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Mathematics Colloquium - Fall 2011

Wednesday, September 28th, 2011
2:00pm - 3:00pm, in Science 2-064

Vanja Dunjko

UMass Boston, Physics Department

Perturbative renormalization group and Padé approximation

Abstract: In the single-variable case, perturbative renormalization group requires no special symmetries and is thus a purely formal method for improving convergence properties of series expansions. In fact, up to a series reversion, it is a type of integral Hermite-Padé approximation. It is especially useful for interpolating between expansions for small values of a variable and a scaling law of known exponent for large values. As an example, we extract the scaling-law prefactor for the one-body density matrix of the Lieb-Liniger gas. Using a recent result for the 4th-order term in the short-distance expansion, we find a remarkable agreement with known ab initio numerical results.




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