Related papers: Evolution equations for a cubic stochastic process
The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of…
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…
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$…
Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time $t$. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
Time dependent dynamics of the chaotic quantum-mechanical system has been studied. Irreversibility of the dynamics is shown. It is shown, that being in the initial moment in pure quantum-mechanical state, system makes irreversible…
A stochastic dynamics framework for the study of complex systems is presented.
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences.…
We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
Many astrophysical problems, ranging from structure formation in cosmology to dynamics of elliptical galaxies, refer to slow processes of evolution of essentially collisionless self-gravitating systems. In order to determine the relevant…
We discuss entanglement evolution of a multi-qubit system when one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multi-qubit concurrence is derived.…
We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
This review discusses (i) dynamical methods for determining the masses of Galactic and extragalactic star clusters, (ii) dynamical processes and their time-scales for the evolution of clusters, including evaporation, mass segregation, core…
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical probabilities it…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…