The phenomenon of resonance in the continuous phase transition of finite-size systems: A passage from Classical World to Quantum World through the resonance?

TL;DR

This paper investigates a resonance phenomenon during continuous phase transitions in finite systems, linking it to the emergence of particles and a transition from classical to quantum behavior.

Contribution

It introduces the concept of resonance within the hysteresis zone of finite-size systems and connects it to particle existence and a classical-quantum transition.

Findings

Resonance maximizes mean waiting time in the hysteresis zone.

Resonance relates to the presence of particles or quasiparticles.

Proposes a classical to quantum transition in finite systems.

Abstract

In finite-size systems undergoing a continuous phase transition, the passage from the symmetric phase to the broken-symmetry phase is accomplished through a hysteresis zone, up to spontaneous symmetry breaking (SSB). In the present work, we find that a resonance phenomenon takes place within this zone. This resonance is manifested as a maximization of the mean waiting time as a function of temperature inside the hysteresis region. An interesting issue concerns how this resonance is connected with the existence of particles (tachyons) or quasiparticles (kink solitons) within the hysteresis zone. Finally, we introduce the idea that this resonance delineates a continuous passage from a "classical" phase to a "quantum" phase for a binary system, such as the three-dimensional Ising model, which belongs to the same universality class as a fermion-antifermion system or, more generally, a matter-antimatter system.