Related papers: An illustration of canonical quantum-classical dyn…
This paper extends the Madelung-Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid…
A new class of random quantum--dynamical systems in continuous space is introduced and studied in some detail. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic,…
For a class of solutions of the fundamental difference equation of isotropic loop quantum cosmology, the difference equation can be replaced by a differential equation valid for {\em all} values of the triad variable. The differential…
We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
The problem of constructing a consistent quantum-classical hybrid dynamics is afforded in the case of a quantum component in a separable Hilbert space and a continuous, finite-dimensional classical component. In the Markovian case, the…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system…
We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum…
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already…
We introduce the Poisson bracket operator which is an alternative quantum counterpart of the Poisson bracket. This operator is defined using the operator derivative formulated in quantum analysis and is equivalent to the Poisson bracket in…
The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics for generic initial states shows…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
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…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between…