advanced_tools:expectation_values
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advanced_tools:expectation_values [2017/05/12 14:24] jakobadmin created |
advanced_tools:expectation_values [2017/11/05 16:13] (current) jakobadmin ↷ Page moved from advanced_notions:expectation_values to advanced_tools:expectation_values |
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| function') | function') | ||
| $$ G(r)=\langle \psi(0) \psi(r)\rangle $$ | $$ G(r)=\langle \psi(0) \psi(r)\rangle $$ | ||
| - | where the angular brackets $$ \langle \cdot \rangle$ denote a statistical average over the thermal fluctuations that characterize all equilibrium systems at nonzero temperature. (Also understood, when $\psi(r)$ is an operator, are the corresponding quantum-mechanical | + | where the angular brackets $ \langle \cdot \rangle$ denote a statistical average over the thermal fluctuations that characterize all equilibrium systems at nonzero temperature. (Also understood, when $\psi(r)$ is an operator, are the corresponding quantum-mechanical |
| expectation values.) | expectation values.) | ||
| Physically, $G(r)$ is important since it provides a direct measure of the influence of | Physically, $G(r)$ is important since it provides a direct measure of the influence of | ||
| Line 38: | Line 38: | ||
| $$ G(r) \approx D/d^{d-2+\eta} $$ | $$ G(r) \approx D/d^{d-2+\eta} $$ | ||
| as $r \to \infty$ | as $r \to \infty$ | ||
| - | which is characterized by the critical exponent (or critical index) $d - 2 + \eta$. | + | which is characterized by the [[advanced_notions:critical_exponent]] (or critical index) $d - 2 + \eta$. |
| <cite>Michael Fisher in Conceptual Foundations of Quantum Field Theory, Edited by Cao</cite> | <cite>Michael Fisher in Conceptual Foundations of Quantum Field Theory, Edited by Cao</cite> | ||
advanced_tools/expectation_values.1494591855.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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