The Zero Range Process Condensation in non-equilibrium systems
The Zero Range Process Condensation in non-equilibrium systems
The Zero Range Process Condensation in non-equilibrium systems
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Yoni Schwarzkopf February 10, 2006<br />
<strong>Condensation</strong> <strong>in</strong> the ZRP<br />
• <strong>The</strong> density (given <strong>in</strong> eq. 9) is clearly an <strong>in</strong>creas<strong>in</strong>g function of the fugacity z.<br />
ρ = z F ′ (z)<br />
F(z) =<br />
∞<br />
m=0 m zm f(m)<br />
∞<br />
m=0 zm f(m)<br />
• <strong>The</strong> maximum density is given by tak<strong>in</strong>g z → 1<br />
ρmax = F ′ (1)<br />
F(1) =<br />
∞<br />
m=0 mf(m)<br />
∞<br />
m=0 f(m)<br />
(11)<br />
(12)<br />
<strong>The</strong> <strong>Zero</strong> <strong>Range</strong> <strong>Process</strong> 16
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