Theory of Quantum-Classical Crossover

Artur Mendes Kur

One of the still unresolved problems in modern physics is the conceptual gap between quantum mechanics and Newtonian classical physics. Quantum mechanics describes probabilistic and indeterminate systems, whereas classical physics describes stable and deterministic systems. This article proposes a preliminary ontological and philosophical framework to interpret the transition from the quantum to the classical state through the Theory of Quantum-Classical Crossover (TQCC). Rather than considering the two regimes as fundamentally distinct, the theory suggests they are stages of a single process: the gradual formation of physical reality from a state whose physical properties are not yet defined. The quantum-classical crossover is therefore not merely mathematical, but ontological. Although decoherence and coarse-graining are well-established mathematical formalisms, the Theory of Quantum-Classical Crossover provides a conceptual bridge between quantum indeterminacy and classical stability. It employs philosophical concepts as visual aids and integrates ideas such as Heisenberg’s potentia, Wheeler’s It from Bit, and Rovelli’s Relational Quantum Mechanics, suggesting that the binary state of matter is not only expected, but necessary. This ontological perspective may provide a conceptual bridge for understanding quantum-to-classical transitions beyond purely mathematical descriptions.

L. De Cesare, L. Craco, Ileana Rabuffo +1 more

A method of investigation of dimensional crossover phenomena in the theory of phase transitions is illustrated for the nite{size crossover.The dimensional crossover phenomena in systems with quenched extended impurities and inhomogeneities as well as the classical{to{quantum crossover at extremely low temperatures are also discussed.The fundamental interrelationship between the effective dimensionality and the ratio of the relevant characteristic lengths of the system is established and applied to the description of dimensional crossover phenomena.

D. I. Blokhint︠s︡ev

Bess Fang, T. Jacqmin, Tarik Berrada +1 more

We investigate the momentum distribution of weakly interacting 1D Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of single 1D Bose gases is measured using a focusing technique, whose resolution we improve via a levitation scheme. The momentum distribution compares very well with quantum Monte Carlo calculations for the Lieb-Liniger model at finite temperature, allowing for an accurate thermometry of the gas that agrees with (and improves upon) the thermometry based on {\it in situ} density fluctuation measurements. The quasi-condensation crossover is investigated via two different experimental parameter sets, corresponding to the two different sides of the crossover. Classical field theory is expected to correctly describe the quasi-condensation crossover of weakly interacting gases. We derive the condition of validity of the classical field theory, and find that, in typical experiments, interactions are too strong for this theory to be accurate. This is confirmed by a comparison between the classical field predictions and the numerically exact quantum Monte Carlo calculations.