Related papers: On the quantization of mechanical systems
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
A classical state-preparation device cannot generate states in relative superposition. We introduce classical models in which devices that are individually unable to generate states with relative superposition can be stochastically…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures…
Simple theorems relating a quantum mechanical system to the corresponding classical one at equilibrium and connecting the quantum eigenvalues to the frequencies of normal modes oscillations are presented. Corresponding to each quantum…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
We show that the separability of states in quantum mechanics has a close counterpart in classical physics, and that conditional mutual information (a.k.a. conditional information transmission) is a very useful quantity in the study of both…
An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave…
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…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
The environment surrounding a quantum system can, in effect, monitor some of the systems observables. As a result, the eigenstates of these observables continuously decohere and can behave like classical states.
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
In this work we developed a general approach to the problem of detecting and quantifying different kind of correlations in bipartite quantum systems. Our method is based on the use of distances between quantum states and processes. We rely…