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Joint Center: Computational Science and Condensed Matter Physics "How is a Bose-Condensed System like a Polymer Melt?"

David Ceperley
NCSA, Dept. of Physics
University of Illinois Urbana-Champaign
November 12, 1999
Feynman(1953) introduced imaginary-time path integrals to understand superfluid 4He. Path integrals are an exact "isomorphism" between quantum systems and the classical statistical mechanics of ring polymers. Bose symmetry of the wave function implies that the polymers are allowed to "cross-link'' or exchange. The specific heat singularity is a consequence of this cross-linking, momentum condensation is related to the end-to-end distribution of a single open-ended polymer: if the ends become delocalized, the quantum system is bose condensed. Superfluidity (coupling to the boundaries) is proportional to the mean squared flux of polymers through a surface. Thus all three phenomena, specific heat, momentum distribution and superfluidity are directly related to macroscopic exchange. We have developed specialized simulation methods(Path Integral Monte Carlo) based on the Metropolis Monte Carlo method, to simulate boson systems.
Over the last few decades, there has been a search for new bose-condensed systems. One of the likely candidates is molecular para-hydrogen, a boson with half the mass of helium which is normally a solid at low temperature. Based on detailed simulation, we predict a monolayer of molecular hydrogen will undergo a Kosterlitz-Thouless superfluid transition below approximately 1.2K if it is placed on a clean silver surface to which alkali metal atoms have also been absorbed.
The methods are generalizable to other quantum system, and with difficulty to fermion systems such as electrons.

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