Related papers: Bohmian measures and their classical limit
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears…
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But…
It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can be explained by the fact that Bohmian mechanics has…
Recently, three experiments have been proposed in order to show that the standard and Bohmian quantum mechanics can have different predictions at the individual level of particles. However, these thought experiments have encountered some…
In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that a concept of time emerges only when the gravitational field is (semi)classical. We show that the…
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to…
Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…
The definition of a length operator in quantum cosmology is usually influenced by a~quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of…