Analytical studies of Spectrum Broadcast Structures in Quantum Brownian Motion

TL;DR

This paper provides an analytical investigation into Spectrum Broadcast Structures within Quantum Brownian Motion, elucidating their formation timescales and efficiency, advancing understanding of quantum-to-classical transition mechanisms.

Contribution

It offers the first analytical analysis of Spectrum Broadcast Structures in Quantum Brownian Motion, moving beyond previous numerical studies.

Findings

Spectrum Broadcast Structures form efficiently in the model.

Analytical timescales for structure formation are identified.

The environment's frequency distribution influences structure emergence.

Abstract

Spectrum Broadcast Structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for an apparent objectivity of a decohered state of a system. Recently they have been shown to appear in the well known Quantum Brownian Motion model, however the final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a massive central system and a somewhat simplified environment being random with a uniform distribution of the frequencies.