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Gabriel Bouch

Publications and source records attributed to Gabriel Bouch.

2 recordsLinked to original sources
arXiv2010

Complex-Time Singularity and Locality Estimates for Quantum Lattice Systems

We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas related to the Eden growth process and lattice trees. Finally, we demonstrate with a specific family of lattice trees in the plane why this approach breaks down in dimensions greater than one and prove that there exist interactions for which the complex-time dynamics blows-up in finite imaginary time.

math-ph↗
arXiv2010

The Expected Perimeter in Eden and Related Growth Processes

Following Richardson and using results of Kesten on First-passage percolation, we obtain an upper bound on the expected perimeter in an Eden Growth Process. Using results of the author from a problem in Statistical Mechanics, we show that the average perimeter of the lattice animals resulting from a very natural family of "growth histories" does not obey a similar bound.

math.CO↗