From 3ba44c5c49395b4065d2d760747c15f27ae2fcd6 Mon Sep 17 00:00:00 2001 From: Kun Chen Date: Sat, 16 Jul 2022 09:47:22 -0400 Subject: [PATCH] Update index.md --- docs/src/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/src/index.md b/docs/src/index.md index 790caa0..345f04f 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -12,7 +12,7 @@ Imaginary-time Green's functions encode the thermodynamic properties of quantum The physical Green's functions always have the analytic structure specified by the Lehmann representation, ```math -G(\tau)=-\int_{-\infty}^{\infty} K(\tau, \omega) \rho(\omega) d \omega +G(\tau)=\int_{-\infty}^{\infty} K(\tau, \omega) \rho(\omega) d \omega ``` where $\tau$ is the imaginary time, $\omega$ is the real frequency. While the spectral density $\rho(\omega)$ depends on the details of the quantum many-body system, the convolution kernel $K(\tau, \omega)$ is universal and is roughly an exponential function $\exp(-\omega \tau)$.