Related papers: Classical and Quantum Parts of the Quantum Dynamic…
A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
We investigate the classical aspects of Quantum theory and under which description Quantum theory does appear Classical. Although such descriptions or variables are known as "ontological" or "hidden", they are not hidden at all, but are…
Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
It was recently shown that Newtonian dynamics of macroscopic particles can be derived from unitary Schr\"odinger evolution under an assumption on the system-environment interaction, namely that the interaction Hamiltonian effectively…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the…
The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
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…
Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the…