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第102行： − [数学][数学][数学][数学][数学][数学]+ − − − − {{NumBlk|:| − − − − [2][3][4][4][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][5][ − − <math>\begin{align} − − dN_\mathrm{coll} & = \left(\frac{\partial f}{\partial t} \right)_\mathrm{coll}\Delta td^3\mathbf{r} d^3\mathbf{p} \\[5pt] − − <math>\int A \left(\frac{\partial f}{\partial t}\right)_\text{coll} \,d^3p = 0,</math> − − 左(frac { partial f }{ partial t } right) _ text { coll } ，d ^ 3p = 0，</math > − − & = f \left (\mathbf{r}+\frac{\mathbf{p}}{m}\Delta t,\mathbf{p} + \mathbf{F}\Delta t, t+\Delta t \right)d^3\mathbf{r}d^3\mathbf{p} - f(\mathbf{r}, \mathbf{p}, t) \, d^3\mathbf{r} \, d^3\mathbf{p} \\[5pt] − −
→The force and diffusion terms “force”项与“diff”项
<math>\int \frac{p_j A}{m}\frac{\partial f}{\partial x_j} \,d^3p = \frac{1}{m}\frac{\partial}{\partial x_j}(n\langle A p_j \rangle),</math>
<math>\int \frac{p_j A}{m}\frac{\partial f}{\partial x_j} \,d^3p = \frac{1}{m}\frac{\partial}{\partial x_j}(n\langle A p_j \rangle),</math>
<math> {m}\Delta t,\mathbf{p} + \mathbf{F}\Delta t, t+\Delta t \right)d^3\mathbf{r}d^3\mathbf{p} - f(\mathbf{r}, \mathbf{p}, t) \, d^3\mathbf{r} \, d^3\mathbf{p} \\[5pt] & = \Delta f \, d^3\mathbf{r} \, d^3\mathbf{p}</math>
<math>\int A F_j \frac{\partial f}{\partial p_j} \,d^3p = -nF_j\left\langle \frac{\partial A}{\partial p_j}\right\rangle,</math>
& = \Delta f \, d^3\mathbf{r} \, d^3\mathbf{p}
where the last term is zero, since A is conserved in a collision. Letting <math>A = m</math>, the mass of the particle, the integrated Boltzmann equation becomes the conservation of mass equation: including the formation of the light elements in Big Bang nucleosynthesis, the production of dark matter and baryogenesis. It is not a priori clear that the state of a quantum system can be characterized by a classical phase space density f. However, for a wide class of applications a well-defined generalization of f exists which is the solution of an effective Boltzmann equation that can be derived from first principles of quantum field theory.
where the last term is zero, since A is conserved in a collision. Letting <math>A = m</math>, the mass of the particle, the integrated Boltzmann equation becomes the conservation of mass equation: including the formation of the light elements in Big Bang nucleosynthesis, the production of dark matter and baryogenesis. It is not a priori clear that the state of a quantum system can be characterized by a classical phase space density f. However, for a wide class of applications a well-defined generalization of f exists which is the solution of an effective Boltzmann equation that can be derived from first principles of quantum field theory.