Quantum particles and classical particles

Victor F. Weisskopf

C. Wetterich

Abstract Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being “classical” or “quantum” ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross‐fertilization between classical statistics and quantum physics.

Michel Gondran, Alexandre Gondran

In the 1927 Solvay conference, three apparently irreconcilable interpretations of the quantum mechanics wave function were presented: the pilot-wave interpretation by de Broglie, the soliton wave interpretation by Schrödinger and the Born statistical rule by Born and Heisenberg. In this paper, we demonstrate the complementarity of these interpretations corresponding to quantum systems that are prepared differently and we deduce a synthetic interpretation: the double-preparation theory. We first introduce in quantum mechanics the concept of semi-classical statistically prepared particles, and we show that in the Schrödinger equation these particles converge, when , to the equations of a statistical set of classical particles. These classical particles are undiscerned, and if we assume continuity between classical mechanics and quantum mechanics, we conclude the necessity of the de Broglie–Bohm interpretation for the semi-classical statistically prepared particles (statistical wave). We then introduce in quantum mechanics the concept of a semi-classical deterministically prepared particle, and we show that in the Schrödinger equation this particle converges, when , to the equations of a single classical particle. This classical particle is discerned and assuming continuity between classical mechanics and quantum mechanics, we conclude the necessity of the Schrödinger interpretation for the semi-classical deterministically prepared particle (the soliton wave). Finally we propose, in the semi-classical approximation, a new interpretation of quantum mechanics, the 'theory of the double preparation', which depends on the preparation of the particles.

Daniel Fargue

Wen-Lei Zhao, Quanlin Jie

We investigate the quantum to classical transition induced by two-particle interaction via a system of periodically kicked particles. The classical dynamics of particle 1 is almost unaffected in condition that its mass is much larger than that of particle 2. Interestingly, such classically weak influence leads to the quantum to classical transition of the dynamical behavior of particle 1. Namely, the quantum diffusion of this particle undergoes the transition from dynamical localization to the classically chaotic diffusion with the decrease of the effective Planck constant ℏ eff. The behind physics is due to the growth of entanglement in the system. The classically very weak interaction leads to the exponential decay of purity in condition that the classical dynamics of external degrees freedom is strongly chaotic.

Masao Nagasawa