Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation

Abstract

Despite recent advances in quantum sciences, a quantum master equation that accurately and simply characterizes open quantum dynamics across extremely long timescales and in dispersive environments is still needed. In this study, we optimize the computation of the fourth-order time-convolutionless master equation to meet this need. Early versions of this master equation required computing a multidimensional integral, limiting its use. Our master equation accounts for simultaneous relaxation and dephasing, resulting in coefficients proportional to the system's spectral density over frequency derivative. In sub-Ohmic environments, this derivative induces infrared divergence in the master equation, invalidating the second-order Bloch-Redfield master equation findings. We analyze the approach to a ground state in a generic open quantum system and demonstrate that it is not reliably computed by the Bloch-Redfield equation alone. The optimized fourth-order equation shows that the ground-state approach is accurate to second order in bath coupling regardless of the dispersion, even though it can diverge in the fourth order at zero temperature.

arXiv comment28 pages, 5 figures Changes: Typos in Eq. 35 and 77 fixed. Rewording of the abstract, introduction and conclusion, in response to review. Title changed to emphasise the main result

References in corpus (47)

• Quantum Darwinism
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Decoherence benchmarking of superconducting qubits
• Stochastic wave function method for non-Markovian quantum master equations
• Quantum Adiabatic Markovian Master Equations
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Universal Lindblad equation for open quantum systems
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Ground States in Non-relativistic Quantum Electrodynamics
• Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits
• Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity
• Open quantum system dynamics and the mean force Gibbs state
• A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
• Preservation of Positivity by Dynamical Coarse-Graining
• Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• Completely positive master equation for arbitrary driving and small level spacing
• Entangling two unequal atoms through a common bath
• Thermodynamics of Quantum Information Flows
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
• Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
• A thermodynamically consistent Markovian master equation beyond the secular approximation
• The Accuracy of Perturbative Master Equations
• Infrared quantum information
• Quantum Markovian master equations: resonance theory shows validity for all time scales
• Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
• A cosmological open quantum system
• Lindbladian approximation beyond ultra-weak coupling
• Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems
• Refined Weak Coupling Limit: Coherence, Entanglement and Non-Markovianity
• A silicon singlet-triplet qubit driven by spin-valley coupling
• Canonically consistent quantum master equation
• Environment induced entanglement in a refined weak-coupling limit
• Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation
• Cumulant Expansions and the Spin-Boson Problem
• Dynamics of Open Quantum Systems II, Markovian Approximation
• Stochastic Bloch-Redfield theory: quantum jumps in a solid-state environment
• Searching for Lindbladians obeying local conservation laws and showing thermalization
• Full counting statistics and coherences: fluctuation symmetry in heat transport with the Unified quantum master equation
• A time-dependent regularization of the Redfield equation
• Higher-order corrections to the Redfield equation with respect to the system-bath coupling based on the hierarchical equations of motion
• Derivation of the Redfield quantum master equation and corrections to it by the Bogoliubov method
• Perturbative Steady States of Completely Positive Quantum Master Equations
• Exact generator and its high order expansions in the time-convolutionless generalized master equation: Applications to the spin-boson model and exictation energy transfer

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