Phy5670/RPA: Difference between revisions
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<math> G_{ph} (\alpha, \beta^{-1}; \gamma, \delta^{-1}; t-t') = \lim_{t_{\beta} \rightarrow t^{+}} | <math> G_{ph} (\alpha, \beta^{-1}; \gamma, \delta^{-1}; t-t') = \lim_{t_{\beta} \rightarrow t^{+}} | ||
\lim_{t_{\gamma} \rightarrow t'^{+}} G_{II} (\alpha t, \delta t', \beta t_{\beta}, \gamma t_{\gamma}) | \lim_{t_{\gamma} \rightarrow t'^{+}} G_{II} (\alpha t, \delta t', \beta t_{\beta}, \gamma t_{\gamma}) | ||
= -\frac{i}{\hbar} </math> | = -\frac{i}{\hbar} \langle \psi_{o}^{N}| T [a_{\beta}^{H+}(t) a_{\alpha}^{H}(t) a_{\gamma}^{H+} (t') a_{\delta}^{H} (t')] | \psi_{o}^{N} \rangle </math> (Eq. 1) | ||
====Random Phase Approximation==== | ====Random Phase Approximation==== | ||
====RPA in Finite Systems and the Schematic Model==== | ====RPA in Finite Systems and the Schematic Model==== | ||
Revision as of 15:33, 4 December 2010
Polarization Propagator
To study excited states in meny-fermion systems, the limit of the two-particle (tp) propagator is used
(Eq. 1)
![{\displaystyle G_{ph}(\alpha ,\beta ^{-1};\gamma ,\delta ^{-1};t-t')=\lim _{t_{\beta }\rightarrow t^{+}}\lim _{t_{\gamma }\rightarrow t'^{+}}G_{II}(\alpha t,\delta t',\beta t_{\beta },\gamma t_{\gamma })=-{\frac {i}{\hbar }}\langle \psi _{o}^{N}|T[a_{\beta }^{H+}(t)a_{\alpha }^{H}(t)a_{\gamma }^{H+}(t')a_{\delta }^{H}(t')]|\psi _{o}^{N}\rangle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/49be2b225bbbca1de8a59e6a990c9d7e75fb2085)