A Martin boundary connected with the ∞-volume limit of the focussing cubic Schrödinger equation

Henry P. McKean
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Henry P. McKean: New York University, Courant Institute of Mathematical Sciences

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 251-259 from Springer

Abstract: Summary The existence of a change of phase in the micro-canonical ensemble for the focussing cubic Schrödinger system was suggested by Lebowitz-Rose-Speer [1989]. Chorin [1994] disputes their numerical evidence; his own is based on a more sophisticated approximation to the micro-canonical distribution and leads him to the opposite conclusion. Perhaps the source of this contradictory testimony is the fact, proved here, that the ∞-volume limit does not exist at any temperature 0

Keywords: Schrodinger Equation; Gibbs State; Formal Density; Martin Boundary; Positive Harmonic Function (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-4-431-68532-6_16

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