Showing papers on "Master equation published in 2016"
TL;DR: In this article, reaction coordinate mapping is used to define the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition.
Abstract: We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate (RC) mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the RC), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.
163 citations
TL;DR: In this paper, a new quantum master equation which improves shortcomings of the local approach known in the so-called local approach is derived, which does not violate the second law of thermodynamics.
Abstract: A system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. A new quantum master equation which improves shortcomings of the master equation known in the so-called local approach is derived. The usual quantum master equation describing the weak coupling of the system with reservoir requires the knowledge of eigenvalues and eigenvectors of the Hamiltonian of the system, so it often becomes impractical. By this reason, when the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. However, recently, it was reported that the local approach master equation leads to the violation of the second law of thermodynamics. We develop a systematic perturbation expansion to derive corrections to the local approach master equation. Using this improvement of the local approach, we derive an expression for the heat flux for a particular model and show that it does not violate the second law of thermodynamics.
115 citations
TL;DR: This work extends the reaction coordinate master equation technique to incorporate system-environment correlations and the resultant non-Markovian dynamical effects and obtains energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters.
Abstract: We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.
115 citations
TL;DR: In this article, the hierarchical quantum master equation approach, which generalizes perturbative master equation methods by including higher-order contributions as well as non-Markovian memory, is used in this context.
Abstract: Quantum transport in nanosystems is often characterized by strong coupling between electronic and vibrational degrees of freedom. Examples include single-molecule junctions, nanoelectromechanical systems, and suspended carbon nanotubes. Electronic-vibrational coupling manifests itself in vibronic structures in the transport characteristics and results in a multitude of nonequilibrium phenomena, such as current-induced local heating and cooling, multistability, switching, hysteresis, and decoherence. The theoretical study of quantum transport, in particular in the strong-coupling regime, requires nonperturbative approaches that can be systematically converged, i.e., numerically exact methods. In this work, the authors outline how the hierarchical quantum master equation approach, which generalizes perturbative master equation methods by including higher-order contributions as well as non-Markovian memory, can be used in this context. The results show that vibrational nonequilibrium effects are important in a broad spectrum of scenarios, which range from the nonadiabatic to the adiabatic regime and include both resonant and off-resonant transport.
108 citations
TL;DR: In this paper, the authors propose a method to study the thermodynamic behavior of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches.
Abstract: We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the reaction coordinate), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.
107 citations
TL;DR: In this article, a self-contained review of master equation approaches to modeling phonon effects in optically driven self-assembled quantum dots is provided, including weak-coupling master equations that are perturbative in the exciton-phonon coupling.
Abstract: We provide a self-contained review of master equation approaches to modelling phonon effects in optically driven self-assembled quantum dots. Coupling of the (quasi) two-level excitonic system to phonons leads to dissipation and dephasing, the rates of which depend on the excitation conditions, intrinsic properties of the QD sample, and its temperature. We describe several techniques, which include weak-coupling master equations that are perturbative in the exciton-phonon coupling, as well as those based on the polaron transformation that can remain valid for strong phonon interactions. We additionally consider the role of phonons in altering the optical emission characteristics of quantum dot devices, outlining how we must modify standard quantum optics treatments to account for the presence of the solid-state environment.
106 citations
TL;DR: In this paper, the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials is presented.
Abstract: We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the $N=2$ case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.
99 citations
TL;DR: In this paper, the authors present a detailed summary of different collision models developed in the framework of the direct simulation Monte Carlo (DSMC) method, i.e., the simplified Bernoulli trial (SBT), which permits efficient low-memory simulation of rarefied gas flows.
97 citations
TL;DR: In this paper, a quantum generalization of the Crooks fluctuation theorem is presented, which not only includes the energy changes in the reservoir, but also the full description of its evolution, including coherences.
Abstract: Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs with the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy, and the control system that implements the dynamic, we here obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir, but the full description of its evolution, including coherences. This approach moreover opens up for generalizations of the concept of fluctuation relations. Here we introduce `conditional' fluctuation relations that are applicable to non-equilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
97 citations
TL;DR: In this article, the authors proposed several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields.
Abstract: We propose several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms. The schemes could be realized in one step without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields. When the Rydberg-Rydberg-interaction (RRI) strength and the parameters of the driving fields satisfy some certain conditions, the effective Rabi oscillation between the two-excitation Rydberg state and the ground state would be generated, which is out of the Rydberg blockade regime and essential for our scheme. In addition, the individual addressing of the atoms is not required. And the schemes can work under strong or weak RRI strength. The imperfections induced by the variation of RRI strength and spontaneous emission are discussed through solving the master equation numerically.
92 citations
TL;DR: In this article, the authors considered a quantum system strongly coupled to multiple heat baths at different temperatures and investigated the heat transport phenomena in this system using two definitions of the heat current.
Abstract: We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)—which have a purely quantum mechanical origin—the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat curren...
01 Jan 2016
TL;DR: In this paper, a generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian was presented.
Abstract: We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian $\mathcal{L}(t)$. We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of $\mathcal{L}(t)$ will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time $T$. In the case of a finite number of level crossings, the scaling becomes ${T}^{\ensuremath{-}\ensuremath{\eta}}$ with an exponent $\ensuremath{\eta}$ that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time $T$ should be long compared to the corresponding minimum inverse gap squared of $\mathcal{L}(t)$. Our results are illustrated with several examples.
TL;DR: In this article, the authors consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior.
Abstract: In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
TL;DR: This work demonstrates the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used.
Abstract: Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
TL;DR: It is concluded that multilevel phaseonium fuel can be utilized to overcome the decoherence in available systems and bring the photonic Carnot engines much closer to the capabilities of current resonator technologies.
Abstract: We investigate scaling of work and efficiency of a photonic Carnot engine with a number of quantum coherent resources. Specifically, we consider a generalization of the "phaseonium fuel" for the photonic Carnot engine, which was first introduced as a three-level atom with two lower states in a quantum coherent superposition by M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], to the case of N+1 level atoms with N coherent lower levels. We take into account atomic relaxation and dephasing as well as the cavity loss and derive a coarse-grained master equation to evaluate the work and efficiency analytically. Analytical results are verified by microscopic numerical examination of the thermalization dynamics. We find that efficiency and work scale quadratically with the number of quantum coherent levels. Quantum coherence boost to the specific energy (work output per unit mass of the resource) is a profound fundamental difference of quantum fuel from classical resources. We consider typical modern resonator set ups and conclude that multilevel phaseonium fuel can be utilized to overcome the decoherence in available systems. Preparation of the atomic coherences and the associated cost of coherence are analyzed and the engine operation within the bounds of the second law is verified. Our results bring the photonic Carnot engines much closer to the capabilities of current resonator technologies.
TL;DR: In this article, it was shown that the usual master equation formalism of Markovian open quantum systems is completely equivalent to a certain state vector formalism, where the state vector of the system satisfies a given frictional Schrodinger equation except for random instant transitions of discrete nature.
Abstract: We show that the usual master equation formalism of Markovian open quantum systems is completely equivalent to a certain state vector formalism. The state vector of the system satisfies a given frictional Schr\"odinger equation except for random instant transitions of discrete nature. Hasse's frictional Hamiltonian is recovered for the damped harmonic oscillator.
TL;DR: In this paper, the authors carried out a sequence of analytical steps utilizing the Dirac constraint quantization and gauge invariant influence functional techniques resulting in a general master equation of a compact form that describes an open quantum gravitational system with arbitrary bosonic fields.
Abstract: Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms of energy and matter causing decoherence. This may have subtle implications on precision laboratory experiments and astronomical observations and could limit the ultimate capacities for quantum technologies prone to decoherence. To establish the essential physical mechanism of decoherence under weak spacetime fluctuations, we carry out a sequence of analytical steps utilizing the Dirac constraint quantization and gauge invariant influence functional techniques resulting in a general master equation of a compact form that describes an open quantum gravitational system with arbitrary bosonic fields. An initial application of the theory is illustrated by the implied quantum gravitational dissipation of light as well as (non)relativistic massive or massless scalar particles. Related effects could eventually lead to important physical consequences including those on a cosmological scale and for a large number of correlated particles.
TL;DR: In this paper, the authors explore energy transfer in a generic three-level system, which is coupled to three non-equilibrium baths, and show that the coupling with the phonon bath not only modifies the steady state, resulting in population inversion, but also introduces a finite steady state coherence which optimizes the energy transfer flux and efficiency.
Abstract: We explore energy transfer in a generic three-level system, which is coupled to three non-equilibrium baths. Built on the concept of quantum heat engine, our three-level model describes non-equilibrium quantum processes including light-harvesting energy transfer, nano-scale heat transfer, photo-induced isomerization, and photovoltaics in double quantum-dots. In the context of light-harvesting, the excitation energy is first pumped up by sunlight, then is transferred via two excited states which are coupled to a phonon bath, and finally decays to the reaction center. The efficiency of this process is evaluated by steady state analysis via a polaron-transformed master equation; thus the entire range of the system-phonon coupling strength can be covered. We show that the coupling with the phonon bath not only modifies the steady state, resulting in population inversion, but also introduces a finite steady state coherence which optimizes the energy transfer flux and efficiency. In the strong coupling limit, the steady state coherence disappears and the efficiency recovers the heat engine limit given by Scovil and Schultz-Dubois (1959 Phys. Rev. Lett. 2 262).
TL;DR: In this article, the authors provide a pedagogic and self-contained introduction to master equations and their representation by path integrals, and discuss analytical and numerical methods for the solution of master equations, keeping their focus on methods applicable even when stochastic fluctuations are strong.
Abstract: This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on methods that are applicable even when stochastic fluctuations are strong. The reviewed methods include the generating function technique and the Poisson representation, as well as novel ways of mapping the forward and backward master equations onto linear partial differential equations (PDEs). Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE obeyed by the generating function. After outlining these methods, we solve the derived PDEs in terms of two path integrals. The path integrals provide distinct exact representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Furthermore, we review a method for the approximation of rare event probabilities and derive path integral representations of Fokker-Planck equations. To make our review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.
Book•
10 Feb 2016
TL;DR: In this article, the concept of single-molecule transport was introduced and a generalized master equation was proposed to solve the problem of nonequilibrium many-body problems.
Abstract: Introduction.- Part I Basic Concepts.- Coherent transport: Green function method.- Tunneling and master equation.- Electron-electron interaction and Coulomb blockade .- Vibrons and polarons.- Part II Advanced methods.- Interacting nanosystems: discrete-level models.- Generalized master equation.- Nonequilibrium Green functions.- Current through an interacting system.- Some nonequilibrium many-body problems.- Time-dependent transport.- Part III Single-molecule transport.- Basic theoretical concepts of single-molecule electronics.- Ab initio transport theory.- Towards single-molecule devices.
TL;DR: The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes and puts into evidence the nonuniqueness of the relationship arising due to the typical quantum issue of operator ordering.
Abstract: We provide a general construction of quantum generalized master equations with a memory kernel leading to well-defined, that is, completely positive and trace-preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes and puts into evidence the nonuniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows us to phenomenologically construct a large class of non-Markovian evolutions taking as the starting point collections of time-dependent maps and instantaneous transformations describing the microscopic interaction dynamics.
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TL;DR: In this paper, a quantum flywheel is studied with the purpose of storing useful work in quantum levels, while additional power is extracted continuously from the flywheel by a quantum heat engine.
Abstract: A quantum flywheel is studied with the purpose of storing useful work in quantum levels, while additional power is extracted continuously from the device The flywheel gains its energy form a quantum heat engine Generally, when a work repository is quantized the work exchange with the engine is accompanied with heat exchange, which may degrade the charging efficiency In the particular realization of a quantum harmonic oscillator work repository, quantum and thermal fluctuations dominates the dynamics Quantum monitoring and feedback control are applied to the flywheel, as it is shown to be an essential part of stabilizing and regulating its state of operation, and bringing the system to a steady state A particular balance between information gained by measuring the system and the information fed back to the system is found to maximize the charging efficiency The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations
TL;DR: This work provides the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics, and derives the master equation unraveled by a non- Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-markovian collapse models.
Abstract: Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrodinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.
TL;DR: In this paper, a master-equation based approach to drive a quantum network with $n$ qubits to a consensus (symmetric) state introduced by Mazzarella et al. is proposed.
Abstract: In this paper, we propose and study a master-equation based approach to drive a quantum network with $n$ qubits to a consensus (symmetric) state introduced by Mazzarella et al. The state evolution of the quantum network is described by a Lindblad master equation with the Lindblad terms generated by continuous-time swapping operators, which also introduce an underlying interaction graph. We establish a graphical method that bridges the proposed quantum consensus scheme and classical consensus dynamics by studying an induced graph (with $2^{2n}$ nodes) of the quantum interaction graph (with $n$ qubits). A fundamental connection is then shown that quantum consensus over the quantum graph is equivalent to componentwise classical consensus over the induced graph, which allows various existing works on classical consensus to be applicable to the quantum setting. Some basic scaling and structural properties of the quantum induced graph are established via combinatorial analysis. Necessary and sufficient conditions for exponential and asymptotic quantum consensus are obtained, respectively, for switching quantum interaction graphs. As a quantum analogue of classical synchronization of coupled oscillators, quantum synchronization conditions are also presented, in which the reduced states of all qubits tend to a common trajectory.
TL;DR: In this paper, a bipartite Lindblad-type master equation (ME) was derived in a closed form for any initial product state of an open quantum system and a detailed microscopic derivation of the result was provided in terms of a mapping between two collision models.
Abstract: A well-known situation in which a non-Markovian dynamics of an open quantum system $S$ arises is when this is coherently coupled to an auxiliary system $M$ in contact with a Markovian bath. In such cases, while the joint dynamics of $S\text{\ensuremath{-}}M$ is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of $S$. Furthermore, there are several instances (e.g., the dissipative Jaynes-Cummings model) in which a closed ME for the $S$'s state cannot even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of $S$ can be derived exactly and in a closed form for any initial product state of $S\text{\ensuremath{-}}M$. We provide a detailed microscopic derivation of our result in terms of a mapping between two collision models.
TL;DR: In this paper, sufficient conditions for the memory kernel which guarantee legitimate (completely positive and trace-preserving) dynamical map are derived. And it turns out that these conditions provide a natural parameterization of the dynamic map being a generalization of Markovian semigroup.
Abstract: We derive sufficient conditions for the memory kernel which guarantee legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide a natural parameterizations of the dynamical map being a generalization of Markovian semigroup. It is shown that this class of maps cover almost all known examples -- from Markovian semigroup, semi-Markov evolution up to collision models and their generalization.
TL;DR: In this paper, the authors consider two bosonic modes coupled to a bath and find that a smooth crossover of the equations of motion between dominant intersystem and system-bath coupling exists, but it requires a nonsecular master equation.
Abstract: Finding efficient descriptions of how an environment affects a collection of discrete quantum systems would lead to new insights into many areas of modern physics. Markovian, or time-local, methods work well for individual systems, but for groups a question arises: Does system-bath or intersystem coupling dominate the dissipative dynamics? The answer has profound consequences for the long-time quantum correlations within the system. We consider two bosonic modes coupled to a bath. By comparing an exact solution against different Markovian master equations, we find that a smooth crossover of the equations of motion between dominant intersystem and system-bath coupling exists---but it requires a nonsecular master equation. We predict singular behavior of the dynamics and show that the ultimate failure of nonsecular equations of motion is essentially a failure of the Markov approximation. Our findings support the use of time-local theories throughout the crossover between system-bath-dominated and intersystem-coupling-dominated dynamics.
TL;DR: A reduction method based on the chemical Langevin equations by the stochastic averaging principle developed in the work of Khasminskii and Yin leads to a limit averaging system, which is an approximation of the slow reactions.
Abstract: The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.
TL;DR: The theoretical findings evidence the existence of a system inherent maximal output power, and by implementing a Lindblad master equation, quantifies the role of thermal relaxations on the cycle efficiency.
Abstract: A quantum thermodynamic cycle with a chiral multiferroic working substance such as LiCu_{2}O_{2} is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite-time quantum thermodynamic cycle, which is found to depend on the spin ordering. The emergent electric polarization associated with the chiral spin order, i.e., the magnetoelectric coupling, renders possible steering of the spin order by an external electric field and hence renders possible an electric-field control of the cycle. Due to the intrinsic coupling between the spin and the electric polarization, the cycle performs an electromagnetic work. We determine this work's mean-square fluctuations, the irreversible work, and the output power of the cycle. We observe that the work mean-square fluctuations are increased with the duration of the adiabatic strokes, while the irreversible work and the output power of the cycle show a nonmonotonic behavior. In particular, the irreversible work vanishes at the end of the quantum adiabatic strokes. This fact confirms that the cycle is reversible. Our theoretical findings evidence the existence of a system inherent maximal output power. By implementing a Lindblad master equation we quantify the role of thermal relaxations on the cycle efficiency. We also discuss the role of entanglement encoded in the noncollinear spin order as a resource to affect the quantum thermodynamic cycle.