Related papers: Anharmonic quantum mechanical systems do not featu…
We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…
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…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Quantum mechanics describes the unitary time evolution of isolated systems. In reality, every quantum system interacts with its environment, leading to an irreversible loss of the phase relation. Path integral based methods provide a…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
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…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
Phase-space techniques are generalized to nonlinear quantum electrodynamics beyond the rotating wave approximation, resulting in an essentially classical picture of radiation dynamics.
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
Acausal features of quantum electrodynamic processes are discussed. While these processes are not present for the classical electrodynamic theory, in the quantum electrodynamic theory, acausal processes are well known to exist. For example,…
We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and derive a classical sum…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…