量子Monte-Carlo方法在非马尔可夫势垒传输中的应用
Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
摘要：
在核聚变和核裂变中，涨落和耗散是由于集体自由度与内部激发的耦合而产生的。接近屏障，量子，统计和非马尔可夫效应预计是重要的。在这项工作中，提出了一种新的方法，基于量子蒙特卡罗解决这个问题。耦合到环境的系统的精确动力学被一组系统密度的随机演化所取代。量子Monte-Carlo方法被应用于具有二次势的系统。在所有的温度和耦合范围内，随机方法都能精确地模拟非马尔可夫效应。与Nakajima-Zwanzig理论或Time-ConvolutionLess理论的比较表明，只有后者才能在耦合常数至少扩展到四阶时具有竞争力。系统地研究了在不同温度和耦合常数下的倒抛物线情形。渐近通过概率估计在不同的方法，包括马尔可夫极限。在后一种情况下，或者当仅考虑耦合强度的二阶时，与精确结果有很大的差异，因为它通常被假定在核输运模型中。反之，若采用四阶耦合或量子Monte-Carlo方法，则可得到完全一致的结果。
英文摘要：
In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte-Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte-Carlo method is applied to systems with quadratic potentials. In all range of temperature and coupling, the stochastic method matches the exact evolution showing that non-Markovian effects can be simulated accurately. A comparison with other theories like Nakajima-Zwanzig or Time-ConvolutionLess ones shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated in different approaches including the Markovian limit. Large differences with the exact result are seen in the latter case or when only second order in the coupling strength is considered as it is generally assumed in nuclear transport models. On opposite, if fourth order in the coupling or quantum Monte-Carlo method is used, a perfect agreement is obtained.
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