From 56033715837edda2f826d4a767da10be1b21bcbc Mon Sep 17 00:00:00 2001 From: Yuichi Motoyama Date: Thu, 5 Oct 2023 17:00:44 +0900 Subject: [PATCH] [doc] correct specific heat formula (added a missing index 2) --- doc/en/dla/users-manual/output.rst | 2 +- doc/jp/dla/users-manual/output.rst | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/en/dla/users-manual/output.rst b/doc/en/dla/users-manual/output.rst index 0c3080e..19b706b 100644 --- a/doc/en/dla/users-manual/output.rst +++ b/doc/en/dla/users-manual/output.rst @@ -152,7 +152,7 @@ Main results are written in a file with the name specified by ``outfile`` keywor ``spe`` The specific heat - :math:`\displaystyle C_V \equiv \frac{\partial \epsilon}{\partial T} = \frac{1}{N_s T^2} \left[\left\langle\left(E_0 - TN_v\right)^2\right\rangle - \left\langle\left(E_0 - TN_v\right)\right\rangle - T^2\left\langle N_v \right\rangle\right]` + :math:`\displaystyle C_V \equiv \frac{\partial \epsilon}{\partial T} = \frac{1}{N_s T^2} \left[\left\langle\left(E_0 - TN_v\right)^2\right\rangle - \left\langle\left(E_0 - TN_v\right)\right\rangle^2 - T^2\left\langle N_v \right\rangle\right]` NOTICE: In quantum Monte Carlo simulations, the specific heat is calculated with poor accuracy compared with other physical quantities. Moreover, the systematic error :math:`1/N` also appears with respect to the number of samples :math:`N` (``nmcs``). diff --git a/doc/jp/dla/users-manual/output.rst b/doc/jp/dla/users-manual/output.rst index ba632b1..1239d7f 100644 --- a/doc/jp/dla/users-manual/output.rst +++ b/doc/jp/dla/users-manual/output.rst @@ -150,7 +150,7 @@ DLA は計算結果を行区切りのプレーンテキストファイルで出 ``spe`` 比熱. - :math:`\displaystyle C_V \equiv \frac{\partial \epsilon}{\partial T} = \frac{1}{N_s T^2} \left[\left\langle\left(E_0 - TN_v\right)^2\right\rangle - \left\langle\left(E_0 - TN_v\right)\right\rangle - T^2\left\langle N_v \right\rangle\right]` + :math:`\displaystyle C_V \equiv \frac{\partial \epsilon}{\partial T} = \frac{1}{N_s T^2} \left[\left\langle\left(E_0 - TN_v\right)^2\right\rangle - \left\langle\left(E_0 - TN_v\right)\right\rangle^2 - T^2\left\langle N_v \right\rangle\right]` NOTICE: 量子モンテカルロ法において, 比熱の計算は他の物理量と比べて精度が悪く, サンプル数 :math:`N` (``nmcs``)に対して :math:`1/N` の系統誤差も現れます. 特に, エネルギーギャップ以下の極低温領域など, 比熱の値が非常に小さくなるような場合には, 計算結果が負になることがあります.