Spontaneous Decoherence of Coupled Harmonic Oscillators Confined in A Ring

TL;DR

This paper investigates how quantum coherence spontaneously diminishes in coupled harmonic oscillators confined in a ring, due to intrinsic boundary conditions and symmetries, without external influences, with effects vanishing in the thermodynamic limit.

Contribution

It reveals the mechanism of spontaneous decoherence arising from ring geometry symmetries and boundary conditions, a phenomenon previously not fully understood.

Findings

Spontaneous decoherence occurs without external environment or fields.

Decoherence is linked to hidden couplings from boundary conditions.

Effect disappears in the thermodynamic limit.

Abstract

We study the spontaneous decoherence of the coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the hidden couplings between the center-of-mass and relative degrees of freedoms, which actually originates from the symmetries of the ring geometry and corresponding nontrivial boundary conditions. Especially, such spontaneous decoherence completely vanishes at the thermodynamical limit because the nontrivial boundary conditions become trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has chance to degrade its quantum properties even without applying an external symmetry breaking field or surrounding environment.