Modeling the Non Markovian Dynamics of Open Quantum System Strongly Coupled to Reservoirs Through Quantum Master Equation by Method of Reaction Coordinate Mapping and the Mesoscopic Lead Construction
In this article we want to present a thorough overview about the well known technique known as the Reaction Coordinate Mapping which is one of the most used theoretical tool in the context of Open quantum system and Quantum thermodynamics of quantum systems which is not weakly coupled to the reservoir. Here we discuss different aspects of the Reaction Coordinate mapping along with detailed mathematical derivations for the Bosonic and Fermionic mappings which can be achieved through the Symplectic and unitary transformations. In the later part of this article we discuss the derivation of the Quantum master equation for the extended systems (System+Reaction Coordinate) coupled to the residual reservoir in the weak coupling limit described by the usual Redfield Quantum Master equation. We observe that though the dynamics of the Extended system is Markovian in nature because of the weak coupling between the extended system and the Residual reservoir but the Reaction coordinate transformation enables us to analyses the dynamics of the system which is essentially non-Markovian.
In this article we want to present a thorough overview about the well known technique known as the Reaction Coordinate Mapping which is one of the most used theoretical tool in the context of Open quantum system and Quantum thermodynamics of quantum systems which is not weakly coupled to the reservoir. Here we discuss different aspects of the Reaction Coordinate mapping along with detailed mathematical derivations for the Bosonic and Fermionic mappings which can be achieved through the Symplectic and unitary transformations. In the later part of this article we discuss the derivation of the Quantum master equation for the extended systems (System+Reaction Coordinate) coupled to the residual reservoir in the weak coupling limit described by the usual Redfield Quantum Master equation. We observe that though the dynamics of the Extended system is Markovian in nature because of the weak coupling between the extended system and the Residual reservoir but the Reaction coordinate transformation enables us to analyses the dynamics of the system which is essentially non-Markovian.
In this article we want to present a thorough overview about the well known technique known as the Reaction Coordinate Mapping which is one of the most used theoretical tool in the context of Open quantum system and Quantum thermodynamics of quantum systems which is not weakly coupled to the reservoir. Here we discuss different aspects of the Reaction Coordinate mapping along with detailed mathematical derivations for the Bosonic and Fermionic mappings which can be achieved through the Symplectic and unitary transformations. In the later part of this article we discuss the derivation of the Quantum master equation for the extended systems (System+Reaction Coordinate) coupled to the residual reservoir in the weak coupling limit described by the usual Redfield Quantum Master equation. We observe that though the dynamics of the Extended system is Markovian in nature because of the weak coupling between the extended system and the Residual reservoir but the Reaction coordinate transformation enables us to analyses the dynamics of the system which is essentially non-Markovian. The idea of the mesoscopic lead construction and brute force chain mapping techniques has been introduced which can be used to bypass the strong system bath coupling situations.
In this tutorial we want to present a thorough overview about the well known technique known as the Reaction Coordinate Mapping which is one of the most used theoretical tool in the context of Open quantum system and Quantum thermodynamics of quantum systems which is not weakly coupled to the reservoir. Here we discuss different aspects of the Reaction Coordinate mapping along with detailed mathematical derivations for the Bosonic and Fermionic mappings which can be achieved through the Symplectic and unitary transformations. In the later part of this article we discuss the derivation of the Quantum master equation for the extended systems (System+Reaction Coordinate) coupled to the residual reservoir in the weak coupling limit described by the usual Redfield Quantum Master equation. We observe that though the dynamics of the Extended system is Markovian in nature because of the weak coupling between the extended system and the Residual reservoir but the Reaction coordinate transformation enables us to analyses the dynamics of the system which is essentially non-Markovian.
The primary pathway to the investigation of exceptional points (EPs) in open quantum systems has been the use of Markovian master equations. However, recently it has been realised that they can arise in settings that show non-Markovian behaviour. The main approach in this direction has been the use of pseudomodes, which allow the influence of a structured environment to be replaced by new damped auxiliary modes. In this work, we use a Heisenberg-equation approach which relies on the reaction-coordinate formalism to obtain exact analytical dynamics. First, we show how our method considerably simplifies the analysis compared to the use of master equations. Second, we utilise it to discuss non-Markovian revivals in systems with second and higher-order EPs, showing that the notion that EPs demarcate the onset of revivals is not generally true. We then utilise our results to discuss the dynamical effects of higher-order non-Markovian EPs, deriving bounds on the number of revivals and investigating enhanced asymptotic relaxation near higher-order EPs. Finally, we investigate non-Markovian EPs with engineered reservoirs and show how they can be utilised to control the rate of irreversible information loss.
The reaction coordinate (RC) technique is emerging as a significant tool in the study of quantum dissipative dynamics and quantum thermodynamics. With the objective to further establish this tool, here we explore to what extent the method can capture non-Markovian dynamics of open quantum systems. As a case study, we focus on the pure decoherence model of a spin coupled to a harmonic reservoir. We compare the spin dynamics and measures for non-Markovianity from the exact analytical solution to simulations based on the RC method at the level of a second-order quantum master equation. We find that the RC method can quantitatively capture non-Markovian effects at strong system-bath coupling and for structured baths. This is rationalized by the fact that the collective RC bath mode, which is made part of the system, maintains system-bath correlations. Lastly, we apply our RC method and study the spin-boson model in the non-Markovian regime.
We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.
In this thesis, we discuss aspects of the simulation, characterisation, and control of the dynamics of open quantum systems. The latter are systems governed by quantum mechanical laws and interacting with an environment, which is typically much larger than the system itself. According to the standard approach, one is usually able to perform a suitable average over the environmental degrees of freedom, resulting in an effective description of the main system dynamics, which accounts for the effects of the interaction with the surroundings. In standard scenarios, usually studied within the so-called Born-Markov approximation, the system-environment coupling is weak and such that we can perform a neat separation of timescales: the environmental dynamics is assumed to be fast compared to the typical evolution timescale of the system of interest. However, nowadays we are able to inspect physical scenarios where the usual Born-Markov approximation breaks down: the interaction between system and environment can be strong, likely leading to non-negligible memory (non-Markovian) effects. In this work, we discuss some instances in which we cannot work in the standard Born-Markov regime. We introduce and analyse some numerical and analytical techniques to characterise and simulate non-standard scenarios. We show that, even in the Markovian regime, the traditional formulation of thermodynamic irreversibility shows flaws and inconsistencies. We thus use phase-space methods to assess the role of initial correlations shared by the two parties of a bipartite harmonic system in the entropy production rate, including non-Markovian effects. Furthermore, we show that certain interactions enable to redraw the boundaries between the system and the environment in an effective manner, resulting in a new picture where the system degrees of freedom are augmented, while the residual environment is rearranged in such a way that the Born-Markov approximation is recovered. This analytical technique, known as reaction coordinate mapping approach, is employed in this work to show that, upon an accurate choice of the parameter regime, a spin-boson model can serve as a quantum analogue simulator of non-Markovian multiphoton Jaynes-Cummings models. These systematic studies shed light on the thermodynamic characterisation of open quantum systems, as well as on their numerical simulation.