Related papers: From quantum to classical without Planck constant …
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
We discuss the transition from a quantum to a classical domain for a model where a separation into environment and system is explicitely not given. Utilizing the coarse graining procedure for free quantum fields we also apply the projection…
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long…
The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…
In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled…
Dirac's Poisson-bracket-to-commutator analogy for the transition from classical to quantum mechanics assures that for many systems, the classical and quantum systems share the same algebraic structure. The quantum side of the analogy…
We study the crossover from classical to quantum phase transitions at zero temperature within the framework of $\phi^4$ theory. The classical transition at zero temperature can be described by the Landau theory, turning into a quantum Ising…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges, and…
We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different…
The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product…
Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
The quantum-classical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for functions on P.…
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…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…