Related papers: A New Wave Equation For a Continuous Nondemolition…
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…
Although nondemolition, reliable, and instantaneous quantum measurements of some nonlocal variables are impossible, demolition reliable instantaneous measurements are possible for all variables. It is shown that this is correct also in the…
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual…
Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We…
Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise…
The wave function transformation of the quantum particle considered as a continuous medium was described by the evolution operator with the kernel in the form of path integral. It is shown that this approach allows considering not only…
Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…
We consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
The hydrodynamical model of quantum mechanics based on the Schroedinger equation is combined with the magnetohydrodynamical term to form so called quantum magnetohydrodynamic equation. It is shown that the quantum correction to the Alfven…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
We consider the linear stochastic wave equation driven by a Gaussian noise. We show that the solution satisfies a certain form of strong local nondeterminism and we use this property to derive the exact uniform modulus of continuity for the…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
Quantum measurements and the associated state changes are properly described in the language of instruments. We investigate the properties of a time continuous family of instruments associated with the recently introduced family of general…
We investigate the previously unexplored quantum dynamics of non-relativistic, spinless particles propagating in curved spaces with torsion. Our findings demonstrate that while torsion has been predominantly associated with spin, it can…
We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at…
The possibility to test quantum measurement theories is discussed in the more phenomenological framework of the quantum nondemolition theory. A simple test of the hypothesis of the state vector collapse is proposed by looking for deviations…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…