# Self-Induced Decoherence in the Bose-Hubbard model

## TL;DR

This paper investigates self-induced decoherence in the Bose-Hubbard model, showing how internal degrees of freedom can cause quantum purity decay without external baths, emphasizing spectral shifts as key factors.

## Contribution

It provides numerical evidence of self-induced decoherence in the Bose-Hubbard model and analyzes the spectral causes of purity loss, a novel perspective in quantum statistical mechanics.

## Key findings

- Quantum purity decays over time due to internal interactions.
- Spectral shifts in the many-body Hamiltonian drive decoherence.
- Self-induced decoherence occurs without external environment coupling.

## Abstract

The conventional conception of decoherence relies on the interaction with an external set of degrees of freedom - the 'bath' - to which the system loses quantum information. But the role of the bath can be played too by any internal degrees of freedom that are not accessible to the observer, and in this sense we can talk about 'Self-Induced Decoherence'. Simulating the exact time-evolution of the few-body Bose-Hubbard Hamiltonian, we provide numerical evidence of the decay of quantum purity in the sense of 'temporal typicality' referred in the context of pure state Quantum Statistical Mechanics. We analyse the causes of such purity loss in terms of the structural differences of the interacting many-body Hamiltonian in comparison with its non-interacting counterpart, finding that the predominant role in the long term behaviour is played by the shifts in the many-body energy spectrum.