Decay of Correlations in a Quantum Gas with Hard Core Potential
2012, v.18, Issue 3, 457-472
We study the decay of correlations in a quantum gas with hard core interaction. Using the Feynman - Kac representation we derive two estimates for two-point truncated correlation functions $\sigma_\Lambda(x,y)$ of the corresponding model of interacting Brownian loops. In contrast to the case of a potential without hard core, the integral of $\sigma_\Lambda(x,y)$ over the loops $y$ that travel at least a distance $a$ from the loop $x$ has a power decay in $a$ but is an increasing function of $x$. An additional integration with respect to $x$ gives an integral type estimate similar to the corresponding one in the case without hard core. The analysis relies on the abstract cluster expansion method.
Keywords: decay of correlations,cluster expansion,hard core,Feynman - Kac representation,Wiener sausages