Hu-Paz-Zhang主方程的精确解
Exact solution of the Hu-Paz-Zhang master equation
摘要：
Hu-Paz-Zhang方程是耦合到线性被动浴的振荡器的主方程。在假设振荡器和浴最初是不耦合的情况下，这是准确的。在这里，一个精确的一般解决方案是在时间t的维格纳函数在初始维格纳函数的表达式的形式获得。将所得结果应用于高斯波包的运动和一对这样的波包的运动。一个严重的分歧所产生的假设的初始非耦合状态被发现是由于零点振荡的浴，并没有删除在一个截止模型。因此，方程的有价值的结果只能在高温极限下得到，其中零点振荡被忽略。在此基础上，得到了相干性的波包扩展和衰减的极限封闭表达式。这些结果与文献中出现的结果在数值因子内一致，文献中出现的结果适用于在零温度下突然耦合到高温浴的颗粒的情况。另一方面，对于粒子的初始温度与熔池的初始温度一致的物理一致的情况，得到了非常不同的结果。
英文摘要：
The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a linear passive bath. It is exact within the assumption that the oscillator and bath are initially uncoupled . Here an exact general solution is obtained in the form of an expression for the Wigner function at time t in terms of the initial Wigner function. The result is applied to the motion of a Gaussian wave packet and to that of a pair of such wave packets. A serious divergence arising from the assumption of an initially uncoupled state is found to be due to the zero-point oscillations of the bath and not removed in a cutoff model. As a consequence, worthwhile results for the equation can only be obtained in the high temperature limit, where zero-point oscillations are neglected. In that limit closed form expressions for wave packet spreading and attenuation of coherence are obtained. These results agree within a numerical factor with those appearing in the literature, which apply for the case of a particle at zero temperature that is suddenly coupled to a bath at high temperature. On the other hand very different results are obtained for the physically consistent case in which the initial particle temperature is arranged to coincide with that of the bath.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
