arXiv subjects

Heinz-Peter Breuer

Publications and source records attributed to Heinz-Peter Breuer.

At least 19 recordsLinked to original sources

arXiv2026

Floquet time-convolutionless master equation for non-Markovian driven quantum systems

We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.

quant-ph↗

arXiv2026

Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems

We develop a recursive perturbative expansion for the time-convolutionless (TCL) generator of an open quantum system in a generalized Lindblad form. This formulation provides a systematic approach to derive the generator at arbitrary order while preserving a Lindblad-like structure, without imposing assumptions on the system or environment beyond an initially uncorrelated state. The generator is written, at all orders, in a canonical form, which also corresponds to the minimal dissipation condition, which uniquely specifies the decomposition of the generator into Hamiltonian and dissipative contributions. To validate the method and show its effectiveness in addressing non-Markovian dynamics and strong-coupling effects, we compute the generator explicitly up to fourth order.

quant-ph↗

arXiv2026

Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion

We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to the time-local generator of the reduced dynamics. We derive a general expression for the effective Hamiltonian and develop a recursive perturbative expansion that expresses it in terms of system-bath interaction terms and bath correlation functions. This expansion provides a systematic tool for analyzing energy renormalization effects across different coupling regimes. Applying our framework to paradigmatic spin systems, we reveal how environmental correlations influence energy shifts and eigenbasis rotations, offering new insights into strong-coupling effects and non-Markovian quantum thermodynamics.

quant-ph↗

arXiv2026

Quantum Otto cycle in the Anderson impurity model

We study the thermodynamic performance of a periodic quantum Otto cycle operating on the single-impurity Anderson model. Using a decomposition of the time-evolution generator based on the principle of minimal dissipation, combined with the numerically exact hierarchical equations of motion (HEOM) method, we analyze the operating regimes of the quantum thermal machine and investigate effects of Coulomb interactions, strong system-reservoir coupling, and energy level alignments. Our results show that Coulomb interaction can change the operating regimes and may lead to an enhancement of the efficiency.

cond-mat.mes-hall↗

arXiv2026

Fluctuations of path-dependent thermodynamic quantities in open quantum systems via two-point system-only measurements

We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat, and to isolate correction factors to Jarzynski's equality, requiring only access to the system degrees of freedom. This framework is flexible and can be applied to the limiting case of closed systems, recovering previous, yet seemingly contradictory, results from the literature. Moreover, the formalism admits a straightforward extension to strongly coupled open quantum systems. We investigate the effect of specific dynamical classes on the fluctuation relations, and show that the pure decoherence case is particularly special, as it deterministically does not contain any heat contribution and thus constitutes a class of open system dynamics for which the Jarzynski equality for work fluctuations is identically true at any coupling strength. Finally, we look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics, both in the weakly-coupled regime and in the deep non-Markovian regime.

quant-ph↗

arXiv2026

Expansion of time-convolutionless non-Markovian quantum master equations: A case study using the Fano-Anderson model

We explore the performance of the time-convolutionless (TCL) projection operator technique using the Fano-Anderson model as a test case. Comparing the exact TCL master equation with an expansion in powers of the strength of the system-environment coupling, we analyze the transient dynamics as well as the steady-state behavior. For a Lorentzian spectral density we demonstrate that the dimensionless expansion parameter corresponds to the ratio of the environmental correlation time to the relaxation time of the system, and we derive the convergence radius for the TCL expansion, which is seen to depend on the ratio of detuning and width of the spectral density. We further study the quantum non-Markovianity of the model based on the evolution of the Bures distance between quantum states and how it is represented by the second and fourth order of the expansion. Our results highlight both the strengths and the limitations of the TCL formalism in capturing key features of open quantum systems and, in particular, the challenges of accurately describing strongly coupled systems and non-Markovian dynamics.

quant-ph↗

arXiv2026

Local approach to entropy production in the nonequilibrium dynamics of open quantum systems

We discuss fundamental features of the local expression for the entropy production rate of the nonequilibrium quantum dynamics of open systems and its relations to memory effects and the spectrum of the generator of the dynamics. Defining the entropy production rate as negative rate of change of the relative entropy with respect to an instantaneous fixed point, it is shown that positivity of the entropy production rate for all possible initial states implies that the real parts of the eigenvalues of the time-local generator for the quantum master equation are always negative. It is further demonstrated that Markovian dynamics, identified as P-divisibility of the quantum dynamical map, implies positivity of entropy production rate, thus providing a kind of generalized second law in the nonequilibrium regime. We also prove by means of the counterexample of a phase covariant quantum master equation that the converse of this statement is not true, i.e., there are non-Markovian dynamics for which the entropy production rate is always positive. Thus, we conclude that the emergence of negative entropy production rates is a sufficient but not necessary condition for non-Markovianity of the quantum dynamics. Finally, we also consider a recently introduced map-based notion of entropy production and show the equivalence between its positivity and Markovianity for general finite-dimensional systems.

quant-ph↗

arXiv2026

Control of memory effects in a spin-boson system by periodic driving

We study the emergence of quantum memory effects in a spin-boson system at finite temperature driven by an external time-periodic force. Quantifying memory effects by the trace-distance based measure for non-Markovianity and performing numerical simulations employing the hierarchical equations of motion approach, we find a pronounced peak structure when plotting the non-Markovianity measure as a function of the driving amplitude. This distinctive feature is interpreted using Floquet theory and the Floquet-Lindblad master equation, associating the peaks with the degeneracies of the quasienergy spectrum which lead to a strong enhancement of the relaxation times of the system. These results suggest strategies for the efficient control of non-Markovianity in open quantum systems by periodic driving.

quant-ph↗

arXiv2025

Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems

We study the nonequilibrium thermodynamics of pure decoherence processes in open quantum systems coupled to a thermal reservoir. We review various definitions of central quantities, such as internal energy, work, heat and entropy production, developed within local and global approaches to quantum thermodynamics. Within local approaches thermodynamic quantities only refer to the open system's degrees of freedom, while in the global approaches certain quantities are defined by referring explicitly to the reservoir degrees of freedom. Employing a microscopic, analytically solvable model, we perform a comparison of these two perspectives, revealing substantial differences in the thermodynamic quantities and in the formulations of the first and second law. The main reason for these discrepancies is the fact that the global approaches involve the system-reservoir interaction which exchanges a large amount of energy with the environment, while the average open system energy is constant in time because the dynamics represents pure decoherence and does not affect the open system populations.

quant-ph↗

arXiv2024

Phase space measures of information flow in open systems: A quantum and classical perspective of non-Markovianity

The exchange of information between an open quantum system and its environment, especially the backflow of information from the environment to the open system associated with quantum notions of non-Markovianity, is a widely discussed topic for years now. This information flow can be quantified by means of the trace distance of pairs of quantum states which provides a measure for the distinguishability of the states. The same idea can also be used to characterize the information flow in classical open systems through a suitable distance measure for their probability distributions on phase space. Here, we investigate the connection between the trace distance based quantum measure and the Kolmogorov distance for differently ordered quasi-probability distributions on phase space. In particular, we show that for any pair of quantum states one can find a unique quasi-probability distribution for which the Kolmogorov distance coincides with the trace distance. We further study the quantum-to-classical transition of the distance measures. Employing the Caldeira-Legget model of quantum Brownian motion as a prototypical example, numerical simulations indicate a particularly rapid convergence of the Kolmogorov distance of the Wigner functions to the trace distance in the classical uncertainty limit, which establishes the Wigner function distance as an optimal tool for measuring semi-classical information backflow and for quantifying non-Markovianity in open continuous variable quantum systems.

quant-ph↗

arXiv2024

Quantum thermodynamics of the spin-boson model using the principle of minimal dissipation

A recently developed approach to the thermodynamics of open quantum systems, on the basis of the principle of minimal dissipation, is applied to the spin-boson model. Employing a numerically exact quantum dynamical treatment based on the hierarchical equations of motion (HEOM) method, we investigate the influence of the environment on quantities such as work, heat and entropy production in a range of parameters which go beyond the weak-coupling limit and include both the non-adiabatic and the adiabatic regimes. The results reveal significant differences to the weak-coupling forms of work, heat and entropy production, which are analyzed in some detail.

quant-ph↗

arXiv2024

Observing Time-Dependent Energy Level Renormalisation in an Ultrastrongly Coupled Open System

Understanding how strong coupling and memory effects influence the energy levels of open quantum systems is a complex and challenging problem. Here, we show these effects by probing the transition frequency of an open two-level system within the Jaynes-Cummings model, experimentally realised using Ramsey interferometry in a single trapped 25Mg+ ion. Measurements of the system, coupled to a single-mode environment, reveal a time-dependent shift in the system's energy levels of up to 15% of the bare system frequency. This shift, accurately predicted using an open system ansatz of minimal dissipation, results purely from ultra-strong system-mode interactions and the buildup of correlations. Time-averaged measurements converge to the dispersive Lamb shift predictions and match dressed-state energies, indicating that this observed shift represents a generalised Lamb shift applicable across all coupling and detuning regimes. Our findings provide direct evidence of dynamic energy level renormalisation in strongly coupled open quantum systems, although the total system-environment Hamiltonian is static; this underscores the significance of memory effects in shaping the reduced system's energy landscape. These results offer more profound insights into Hamiltonian renormalisation, essential for strong-coupling quantum thermodynamics and advancements in all quantum platforms.

quant-ph↗

arXiv2024

Thermodynamic Roles of Quantum Environments: From Heat Baths to Work Reservoirs

Environments in quantum thermodynamics usually take the role of heat baths. These baths are Markovian, weakly coupled to the system, and initialized in a thermal state. Whenever one of these properties is missing, standard quantum thermodynamics is no longer suitable to treat the thermodynamic properties of the system that result from the interaction with the environment. Using a recently proposed framework for open system quantum thermodynamics which is valid for arbitrary couplings and non-Markovian effects, we show that within the very same model, described by a Fano-Anderson Hamiltonian, the environment can take three different thermodynamic roles: a standard heat bath, exchanging only heat with the system, a work reservoir, exchanging only work, and a hybrid environment, providing both types of energy exchange. The exact role of the environment is determined by the strength and structure of the coupling, and by its initial state. The latter also dictates the long time behaviour of the open system, leading to thermal equilibrium for an initial thermal state and to a nonequilibrium steady state when there are displaced environmental modes.

quant-ph↗

arXiv2024

On positively divisible non-Markovian processes

There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process to be classified as a stochastic process. Combining the Kolmogorov consistency conditions with the Chapman-Kolmogorov equation, we derive a necessary condition for positively divisible stochastic processes on a finite sample space. This necessary condition enables a systematic approach to the manipulation of certain Markov processes in order to obtain a positively divisible non-Markovian process. We illustrate this idea by an example and, in addition, analyze a classic example given by Feller in the light of our approach.

math.PR↗

arXiv2023

Dynamically Emergent Quantum Thermodynamics: Non-Markovian Otto Cycle

Employing a recently developed approach to dynamically emergent quantum thermodynamics, we revisit the thermodynamic behavior of the quantum Otto cycle with a focus on memory effects and strong system-bath couplings. Our investigation is based on an exact treatment of non-Markovianity by means of an exact quantum master equation, modelling the dynamics through the Fano-Anderson model featuring a peaked environmental spectral density. By comparing the results to the standard Markovian case, we find that non-Markovian baths can induce work transfer to the system, and identify specific parameter regions which lead to enhanced work output and efficiency of the cycle. In particular, we demonstrate that these improvements arise when the cycle operates in a frequency interval which contains the peak of the spectral density. This can be understood from an analysis of the renormalized frequencies emerging through the system-baths couplings.

quant-ph↗

arXiv2022

Quantifying the influence of the initial state on the dynamics of an open quantum system

A small system in contact with a macroscopic environment usually approaches an asymptotic state, determined only by some macroscopic properties of the environment such as the temperature or the chemical potential. In the long-time limit, the state of the small system is thus expected to be independent of its initial state. In some situations, however, the asymptotic state of the system is influenced by its initial state and some information about the initial state is kept for all times. Motivated by this finding, we propose a measure to quantify the influence of the initial state of an open system on its dynamics. Using this measure we derive conditions under which the asymptotic state exists and is unique. We demonstrate our concepts for the dynamics of the spin-boson model, identify three qualitatively different long-time behaviors, and discuss how they can be distinguished based on the proposed measure.

quant-ph↗

arXiv2022

Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations

We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect to the corresponding uncorrelated dynamical behavior with the same fixed initial environmental state, described by a completely positive dynamical map. We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system which acts like the proper dynamical map on the set of physical states and represents its unique linear extension. Furthermore, we demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure involving time-dependent, possibly negative transition rates. Thus, the general non-Markovian dynamics of an open quantum system can be described by means of a time-local master equation even in the case of arbitrary, fixed initial system-environment correlations. We present some illustrative examples and explain the relation of our approach to several other approaches proposed in the literature.

quant-ph↗

arXiv2022

Witnessing non-Markovianity by Quantum Quasi-Probability Distributions

We employ frames consisting of rank-one projectors (i.e. pure quantum states) and their induced informationally complete quantum measurements (IC-POVMs) to represent generally mixed quantum states by quasi-probability distributions. In the case of discrete frames on finite dimensional systems this results in a vector like representation by quasi-probability vectors, while for the continuous frame of coherent states in continuous variable (CV) systems the approach directly leads to the celebrated representation by Glauber-Sudarshan P-functions and Husimi Q-functions. We explain that the Kolmogorov distances between these quasi-probability distributions lead to upper and lower bounds of the trace distance which measures the distinguishability of quantum states. We apply these results to the dynamics of open quantum systems and construct a non-Markovianity witness based on the Kolmogorov distance of the P- and Q-functions. By means of several examples we discuss the performance of this witness and demonstrate that it is useful in the regime of high entropy states for which a direct evaluation of the trace distance is typically very demanding. For Gaussian dynamics in CV systems we even find a suitable non-Markovianity measure based on the Kolmogorov distance between the P-functions which can alternatively be used as a witness for non-Gaussianity.

quant-ph↗