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

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EE81-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EE82-7
Genre: Journal Article

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 Creators:
Caravelli, Francesco1, Author
Hamma, Alioscia, Author
Markopoulou, Fotini1, Author              
Riera, Arnau, Author
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Free keywords: High Energy Physics - Theory, hep-th, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,General Relativity and Quantum Cosmology, gr-qc,Quantum Physics, quant-ph
 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.

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 Dates: 2011-08-092011-12-232012
 Publication Status: Published in print
 Pages: 16 pages two columns, 12 figures; references added, typos corrected
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1108.2013
DOI: 10.1103/PhysRevD.85.044046
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 85 Sequence Number: 044046 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258