Related papers: The two classes of hybrid classical-quantum dynami…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
All physical theories should obey the second law of thermodynamics. However, existing proposals to describe the dynamics of hybrid classical-quantum systems either violate the second law or lack a proof of its existence. Here we rectify…
In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…
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…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be…
In the case of a quantum-classical hybrid system with a finite number of degrees of freedom, the problem of characterizing the most general dynamical semigroup is solved, under the restriction of being quasi-free. This is a generalization…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…
The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar…
A concise and self-contained derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Many previously known results are re-derived, revised, some of them completed or corrected. Using as simple method…
Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates $\gamma_z(t)$, $\gamma_-(t)$, and $\gamma_+(t)$,…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…