Related papers: Numerical solution of stochastic master equations …
The $O(N)$ stochastic propagation method, which relies on the numerical solution of the time-dependent Schr\"odinger equation using random initial states, is widely used in large-scale first-principles calculations. In this work, we…
Non-Markovian dynamics of two interacting two-level qubits coupled to a bosonic bath was previously studied using the quantum-state-diffusion (QSD) equation, where a stochastic state is used to describe the system. In this study, we provide…
We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
We study stochastic evolution equations describing the dynamics of open quantum systems. First, using resolvent approximations, we obtain a sufficient condition for regularity of solutions to linear stochastic Schroedinger equations driven…
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions.
We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear…
We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
Deep quantum neural networks may provide a promising way to achieve quantum learning advantage with noisy intermediate scale quantum devices. Here, we use deep quantum feedforward neural networks capable of universal quantum computation to…
Due to the good performance of neural networks in high-dimensional and nonlinear problems, machine learning is replacing traditional methods and becoming a better approach for eigenvalue and wave function solutions of multi-dimensional…
Interacting spin-boson models encompass a large class of physical systems, spanning models with a single spin interacting with a bosonic bath -- a paradigm of quantum impurity problems -- to models with many spins interacting with a cavity…
A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory.…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
We present a class of exponential integrators to compute solutions of the stochastic Schr\"odinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the…
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
A novel quantum dynamical method to simulate vibronic reaction dynamics in molecules at metal surfaces is proposed. The method is based on the hierarchical quantum master equation approach and uses a discrete variable representation of the…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…