相关论文: Euler & Lagrange versus Heisenberg & Schroedinger…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are…
The Heisenberg, interaction, and Schr\"odinger pictures of motion are considered in Lagrangian (canonical) quantum field theory. The equations of motion (for state vectors and field operators) are derived for arbitrary Lagrangians which are…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
Quantum hydrodynamics represents quantum mechanics through two complementary models: the Eulerian picture, a direct transcription of wave mechanics, and the Lagrangian picture, in which the quantum state is represented by the collective…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
A generalized Euler equation of fluid dynamics is derived for describing many-body states of quantum mechanics. The Eulerian Eq. can be viewed as representing the interaction of two substates, where each substate has its own velocity and…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
We consider the dynamics of interacting quantum and classical systems in the Heisenberg representation. Unlike the usual construction in standard quantum mechanics, mixed quantum-classical systems involve the interplay of unitary operators…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…