Dissipative Dynamics of Quantum Fluctuations

TL;DR

This paper investigates how microscopic dissipative quantum dynamics in an infinite spin chain lead to emergent mesoscopic bosonic fluctuations that can generate entanglement, revealing complex quantum-classical interface behaviors.

Contribution

It demonstrates that mesoscopic fluctuations in a dissipative quantum spin chain form bosonic operators with dynamics that can produce entanglement, a novel phenomenon at this scale.

Findings

Emergence of bosonic operators from microscopic spin fluctuations.

Mesoscopic dynamics can generate entanglement, not just decoherence.

Gaussian states are preserved under the mesoscopic dissipative evolution.

Abstract

One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity at the quantum level can only be inherited from complexity at the classical level. Instead, fluctuations of microscopic observables scale as $1/\sqrt{N}$ and exhibit collective Bosonic features, typical of a mesoscopic regime half-way between the quantum one at the microscopic level and the classical one at the level of macroscopic averages. Here, we consider the mesoscopic behaviour emerging from an infinite quantum spin chain undergoing a microscopic dissipative, irreversible dynamics and from global states without long-range correlations and invariant under lattice translations and dynamics. We show that, from the fluctuations of one site spin observables whose linear span is mapped into itself by the dynamics, there emerge bosonic operators obeying a mesoscopic dissipative dynamics mapping Gaussian states into Gaussian states. Instead of just depleting quantum correlations because of decoherence effects, these maps can generate entanglement at the collective, mesoscopic level, a phenomenon with no classical analogue that embodies a peculiar complex behaviour at the interface between micro and macro regimes.