de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

MPS-Authors

Caravelli,  Francesco
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons41566

Markopoulou,  Fotini
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

1108.2013
(Preprint), 684KB

PRD85_044046.pdf
(Any fulltext), 524KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Caravelli, F., Hamma, A., Markopoulou, F., & Riera, A. (2012). Trapped surfaces and emergent curved space in the Bose-Hubbard model. Physical Review D, 85: 044046. doi:10.1103/PhysRevD.85.044046.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-EE81-9
Abstract
A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, fall-off of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region.