Related papers: On classical and quantum liftings
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of…
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…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
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…
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to…
When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here…
In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories.…
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Born's Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
Artificial intelligence and machine learning have been widely adopted both in the industry and in everyday life, but at the cost of high compute demands. Recent studies show that implementing machine learning in physical systems in the deep…
Recently it has been shown that the evolution of open quantum systems may be ``unraveled'' into individual ``trajectories,'' providing powerful numerical and conceptual tools. In this letter we use quantum trajectories to study mesoscopic…
The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
Consider a situation in which a quantum system is secretly prepared in a state chosen from the known set of states. We present a principle that gives a definite distinction between the operations that preserve the states of the system and…