The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which features a constant current and a characteristic density profile. While the Lindblad equation complements other approaches to transport in closed quantum systems, it has become clear that a connection between closed and open systems exists in certain cases. Here, we build on this connection for magnetization transport in the spin-1/2 XXZ chain with and without integrability-breaking perturbations. Specifically, we study the question of whether the time evolution of the open quantum system can be described on the basis of classical correlation functions, as generated by the Hamiltonian equations of motion for real vectors. By comparing the results to exact numerical simulations of the Lindblad equation, we find a good accuracy of such a description for a range of model parameters which is consistent with previous studies on closed systems. While this agreement is an interesting physical observation, it also suggests that classical mechanics can be used to solve the Lindblad equation for comparatively large system sizes which lie outside the possibilities of a quantum mechanical treatment. We also point out counterexamples and limitations for the quantitative extraction of transport coefficients. Remarkably, our classical approach to large open systems allows us to detect superdiffusion at the isotropic point.
We present a comprehensive analytical and numerical study of time-dependent decoherence in open quantum systems, focusing on a single-qubit model with time-varying Lindblad dissipation rates. Employing a master equation framework, we derive exact solutions for the evolution of off-diagonal density matrix elements and characterize the emergence of robust pointer states. Our findings reveal an initial rapid coherence decay followed by a gradual slowdown, mirroring experimental trends observed in superconducting qubits influenced by quasiparticle dynamics and in photonic cavities subject to fluctuating environments. By incorporating real experimental parameters and validating the model through quantum simulations using QuTiP, we provide a robust quantitative tool for analyzing decoherence in quantum technologies. This extended model addresses limitations in static-rate approximations, offering insights into non-Markovian effects without resolving the measurement problem, and suggests extensions to multi-qubit systems.
We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved charge commuting with the Hamiltonian and Lindblad operators. We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, which is solvable by representing the spins in terms of Majorana fermions. This allows us to study the Liouvillian gap, the inverse of relaxation time, in detail. We find that the Liouvillian gap increases monotonically when the dissipation strength $\ensuremath{\gamma}$ is small, while it decreases monotonically for large $\ensuremath{\gamma}$, implying a kind of phase transition in the first decay mode. The Liouvillian gap and the transition point are obtained in closed form in the case where the spin chain is critical. We also obtain the explicit expression for the autocorrelator of the edge spin. The result implies the suppression of decoherence when the spin chain is in the topological regime.
Abstract Understanding thermalization and irreversibility in open quantum systems requires char-acterizing the competition between coherent unitary dynamics and dissipative environmen-tal interactions. In this work, we present a systematic numerical study of thermalization dynamics in a two-qubit open quantum system governed by a completely positive and trace-preserving Lindblad master equation. The coherent evolution rate is controlled by a real scaling parameter α multiplying the Hamiltonian commutator, while decoherence is indepen-dently controlled by a dephasing rate γ . Although such a scaling of coherent dynamics can be absorbed into a rescaling of time in isolated systems, it becomes physically meaningful in open systems where decoherence introduces an absolute timescale. We investigate how the relative strength of coherent evolution and decoherence influences observable dynamics, purity decay, entropy production, and thermalization times. Using robust local and two-site observables, we show that varying α at fixed γ produces distinct transient trajectories, even though all evolutions converge to the same steady state. We further define an operational thermalization time τ ( γ, α ) based on a purity threshold and map the resulting thermalization-time surface across a broad parameter range. Increasing α generally accelerates oscillatory dynamics and modifies the approach to equilibrium, leading to measurable shifts in thermalization times without altering asymptotic states. These findings provide a clear and physically consistent characterization of how Hamil-tonian strength and decoherence rate jointly determine thermalization behavior in open quantum systems. The framework offers a practical parameterization for numerical mod-eling and experimental studies of coherent–dissipative competition in quantum information processing, quantum control, and open-system dynamics.
We show that the
d+0-dimensional Yang-Lee theory describing classical Ising spins in an imaginary magnetic field can be realized, without post-selection, within a
(d−1)+1 open quantum system whose dynamics consist of local unitaries and engineered dissipation. Competition between the coherent unitary and dissipative dynamics drives a transition wherein the time-dependence of a particular class of linear observables changes from damped oscillatory "underdamped" to purely exponential "overdamped" decay. Our construction relies on an extensive number of weak-symmetries of the Lindbladian fixed by the choice of observable but is otherwise exact. Consequently, we show that the dynamics are described by the non-Hermitian generator of the Yang-Lee transfer matrix, leading to an effective Yang-Lee theory defined on the spacetime history of the open system. By locally modifying the dynamics, we directly measure spin correlation functions of the Yang-Lee theory as well as a related "Loschmidt Echo" correlator which we detail. We explicitly show that the required dissipation channels can be obtained through local
2-qubit gates and discuss potential realization on near-term quantum simulator devices. Finally, we generalize our construction to embed arbitrary non-Hermitian Hamiltonians within an open quantum system under Lindbladian time-evolution without post-selection, drawing connections between unconditional open quantum dynamics, exceptional point physics, and non-unitary statistical mechanics.
This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For
s<1 the system is localized at zero temperature, and at finite
T relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For
s>2 it undergoes underdamped coherent oscillations for all relevant temperatures, while for
1<s<2 there is a crossover from coherent oscillation to overdamped relaxation as
T increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case,
s=1, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature
T: over most of the ($\ensuremath{\alpha}$,
T) plane (including the whole region $\ensuremath{\alpha}>1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low
T and $0<\ensuremath{\alpha}<\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.