超越平均场的随机量子动力学
Stochastic quantum dynamics beyond mean-field
摘要：
用自洽平均场中的独立粒子系综来代替复杂的费米子多体问题的平均场方法可以描述许多静态和动态方面。它通常提供了一个相当好的近似的平均性能的单体自由度。然而，平均场近似一般不能产生集体运动的量子涨落。为了克服这个困难，噪声可以添加到平均场论导致随机描述的多体问题。在目前的工作中，我们总结了在这一领域的最新进展，并讨论的方法，波动已被添加到初始时间，如在随机平均场论或连续的时间，如在随机时间依赖Hartree-Fock。在某些情况下，初始问题甚至可以通过实时引入量子蒙特卡罗方法来精确地重新表述。描述超流体系统的可能性也被调用。讨论了各种超平均场论的成功与不足.
英文摘要：
Mean-field approaches where a complex fermionic many-body problem is replaced by an ensemble of independent particles in a self-consistent mean-field can describe many static and dynamical aspects. It generally provides a rather good approximation for the average properties of one-body degrees of freedom. However, the mean-field approximation generally fails to produce quantum fluctuations of collective motion. To overcome this difficulty, noise can be added to the mean-field theory leading to a stochastic description of the many-body problem. In the present work, we summarize recent progress in this field and discuss approaches where fluctuations have been added either to the initial time, like in the Stochastic Mean-Field theory or continuously in time as in the Stochastic Time-Dependent Hartree-Fock. In some cases, the initial problem can even be re-formulated exactly by introducing Quantum Monte-Carlo methods in real-time. The possibility to describe superfluid systems is also invoked. Successes and shortcomings of the different beyond mean-field theories are discussed and illustrated.
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