakowski-Sudarshan formalism evolving under equilibrium or nonequilibrium conditions. We find that the

Enhancing energy transfer in quantum systems via periodic driving: Floquet master equations

We provide a comprehensive study of the energy transfer phenomenon—populating a given energy level—in 3-and 4-level quantum systems coupled to two thermal baths. In particular, we examine the effects

Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: Phenomenological description and its microscopic foundation

We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by coupling each site to a local fermionic bath. To derive the proper form of the Lindblad



Preservation of positivity by dynamical coarse graining

We compare different quantum master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with

Refined weak-coupling limit: Coherence, entanglement, and non-Markovianity

We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system

Systematic perturbation theory for dynamical coarse-graining

We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we

Environment-induced entanglement in a refined weak-coupling limit

Two non-directly interacting qubits with equal frequencies can become entangled via a Markovian, dissipative dynamics through the action of a weakly coupled Ohmic heat bath. In the standard

Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems

We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a


The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion

Extending the validity range of quantum optical master equations

This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each

Coarse graining can beat the rotating-wave approximation in quantum Markovian master equations

We present a first-principles derivation of the Markovian semigroup master equation without invoking the rotating-wave approximation (RWA). Instead we use a time coarse-graining approach that leaves

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which