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We present a collection of methods to simulate entangled dynamics of open quantum systems governed by the Lindblad equation with tensor network methods. Tensor network methods using matrix product states have been proven very useful to…

We examine the effectiveness of Lindblad master equation in capturing the short-time dynamics of entanglement and purity in open quantum systems. Focusing on two interacting two-level systems interacting with a larger environment, we…

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated…

In this paper we consider the modelling and simulation of open quantum systems from a device engineering perspective. We derive master equations at different levels of approximation for a Superconducting Quantum Interference Device (SQUID)…

Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic…

Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum…

In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the…

Contrary to conventional quantum mechanics, which treats measurement as instantaneous, here we explore a model for finite-time measurement. The main two-level system interacts with the measurement apparatus in a Markovian way described by…

We obtain a Gorini-Kossakowski-Sudarshan-Lindblad -like master equation for two or more quantum systems connected locally to a combination of Markovian and non-Markovian heat baths. The master equation was originally formulated for…

Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the…

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the…

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows to eliminate the bosonic…

A non-Markovian stochastic Schroedinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. Its solutions, when averaged over the noise, reproduce the standard reduced density operator without any…

We derive a Markovian master equation for driven open quantum systems based on the Lewis-Riesenfeld invariants theory, which is available for arbitrary driving protocols.The role of the Lewis-Riesenfeld invariants is to help us bypass the…

Determining the Markovianity and non-Markovianity of a quantum process is a critical problem in the theory of open quantum systems, as their behaviors differ significantly in terms of complexity. It is well recognized that a quantum process…

The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body Liouvillians based on Richardson-Gaudin models…

Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in…

It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo…

Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of…

Redfield master equation was applied to study the dynamics of an ensemble of interacting pairs of unlike spins at room temperature. This spin quantum system is a workbench quantum model to analyze the relaxation dynamics of a heteronuclear…