Related papers: Stochastic jump processes for non-Markovian quantu…
Understanding the behaviour of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
Do stochastic Schr\"odinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system {\em on average} obeys a master equation, the answer is yes. Markovian stochastic Schr\"odinger…
We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schr\"odinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves…
The stochastic methods in Hilbert space have been used both from a fundamental and a practical point of view. The result we report here concerns only the idea of applying these methods to model the evolution of quantum systems and does not…
We present the stochastic Schroedinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
We derive a time-convolutionless master equation for the spin-boson model in the weak coupling limit. The temporarily negative decay rates in the master equation indicate short time memory effects in the dynamics which is explicitly…
In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical…
We propose an extension of the Schr\"odinger equation for a quantum system interacting with environment. This equation describes dynamics of auxiliary wave-functions $\mathbf{m}$, from which the system density matrix can be reconstructed as…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
The paper is devoted to the study of nonlinear stochastic Schr\"{o}dinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born--Markov approximations, this…
A systematic first-order correction to the standard Markov master equation for open quantum systems interacting with a bosonic bath is presented. It extends the Markov Lindblad master equation to the more general case of non-Markovian…
Realistic quantum mechanical systems are always exposed to an external environment. The presence of the environment often gives rise to a Markovian process in which the system loses information to its surroundings. However, many quantum…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
The interrelationship between the non-Markovian stochastic Schr\"odinger equations and the corresponding non-Markovian master equations is investigated in the finite temperature regimes. We show that the general finite temperature…
Continuity equations associated to continuous-time Markov processes can be considered as Euclidean Schr\"odinger equations, where the non-hermitian quantum Hamiltonian $\bold{H}={\bold{div}}{\bold J}$ is naturally factorized into the…
Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases,…
Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects…
Starting from a generalization of the quantum trajectory theory (based on the stochastic Schr\"odinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in…