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We develop a systematic field-theoretical approach to open quantum systems based on condensed-matter many-body methods. The time evolution of the reduced density matrix for the open quantum system is determined by a transmission matrix.…
In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum…
We present an introduction to the theory of open extended quantum systems. We begin with a microscopic derivation of the so-called Lindblad equation followed by a more abstract approach. Next, we introduce collision models, a versatile…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly…
For the efficient simulation of open quantum systems we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
By exploiting the peculiarities of a recently introduced formalism for describing open quantum systems (the Parametric Representation with Environmental Coherent States) we derive an equation of motion for the reduced density operator of an…
Markovian open quantum systems are described by the Lindblad master equation $\partial_t\rho =\mathcal{L}(\rho)$, where $\rho$ denotes the system's density operator and $\mathcal{L}$ the Liouville super-operator, which is also known as the…
We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open N-level systems. The Lindblad operators that govern the evolution of the system are…
We propose a model to simulate different traffic-flow conditions in terms of quantum graphs hosting an (N+1)-level dot at each site. Our model allows us to keep track of the type and of the destination of each vehicle. The traffic flow…
The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of…
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…
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…
We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal driving in…
Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by Completely Positive (CP) maps, for which several quantum simulation schemes exist. We present a…
The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus…
We study a 1-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in [J.Stat.Mech.,…
We introduce the concept of Magic Subspaces for the control of dissipative N- level quantum systems whose dynamics are governed by Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for…
We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced in [EPL 77, 50007 (2007)]. The resulting Lindblad master equation…