2025/08/02 by Marco Bilardello, Bilardello, Marco
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2508.01362
openalex publication_date 2025/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical limit of quantum mechanics is investigated, by focusing on the study of the center of mass of a many-body system where each particle is described by quantum mechanics. We study how, in the limit when the number of particles diverges and under quite general assumptions, the center of mass of the system is not anymore described by quantum mechanics but by classical mechanics: the center of mass of the system becomes with a well-defined position and momentum, the state of the center of mass is fully determined by its position and by its momentum, and its dynamics is given by the classical law of dynamics. In order to get this result, three assumptions on the many-body system are necessary: the total mass of the system must be much larger than the mass of each particle composing the system; at most a finite number of particles has non-zero correlation in position with an infinite number of particles; finally, when the number of particles composing the system diverge, the variance in position of each particle converges to a finite value. These assumptions are commonly realized for a macroscopic solid and liquid systems. The results obtained in this paper show how the classical limit of quantum mechanics can be naturally achieved without the need to modify quantum mechanics, without the need to have an external environment and without the need of changing the interpretations of quantum mechanics.