相关论文: Exact semiclassical wave equation for stochastic q…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
We analyze the quantum dynamics of radiation propagating in a single mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component $\phi_j$ of the wave vector is understood as a…
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.…
A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…