Related papers: A perturbative approach to non-Markovian stochasti…
A number of non-Markovian stochastic Schr\"odinger equations, ranging from the numerically exact hierarchical form towards a series of perturbative expressions sequentially presented in an ascending degrees of approximations are revisited…
Firstly, the Markovian stochastic Schr\"odinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation…
We present embedding procedures for the non-Markovian stochastic Schr\"{o}dinger equations, arising from studies of quantum systems coupled with bath environments. By introducing auxiliary wave functions, it is demonstrated that the…
Non-Markovian stochastic Schr\"odinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only…
We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equations for open quantum systems coupled to an environment up to arbitrary orders of noises or coupling strengths. As an…
We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schr\"odinger equations driven by additive It\^o noise. The class of nonlinearities of interest includes nonlocal…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…
Principles of monitoring non-Markovian open quantum systems are analyzed. We use the field representation of the environment (Gardiner and Collet, 1985) for the separation of its memory and detector part, respectively. We claim the…
Perturbative methods are attractive to describe the electronic structure of molecular systems because of their low-computational cost and systematically improvable character. In this work, a two-step perturbative approach is introduced…
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…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have…
In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a…
We develop a new approach for solving stochastic quantum master equations with mixed initial states. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a…
In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method 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 propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…
We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation.…