文档介绍：计算凝聚态物理
凝聚态物质的数值模拟方法(5)
分子模型,分子动力学方法
马红孺
./Ccmp/
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
Molecular systems:
In most cases the interaction part can be approximated by pair interactions:
One famous example is the Lennard-Jones potential
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
A very important quantity in statistical mechanics is the pair correlation function g( r,r0 ), defined as
where
It may also be written as
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
For a homogeneous system the pair correlation function depends only on the distance between r and r0 . In this case we denote it as g(r) .
The g( r,r0 ) is proportional to the probability that given a particle at point r and find another particle at point r0 . At large distance g(r) tends to 1, we may define the total correlation function
The Fourier transform of the above function gives the static structure function (or structure factor)
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
The structure function is defined as the correlation function of ponent of density fluctuations
[ The density is defined as: ,
and the density fluctuation is: ,
and its ponent is:
]
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
当体积趋于无限时, 红颜色的部分可以略去.
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
The structure factor can be measured directly by scattering experiments and can also be calculated by simulations.
Many physical quantities can be expressed in terms of the pair correlation functions, for example the energy in NVT ensemble is
The pressure is
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
pressibility
This expression can be derived from the fluctuations of particle numbers
Since so
2003-10-21
上海交通大学理论物理研究所马红孺
分子模型
On the other hand, it can be proved that
We have the final result.
The time correlation function is the correlations of two physical quantities at different times,
For systems at equilibrium the time correlation function is a function of the time difference only and can be written as
2003-10-21
上海交通大学理论物理研究所马红孺
分