Related papers: Revisiting semiclassical effective dynamics for qu…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…
During the last three decades, P. B\'{o}na has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence of…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
We propose a new method of quantization of a wide class of dynamical systems that originates directly from the equations of motion. The method is based on the correspondence between the classical and the quantum Poisson brackets, postulated…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…
Semiclassical states in isotropic loop quantum cosmology are employed to show that the improved dynamics has the correct classical limit. The effective Hamiltonian for the quantum cosmological model with a massless scalar field is thus…
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the…
Realizations of algebras in terms of canonical or bosonic variables can often be used to simplify calculations and to exhibit underlying properties. There is a long history of using such methods in order to study symmetry groups related to…
A common approach to the theory of nonlocal Poisson brackets, seen from the operatorial point of view, has been to keep implicit the sets on which these brackets act. In this paper we aim to explicitly define appropriate functional spaces…
We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…
We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in R^D, whose effective metric depends on the embedding as…
When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods…
We provide a synopsis of an effective approach to the problem of time in the semiclassical regime. The essential features of this new approach to evaluating relational quantum dynamics in constrained systems are illustrated by means of a…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
In this work we analyze the evolution of the quantum Mixmaster cosmological model within an effective approach. In particular, we study the behaviour of the scale factor and anisotropies of the theory, and determine how it deviates from its…