图 书 馆
耗散保守系统的随机变分原理Stochastic variational principles for dissipative and conservative systems |
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| 课程网址: | http://videolectures.net/cyberstat2012_guerra_time_reversal_invar... |
| 主讲教师: | Francesco Guerra |
| 开课单位: | 罗马萨皮恩扎大学 |
| 开课时间: | 2012-10-16 |
| 课程语种: | 英语 |
| 中文简介: |  在统计集合方法的框架中，可以通过使用随机微分方程有效地描述对热力学平衡的松弛。该方案在时间反转方面本质上是不变的。但是，我们可以考虑一个称为重要性函数的附加动力学变量，其意义和动机来自中子扩散理论。现在，所得方案是时间反转不变的，具有完整的辛结构。密度和重要性函数的方程式是经过适当选择的哈密顿量的哈密顿方程式，它服从随机变分原理。另一方面，根据爱德华·尼尔森（Edward Nelson）设计的随机方案，我们可以考虑量子力学的表述。在这个框架中，可以容易地引入随机变分原理。该理论本质上是时间反转不变的。我们仍然有一个辛结构，以及规范的汉密尔顿方程。在这里，共轭变量是量子力学概率密度和波函数的相位。通过指出它们的结构相似性和深层的物理差异，我们对这两种方案进行了综合描述。 |
| 课程简介: | In the frame of the method of statistical ensembles, relaxation to thermodynamic equilibrium can be efficiently described by using stochastic differential equations. This scheme is intrinsically non-invariant with respect to time reversal. However, we can consider an additional dynamical variable, called the importance function, whose meaning and motivation arises from the neutron diffusion theory. The resulting scheme is now time reversal invariant, with a complete symplectic structure. The equations for the density and the importance function are Hamilton equations for a properly chosen Hamiltonian, and obey a stochastic variational principle. On the other hand, we can consider the formulation of quantum mechanics, according to the stochastic scheme devised by Edward Nelson. In this frame a stochastic variational principle can be easily introduced. The theory is intrinsically time reversal invariant. We have still a symplectic structure, and canonical Hamilton equations. Here the conjugated variables are the quantum mechanical probability density and the phase of the wave function. We give a synthetic description of the two schemes, by pointing out their structural similarity, and their deep physical difference. |
| 关 键 词: | 微分方程; 随机变分原理 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-10-23：zyk |
| 最后编审: | 2020-10-27：yxd |
| 阅读次数: | 75 |