English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A Bose-Hubbard model on a dynamical lattice was introduced in previous workas a spin system analogue of emergent geometry and gravity. Graphs with regionsof high connectivity in the lattice were identified as candidate analogues ofspacetime geometries that contain trapped surfaces. We carry out a detailedstudy of these systems and show explicitly that the highly connected subgraphstrap matter. We do this by solving the model in the limit of no back-reactionof the matter on the lattice, and for states with certain symmetries that arenatural for our problem. We find that in this case the problem reduces to aone-dimensional Hubbard model on a lattice with variable vertex degree andmultiple edges between the same two vertices. In addition, we obtain a(discrete) differential equation for the evolution of the probability densityof particles which is closed in the classical regime. This is a wave equationin which the vertex degree is related to the local speed of propagation ofprobability. This allows an interpretation of the probability density ofparticles similar to that in analogue gravity systems: matter inside thisanalogue system sees a curved spacetime. We verify our analytic results bynumerical simulations. Finally, we analyze the dependence of localization on agradual, rather than abrupt, fall-off of the vertex degree on the boundary ofthe highly connected region and find that matter is localized in and aroundthat region.

Trapped surfaces and emergent curved space in the Bose-Hubbard model