Related papers: Linear stochastic wave-equations for continuously …
A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear stochastic wave equation.…
During a continuous measurement, quantum systems can be described by a stochastic Schr\"odinger equation which, in the appropriate limit, reproduces the von Neumann wave-function collapse. The average behavior on the ensemble of all…
Starting from an experimentally feasible atomic setup, we derive a stochastic Schr\"{o}dinger equation that captures the homodyne detection record of a strongly interacting system. Applying the rotating wave approximation to the linear…
The stochastic Schr\"odinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties…
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…
We derive the stochastic Schrodinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von…
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir…
We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We…
The superposition principle is one of the most fundamental principles of quantum mechanics. According to the Schr\"odinger equation, a physical system can be in any linear combination of its possible states. While the validity of this…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are…
We propose a nonlinear modification of the Schr\"{o}dinger equation that possesses the main properties of this equation such as the Galilean invariance, the weak separability of composite systems, and the homogeneity in the wave function.…
A stochastic model for a continuous photon counting and heterodyne measurement of a coherent source is proposed. A nonlinear filtering equation for the posterior state of a single-mode field in a cavity is derived by using the methods of…
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
Two essential shortcomings of the axiomatics of wave mechanics are revealed, which make its consistent interpretation impossible. The first is that the standard formulation of the superposition principle contradicts the exact solutions of…
We study nonlinear dynamics of superposition of quantum wavepackets in various systems such as Kerr medium, Morse oscillator and bosonic Josephson junction. The prime reason behind this study is to find out how the superposition of states…